flW 11^^^ United States Department of Commerce

I XI I National Institute of Standards and Technology

NISTIR 3965

NEW NIST PUBLICATION

June/July 1??1

HEAT TRANSFER

AND PRESSURE DROP

IN A COMPACT PIN-FIN HEAT

EXCHANGER WITH PIN ORIENTATION

AT 18° TO THE FLOW DIRECTION

Douglas A. Olson

NISTIR 3965

HEAT TRANSFER

AND PRESSURE DROP

IN A COMPACT PIN-FIN HEAT

EXCHANGER WITH PIN ORIENTATION

AT 18° TO THE FLOW DIRECTION

Douglas A. Olson

Chemical Engineering Division

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

February 1991

Sponsored by

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23665

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director

CONTENTS

Page

Nomenclature vii

Abstract 1

1. Introduction 2

2 . Description of experimental apparatus 3

2.1. Flow apparatus 3

2.2. 18° Pin-fin specimen 4

2.3. Instrumentation 4

3. Description of experiments and analysis techniques 6

3.1 Experiments conducted 6

3.2. Friction factor 7

3.3. Heat transfer coefficient 8

3.4. Uncertainty analysis 12

4. Results of experiments 13

4.1 Friction factor 13

4.2 Temperature distributions and heat transfer 14

5. Summary and conclusions 17

6. References 18

Appendix A. Calculation of open volume, wetted- wall area, and flow area

for pin- fin specimens 19

iii
LIST OF TABLES

Table page

1. Uncertainties in experimental measurements and gas properties at a

95 percent confidence interval 21

2. Summary of geometrical parameters and experimental conditions for

18° pin-fin specimen 22

3. Data tables for all experiments 23

4. Uncertainties in data analysis parameters and calculated

quantities 54

IV
LIST OF FIGURES

Figure page

1. Heliurn flow apparatus 55

2. Specimen furnace, showing location of inlet gas temperature (A),

upstream pressure (0)

,

outlet gas temperature (B)

,

and downstream

pressure (1) 56

3. 18° pin-fin specimen 57

4. Top view of pin- fin specimen showing locations of unbonded pins and

pressure taps 58

5. Method for attaching thermocouples to the heated side of the pin- fin

specimen 59

6. Friction factor (f) as a function of Reynolds number (Re) for

experiment 1, no heating 60

7. Percent difference between predicted and measured pressure drop

(Po-Pi) as a function of helium flow rate (m) for heat transfer

experiments 61

8. Wall (Tw ) and gas (Tf ) temperatures as a function of x/L;

experiment 5, 11.4 kg/h helium flow, and y/W = 0.0 62

9. Wall temperature (Tw ) as a function of y/W at several x/L locations;

experiment 5, 11.4 kg/h helium flow 63

10. Wall-to-gas temperature difference (Tw -Tf ) and heat transfer

coefficient (h) as a function of x/L; experiment 5, 11.4 kg/h helium

flow and y/W = 0.0 64

11. Reynolds number (Re), Nusselt number (Nu) , and modified Nusselt

number (Nu,,,) as a function of x/L; experiment 5, 11.4 kg/h helium

flow and y/W = 0.0 65

12. Modified Nusselt number (Ni^) as a function of Reynolds number (Re);

heated experiments 3-6 with 0.07 < x/L < 0.93 and y/W = 0.0 66

13. Wall Nusselt number (Nu„) as a function of Reynolds number (Re);

heated experiments 3-6 with 0.07 < x/L <0.93 and y/W = 0.0 67

A.l. Definition of pin geometry for calculating open volume, wetted-wall

area, and flow area 68

v

Nomenclature

A

Af

An =

a* - Vp -

B

Bi

c

p =

d

Dh -

f

G

h

h

tly, k

kni

L

m =

n =

N

Nu

Nu* =

Nu, =

P

Pr

qn Qpx

Qt =

qw

r =

Re

S

t =

T

Taw =

Tf -

T = •*-w V

Vf =

V =

V0 «

vv o,no.p

inlet manifold location

flow normal area = V0 /L

specimen normal area = L-W

wetted wall area (total wall area exposed to fluid)

wetted wall area per pin

outlet manifold location

Biot number = t^-Db/k^

specific heat at constant pressure

pin diameter at braze joint

pin diameter

specimen hydraulic diameter = 4V0 /A,

friction factor

friction factor used by Metzger et al. [1982]

heat flux distribution function

mass flow rate per unit flow normal area = m/Af heat transfer coefficient

enthalpy

heat transfer coefficient based on temperature of wall- fluid interface

thermal conductivity

nickel thermal conductivity

heated length of specimen

mass flow rate

number of pins

number of rows of pins in flow direction in Metzger friction factor

Nusselt number = h-Db/k

modified Nusselt number = Nu- (Tw/Tf )°- 55

wall Nusselt number (adjusted for finite pin conduction)

VDhA-CTw/Ta 0 - 55

pressure

Prandtl number = /z-c

p

/k

local normal heat flux

fraction of total heat flow on specimen added up to position x

integration of furnace calibration function f

q

, 0 to x

total heat transfer to specimen

local heat flux (heat flow per unit area) into the cooling fluid based

on total wetted-wall area of the specimen

recovery factor = Pr 1/3 for turbulent flow

Reynolds number = pVDh//x

pin-to-pin on-center separation

maximum pin diameter

pin height

temperature

cooling fluid adiabatic wall temperature

local bulk fluid temperature

specimen wall temperature

velocity

heater voltage

maximum velocity in specimen

open volume in specimen

= volume of hexagon of diameter S and height t

vii
V0>p = open volume around each pin

Vs p = volume of pin between top and bottom plates

W = width of specimen

Wf = uncertainty in friction factor

Wh = uncertainty in heat transfer coefficient

Wnu = uncertainty in Nusselt number

Wqt = uncertainty in total heat transfer

Wre = uncertainty in Reynolds number

Wtf = uncertainty in fluid temperature

Wtw = uncertainty in wall temperature

x = position coordinate parallel to flow direction

y = position coordinate perpendicular to flow direction

z = position coordinate in vertical direction on pin; z = 0 at braze

location on pin

P = coefficient of thermal expansion

rj = pin efficiency

\i = dynamic viscosity

p = density

0 = location where heating begins (x/L=0)

1 = location where heating ends (x/L=l)

viii
Heat Transfer And Pressure Drop in a Compact Pin- fin

Heat Exchanger With Pin Orientation at 18° to the Flow Direction

Douglas A. Olson

Chemical Engineering Division

National Institute of Standards and Technology

Boulder, CO 80303-3328

We have measured the heat transfer and pressure drop

characteristics of a novel, compact heat exchanger in helium gas

at 3.5 MPa and Reynolds numbers of 450 to 12 000. This "pin- fin"

specimen consisted of pins, 0.51 mm high and spaced 2.03 mm on

centers, spanning a channel through which the helium flows; the

angle of the row of pins to the flow direction was 18°. The

specimen was radiatively heated on the top side at heat fluxes up

to 74 W/cm2 and insulated on the back side. Correlations were

developed for the friction factor and Nusselt number. The NusSelt

number compares favorably to those of past studies of staggered

pin- fins, when our measured temperatures are extrapolated to the

temperature of the wall -fluid interface.

Key words: apparatus; compact heat exchanger; convection heat

transfer; friction factor; high temperature; National Aerospace

Plane; pin- fin; radiative furnacfe ; turbulent flow; variable

property effects.

This work was supported by NASA Langley Research Center under contract L7400C.

1
1. Introduction

This is the third report in a series of experimental studies in which we

have measured heat transfer and pressure drop in compact heat exchangers. The

compact heat exchangers are candidate cooling jackets for the engine struts of

the National Aerospace Plane (NASP) . Due to aerodynamic heating associated

with the combustion of the hydrogen fuel, along with thermal radiation from

the fuel combustion, the engine struts are expected to receive a normal

heating load in excess of 2000 W/cm2 [Scotti et al . , 1988, Shore, 1986].

Researchers at NASA Langley plan to cool the struts by attaching a cooling

jacket heat exchanger to the surface facing the high heat flux. Hydrogen gas

will flow through the cooling jacket and absorb the heat before entering the

engine. The anticipated conditions are that the hydrogen gas will enter the

heat exchangers at 56 K and 6.9 MPa (1000 psi) , and exit at 890 K and 4.8 MPa

(700 psi) . The heat exchangers are expected to be thin (6 mm or less)

perpendicular to the flow direction to add minimal weight and thickness to the

struts. Small flow passages will also produce high rates of convective heat

transfer, which will reduce the temperatures of the strut. Reynolds numbers

are expected to be in the range from 10 000 to 30 000, with the variation due

to the flow rate and the specific design of the flow passage.

In an earlier work, we constructed an apparatus which can provide helium

gas flow and a well -characterized heat flux to a heat exchanger specimen

[Olson, 1989], This apparatus was previously used to test two prototype heat

exchangers for the NASP application. The first was a "tube specimen," which

consisted of 20, 1 mm ID nickel tubes lying in parallel on a nickel base plate

[Olson and Glover, 1990]. The second was a "channel specimen", which

contained 12 rectangular channels in parallel, 3.18 mm wide by 0.56 mm high,

milled in a nickel plate [Olson, 1990]. For both specimens, the Nusselt

numbers we measured were in good agreement with the Nusselt numbers for flow

in a single tube with well -characterized boundary conditions.

In this work we present the experimental results of a heat exchanger

configuration for the NASP cooling jacket which has a much higher heat

transfer coefficient than either the "tube" or "channel" specimens. The

specimen tested has a "pin- fin" internal geometry, in which short cylinders

(of varying diameter) span the height of the cooling passage. The centers of

the pins are at the corners of equilateral triangles. This specimen was

constructed and partially instrumented by NASA Langley Research Center and has

internal geometry identical to that of a full-size strut, which they are

developing. The pin- fins increase both the wetted heat transfer area and the

flow turbulence [VanFossen, 1982].

Banks of pin- fins have been used in the gas turbine industry to cool

turbine blades or vanes [Armstrong and Winstanley, 1987]. In this

application, the length- to-diameter ratio of the pins varies from 1/2 to 4,

and the pin diameter is constant across the span of the channel. Long pinfins (length- to-diameter ratio of 8 or greater) have been used by the heat

exchanger industry and were studied by Kays and London [1964]. There are

several geometric differences between the pin- fins of this work and those of

past studies in the literature, which make the accuracy of using existing

correlations uncertain. Due to the manufacturing technique (explained in more

2
detail below) , the pin diameter decreases from one side of the channel to the

other (length- to -diameter ratio varies from 1/4 to 1/2). In addition, the top

end-wall surface (area between adjacent pins) is not smooth or flat. Pin

banks of past works are often "staggered" in the flow direction to break up

the flow path. The pins of the present work are also staggered, but the angle

of stagger is different (18°) from that used in the past work (30° stagger).

In the present use of the pin-fin specimen, high rates of heating will

accelerate the flow. In the only past study with pin- fins where flow

acceleration was significant, Metzger et al. [1986] used a converging channel

containing pin- fins to accelerate the flow.

2. Description of experimental apparatus

The apparatus description which follows is based on that in Olson [1989]

and in Olson and Glover [1990]. The apparatus was designed to test a subset

of the conditions required for the NASP application. Those conditions are (1)

a heating rate of 0 to 80 W/cm2

; (2) an inlet temperature of 300 K; (3) a

cooling- gas pressure of up to 6.9 MPa at the inlet; and (4) an outlet

temperature of 810 K or less. We used helium as the coolant gas because of

the similarities in specific heat, thermal conductivity, and dynamic viscosity

to the corresponding properties of hydrogen. In addition, helium does not

have the explosive hazard of hydrogen. Because of the property similarities,

the Reynolds number, Prandtl number, and temperature rise from specimen inlet

to outlet can be matched between helium and hydrogen.

2.1. Flow apparatus

The helium flow apparatus is shown in figure 1, with the details of the

specimen furnace section given in figure 2. Helium gas at 17 MPa (2500 psi)

or less was supplied from a tube trailer outside the laboratory. The tube

trailer contained 1100 m

3 of gas (STP) . With valves 1 and 2 open, gas flowed

from the trailer, through the inlet piping, and was filtered before entering

the dome-loaded pressure regulator (valve 3). The regulator set the flow

pressure downstream of the regulator to the value of an external control

pressure, which was about 3.5 MPa (500 psi) for these experiments.

Within the furnace (fig. 2), the gas flowed into an inlet distribution

manifold which directed the gas to the heat exchanger specimen. A similar

distribution manifold collected the gas exiting the specimen and directed it

to the outlet tubing. Gas pressure was measured at the pressure taps as shown

at location 0 (start of heated zone) and at location 1 (end of heated zone)

The specimen was located in the target area of the furnace (7.8 cm wide by

15.2 cm long), which delivered radiant heat to the specimen and raised the

temperature of the helium as it flowed through the specimen.

The furnace consisted of a high- intensity infrared radiant heater,

surrounded by highly reflective walls which reflected the heat from the heater

to the specimen [Olson, 1990]. The reflective walls were made of 6.4 mm thick

aluminum plates, polished on the inner surface, with a water-cooled cooling

jacket soldered to the outside. The heater contained six high- temperature

infrared lamps mounted in an aluminum housing. A phase-angle power controller

3
which used 480 VAC, single phase, and 75 A at maximum voltage powered the

heater

.

Downstream of the furnace section, the hot gas flowed through a cooling

coil immersed in a water bath. The rate of gas flow was manually adjusted at

the bath outlet by valve 4, which also dropped the gas pressure to atmospheric

pressure. Beyond the valve, we measured helium flow rate with a heated- tube

thermal mass flow meter. After exiting the flow meter the gas was vented

outside the laboratory.

2.2. 18° Pin-fin specimen

The pin- fin specimen was constructed at NASA Langley Research Center and

is shown in figure 3. Heating was from the top in figure 3. The specimen

consisted of an upper plate with integral pins, and a lower plate onto which

the upper plate was brazed (the perspective view shows the specimen separated

to view the detail of the pins) . Both plates were made of commercially pure

nickel (UNS 02200). The total thickness of the upper plate was 0.89 mm, with

0.51 mm high pins and 0.38 mm plate thickness above the pins. The lower plate

was 1.27 mm thick. The pins were formed in the upper plate by photochemical

etching. The pin diameter varied from 2.03 mm at the widest point to 1.02 mm

at the point of braze to the bottom plate. The centers of the pins were at

the corners of equilateral triangles. The separation between pin centers was

2.03 mm. The angle of a line drawn through the pin centers, with respect to

the flow direction, was 18°. (Refer to figure 3: the angle for maximum

channeling of the flow would be 0°; the angle for maximum stagger would be

30.°) The pressure taps were stainless steel tubes, 1.5 mm OD and 1.0 mm ID,

brazed into holes in the specimen at locations shown in figure 4.

The top and bottom plates were brazed together in a vacuum oven using a

braze alloy foil of 50 percent gold, 25 percent palladium, and 25 percent

nickel (AMS-4784, 1394 K liquidus) . The foil was 0.025 mm thick. Prior to

brazing, the inner- facing surface of both plates was lapped to a flatness of

±0.01 mm. After brazing, the specimen was pressurized by NASA Langley to 10.3

MPa (1500 psi) . This caused the top plate to deflect from the bottom plate at

six spots, shown in figure 4, where the pins did not braze to the lower plate.

The assembled specimen was brazed to slots in the inlet and outlet

manifolds using a braze alloy of 82 percent gold and 18 percent nickel (AMS4787, 1223 K liquidus). The pressure tap tubes were brazed to the specimen

during the same braze cycle. We pressurized the manifold and specimen to 7

MPa (1000 psi) prior to installing it into the flow apparatus, and there were

no leaks. The specimen was tested with helium flow and heat transfer only up

to 3.5 MPa to avoid separating the plates, since we did not know how the

"disbond" areas affected the strength of the specimen at high temperature and

high pressure. We painted the top side of the specimen (the upper plate side)

a flat black over the 15.2 cm length to establish a uniform and highly

absorptive surface over the heated area. The paint was rated to 1000 K.

2.3. Instrumentation

We measured the temperature of the gas in the inlet and outlet manifolds,

4
gas pressure in the specimen, specimen temperatures, and the gas flow rate.

The measurement technique and uncertainties, along with the gas property

uncertainties, are summarized in table 1.

We determined the distribution of heat flux on the specimen by

calibrating the furnace prior to installing the specimen. The heat flux

distribution was defined as the local, normal (perpendicular) heat flux as a

function of position over the furnace target. The heat flux was constant in

the direction perpendicular to flow (y) , and varied by no more than ±7 percent

in the direction parallel to flow (x) except within 6 percent of the end

walls

The gas inlet and outlet temperatures were measured with platinum

resistance thermometers, 4.8 mm diameter, inserted in the gas manifolds at

locations A and B of figure 2. We measured the gas pressure at location 0 in

the specimen with a variable -reluctance pressure transducer which had a 8.6

MPa full scale output. Difference in pressure between locations 0 and 1 in

the specimen was measured with a differential pressure transducer, also a

variable -reluctance type with a 1.4 MPa (200 psi) full-scale output.

We measured specimen temperatures with thermocouples made from type N

wire, with a wire diameter of 0.25 mm. We spot-welded 29 thermocouples to the

side opposite the radiant heat flux (insulated side) . Specimen temperatures

were also measured with platinum resistance thermometers (PRT) bonded to the

insulated side at 4 locations. The PRTs were installed by NASA Langley.

These had a nominal 1000 ohm sensing element mounted on a 2.8 mm by 6.4 mm

base of alumina. Due to the large size of the sensors, the PRTs could not

provide sufficient spatial resolution in specimen temperature, and were not

used in calculating the heat transfer performance. We used the PRTs as a

check for drift or aging of the thermocouple sensors.

The temperature of the heated side was measured at 19 locations with type

N thermocouples mounted as shown in figure 5. These probes were installed at

NASA Langley. Two holes, 0.33 mm diameter, were drilled in adjacent pins as

close to perpendicular to the flow direction as possible (12° from

perpendicular). The holes were back-drilled to within 0.13 mm of the surface

with a 0.57 mm diameter drill. Each wire of the pair was spot-welded to the

heated surface, with the lead extending out the hole on the insulated side.

The thermocouple circuit was completed by the specimen material between the

two wires. A quartz sleeve, 0.48 mm outer diameter, was inserted over the

wire into the hole to electrically insulate the wire from the wall of the

hole. Because a portion of the specimen was removed and replaced by wire plus

quartz , each of which had a thermal conductivity lower than that of the

specimen, mounting the thermocouple locally increased the specimen

temperature. We estimated the magnitude of this temperature rise from a

finite -element analysis as 2 to 5 K at a radiant heat flux of 50 W/cm2

. Temperatures measured with the insulated- side thermocouples were used to

determine the heat transfer coefficient, as the installation technique did not

disturb the specimen temperatures and conduction errors were insignificant.

All thermocouples were connected to terminals in an isothermal reference

box. We measured the temperature of the reference box with a platinum

5
resistance thermometer. Copper conductor wire connected from the terminals in

the reference box to the data scanner. The reference box introduced

negligible error in the temperature measurement [Olson, 1989]

.

All instrument signals were multiplexed through an automated scanner and

measured with a digital voltmeter. The scanner and voltmeter were controlled

with a personal computer through an IEEE-488 bus. Raw signals were stored on

a hard disk and copied to floppy disk for backup. Signals were converted to

SI units and the data analyzed at the completion of an experimental run. Some

signal readings were converted immediately to SI units and displayed on the

video terminal to assist in monitoring and operating the experiment. We have

included the measurement uncertainties introduced by the data acquisition

system in the stated uncertainties of each sensor.

3. Description of experiments and analysis techniques

3 . 1 Experiments conducted

A summary of the conditions for the six experiments conducted with the

18° pin- fin specimen is shown in table 2. Also listed are the values for the

geometrical parameters required for the data analysis. Table 3 lists values

for all the measured and calculated parameters at each data point for each

experiment. Tests were conducted at a system pressure of approximately 3.5

MPa (500 psi) . In experiment 1, we tested a range of helium flow rates

without heating the specimen to determine the friction factor. In experiments

2 to 6 , we varied the heater lamp voltage to vary the rate of specimen

heating; at each heating rate a range of helium flow rates was tested up to 28

kg/h. We were not able to test a helium flow rate in these experiments as

high as those which we tested the tube and channel specimens, since the

pressure drop for the pin- fin specimen was much higher, on the order of 1.4

MPa (200 psi) at 28 kg/h. Operating the flow apparatus at higher inlet

pressure would reduce the pressure drop, however we felt that the braze joint

of the specimen was not strong enough to withstand a higher pressure during

heating

.

The range in Reynolds number was 450 to 12 000, while the range in normal

heat flux was 0 to 74 W/cm2 (65 Btu/(s • ft2

) ) . The minimum inlet gas

temperature was 284 K (52 °F) , while the maximum gas outlet temperature was

742 K (877 °F) . The maximum specimen temperature we measured was 761 K (910

°F) . Because of the high heat fluxes generated by the furnace, we followed

the operating procedure described in Olson and Glover [1990] to prevent

overheating the specimen during experimental set-up, run, and shut-down.

Before taking the first data point, we waited at least 15 min with the

heater lamp at steady power to allow the specimen and manifolds to reach

thermal steady- state . The outlet manifold had the longest time constant due

to its large thermal capacitance. We scanned the sensors at least twice at

each setting. After sampling all the sensors, we changed the helium flow rate

by adjusting valve 4. At each new flow rate, we waited a at least 5 min to

establish thermal steady- state before taking data, since a change of flow rate

also affected gas, specimen, and manifold temperatures. Gas pressure, furnace

6
heating, helium flow rate, and gas inlet pressure remained sufficiently steady

while taking data to ignore thermal transients in the data analysis.

We analyzed the measured data to determine the heat transfer coefficient,

h, and the friction factor, f. The heat transfer coefficient was nondimensionalized as a Nusselt number, Nu. A modified Nusselt number, Ni^, was

calculated to include the effects of variations in thermophysical properties,

which we found to be significant in the tube specimen experiments. We

calculated a wall Nusselt number, Ni^, in which we extrapolated the

temperature of the insulated side to the temperature of the wall -fluid

interface. This was used for comparing our results to work in the literature

on pin-fin configurations. Nu, NUm, and Ni^ were correlated with the Reynolds

number, Re. The parameters h, Re, and Nu were calculated at each location of

an insulated- side thermocouple.

3.2. Friction factor

The friction factor is derived from integrating the one -dimensional

momentum equation in the flow direction:

Po-Pi - G

2 (l/Pl -l/p0 ) + (2G2/Dll )

• P(f/„)dx, (1)

where P

G

m

Af

P

V

Dh

0

1

= pressure;

= mass flow rate per unit flow normal area

= m/Af = pV

= mass flow rate in channel; = volume -average flow normal area = V0/L; = density; = average velocity based on flow normal area; = specimen hydraulic diameter = AA/q/A,,; = location of upstream pressure tap (x/L = 0)

= location of downstream pressure tap (x/L = 1)

The first term on the right hand side of the equation is the pressure decrease

due to flow acceleration, and the second term is the pressure drop due to

friction. Temperatures measured perpendicular to the flow direction for

experiments with heating indicated that the flow was evenly distributed along

the width of the specimen. Both the velocity and hydraulic diameter are based

on the open volume, VQ , in the specimen, which is the method used by VanFossen

[1982]

Appendix A shows how VQ is calculated.

The experiments show that f depends on Re only. Because Re does not

change from the specimen inlet to outlet if the specimen is unheated, f can be

removed from within the integral. For the tube and channel specimens which we

tested earlier, the density change was small compared to the absolute density,

and the integral could be approximated as a constant. However, for the pinfin specimen, even with no heating, at high helium flow rate the pressure drop

could be 40 percent of the inlet pressure. If we assume a linear pressure

drop and density drop through the specimen, we may evaluate the integral; the

resulting expression for f is

7
Po-p, - G

z a/Pi-i/p0 ) f (2) =

2 •

G

2 • (L/Dh)

InCpo/Pi)

(Po-Pi)

Equation (2) is valid when there is no heating, but when the specimen is

heated the Reynolds number and f change with position, and f can not be

calculated from eq (2) . The friction factor was determined for the tests with

no heating as a function of Reynolds number, where

Re = PVT)*//*. (3)

Past studies in the literature in which friction factors were measured in

pin-fin geometries used a different definition for f [Metzger et al . , [1982]:

Po-p, - G

2 a/Pi-i/p0 )

fM

, w

2-p-Vm„

2 -N

where Vmax = gas velocity at minimum flow area, and

N = number of rows of pins in flow direction.

In this definition, the pressure drop is assumed to scale like the pressure

drop of flow around an isolated cylinder; the rows of pins are perpendicular

to the flow, and there are N rows of cylinders in the flow direction. For our

pin- fin specimen, the rows are not perpendicular to the flow direction, so it

is not obvious how many pins the gas circumvents as it passes through the

specimen. Because the pin diameter varies with height, even if the rows were

perpendicular to the flow direction it would be difficult to define a minimum

area and therefore maximum velocity. The definition of f used in our work

assumes a similarity of the pin- fin specimen to a channel flow, and our

hydraulic diameter is defined to include the effects of the pins. In our

work, specimens with different orientation of the pins to the flow, but the

same pin height, diameter, and spacing will produce the same values of the

geometric parameters used in the definition of f (but not necessarily the same

magnitude of f )

.

To determine whether specimen heating had an effect on the friction

factor, eq (1) was integrated in a summation form from the inlet to outlet to

predict the pressure drop, Pq-P-l, for the experiments with specimen heating.

The integral was evaluated at each location where wall temperature was

measured, with f found from the correlation of f vs Re for experiment 1 and

the local density found from the gas temperature and pressure. This predicted

pressure drop was compared with the measured pressure drop.

3.3. Heat transfer coefficient

The heat transfer coefficient, h, is defined through the equation

qw - h-(Tw -Taw), (5)

8
where qw = local heat flux (heat flow per unit area) into the cooling

fluid based on total wetted-wall area of the specimen;

h = heat transfer coefficient;

Tw = specimen wall temperature;

Taw = adiabatic wall temperature of the cooling fluid.

The adiabatic wall temperature is used in gas flows whenever the kinetic

energy is significant compared to enthalpy changes [Rohsenow and Choi, 1961].

Friction can cause the local wall temperature to exceed the bulk fluid

temperature for an adiabatic specimen, and the adiabatic wall temperature

approximates this effect. It is defined as

Taw = Tf + rV2/(2cp ), (6)

where Tf = local bulk fluid temperature

r = recovery factor = Pr 1/3 for turbulent flow.

Adiabatic heating was as much as 2 K, and was greatest for high flow rate and

high heating rate. The local heat flux in eq (5) is expressed in terms of the

total heat transfer to the specimen, QT , the total wetted wall area, and the

furnace calibration function, f

q [Olson, 1989], which is a dimensionless

expression of the local normal heat flux:

qw = (Qt/AJ

fq* (K/K) > (?)

with A„ = wetted wall area;

An = specimen heated normal area = L-W.

The function f

q

is on the order of 1; if the heat flux were constant then f

q would be 1 everywhere. The wall temperature used in eq (5) was measured with

the thermocouples on the insulated side of the specimen. Measured wall

temperatures show that wall conduction was negligible both in the flow

direction (x) (except close to the end manifolds) and perpendicular to the

flow direction (y)

At each position the heat incident on the specimen is all

convected into the fluid.

Combining eqs (5), (6) and (7) and rearranging, we get

(Qt/Aw) * f

q

h . (8)

(Tw - [T£+(rV2 )/ (2cp ) ]

)

The flow-direction energy equation was used to calculate QT (to follow) . Gas

temperature Tf was calculated using the flow-direction energy equation along

with the furnace calibration (also to follow)

The total heat absorbed by the specimen was calculated from the

temperatures of the gas inlet and outlet, the helium flow rate, and the gas

pressure drop. It was not necessary to adjust for a heat leak from the

specimen to the furnace wall, as the heat leak was negligible due to the low

temperatures of the reflective furnace.

9
Qt = m(hB -hA ) , (9)

where h = enthalpy;

A = location in inlet manifold of PRT;

B = location in outlet manifold of PRT;

We neglected kinetic energy changes from A to B since they were insignificant

compared to the uncertainties of the temperature measurement. The change in

enthalpy is given by

hB -hA - c

p

- (Tb -Ta) + P[(l-0T)/p]dP , ( 10 )

where = coefficient of thermal expansion.

The specific heat was constant for the range of conditions tested. The

pressure term was included for the slight divergence from the ideal gas state

for helium at these temperatures and pressures. The pressure at A and B is

estimated by assuming a linear drop along the specimen and extrapolating the

pressure from 0 and 1. This assumption introduces less than 0.1 percent error

in Qt

. The integral was evaluated using the virial equation of state for the

gas [McCarty, 1973]. Combining eqs (9) and (10) yields for QT

:

Qt ~ ^ '

(

cp * (Tb

_ Ta) + [ (1-/3T)/p ] dP} . J A

(ID

The fluid temperature, Tf , was calculated by integrating the flow energy

equation from the inlet manifold up to the location of interest (designated as

x) , now including kinetic energy:

Qt ' Q

fx - Ta +

px j:

[(l-0T)/p]dP

m- cY

V.

2 cp’

( 12 )

where Qpx = fraction of total heat flow on specimen added up to

position x; = integration of furnace calibration function f

q

, 0 to x.

The fluid temperature requires the velocity at x, given by

Vx = m/(Af px ),

and the density is given by the equation of state [McCarty, 1973] as

Px = Px( Tfx> px)

We assume the pressure varies linearly between locations 0 and 1:

Px = P0

- (P0 -Pi)-x/L.

(13)

(14)

(15)

10
The maximum error in Tf introduced by assuming a linear pressure variation was

less than 0.15 K, which produces errors in h and in Nu of less than 1 percent.

With eq (15) substituted into eq (12) to evaluate the pressure term, eqs

(12), (13), and (14) form a system of three equations in the unknowns of

temperature, velocity, and density. They were solved by iteration. After

determining Tf and V at location x, the heat transfer coefficient was

calculated using eq (8). The Nusselt number, Prandtl number, and Reynolds

number were then calculated, with the transport properties evaluated at the

bulk fluid temperature, Tf

:

Nu = h-Dh/k,

Pr = /i-c

p

/k. (16)

Transport properties were calculated from the functions given in McCarty

[1972]. Using Nu to evaluate the heat transfer performance assumes constant

fluid properties at the location x. Temperature differences between the wall

and fluid, produced by the finite heat transfer, will produce differences in

fluid properties between the wall and the fluid. The wall- to -fluid

temperature difference was much smaller for the pin- fin specimen than for the

tube and channel specimens, due to the higher heat transfer coefficient in the

pin- fin specimen. Even though property variations were small, we continued to

use the temperature ratio method of Rohsenow and Hartnett [1973] to compensate

for the property variations:

Niv = Nu-(T„/Tf ) 0 - 55. (17)

In the NASP application of the cooling jacket, heat fluxes would be much

higher than those tested here, and the property differences between the wall

and fluid would be larger due to the larger temperature difference. NUu, was

then correlated with Re.

The heat transfer coefficient, h, is defined in terms of the insulated

wall temperature, because that temperature was measured with the least

uncertainty. To predict the performance of the specimen from correlations

developed in our experiments, this definition is satisfactory, and will

predict the insulated wall temperature for given conditions of heat flux and

gas flow rate. However, we desire to compare our results to the literature

where h is defined in terms of a solid- fluid interface temperature. Because

the specimen was heated from one side only and the solid thermal conductivity

was finite, specimen temperatures will vary between the heated side, the

insulated side, and the solid-fluid interface. For the previously tested tube

and channel specimens, the fluid convection compared to the solid conduction

was low enough that the temperature variations in the solid were small

compared to the temperature difference between the wall and the fluid. In the

pin- fin specimen, the heat transfer is much better, and the insulated wall

temperature can no longer be considered the same as the solid- fluid interface

temperature

To compare our results to those of past studies where the heat transfer

coefficient was defined in terms of the solid- fluid interface temperature, we

11
computed temperature distributions in the pin with a finite element conduction

analysis. Our inputs to the model were the anticipated values of the wall

heat transfer coefficient, 1^,, anticipated normal heat fluxes, and the

adiabatic wall temperature. We assumed the heat transfer coefficient was

uniform around a pin and on the top and bottom plates. Then, we calculated a

pin efficiency, rj

, defined by

Qt/Ati

V = • (IB)

V(TW -Taw )

The temperature of the insulated wall, Tw , was calculated in the analysis.

The analysis was repeated for the range of h^ expected experimentally, and ij was calculated for each set of conditions. rj was then correlated as a

function of the Biot number

rj = 1.0024 + 1.5229-Bi - 0.3142-Bi2

, (19)

with Bi = t^-Db/kni.

To calculate 1^ from the experimental data, we measure Qx/^ and Tw , and

calculate Taw from eqs (6) and (12) . Then we use eq (18) in conjunction with

eq (19) to solve for h„. h^ is then normalized as a wall Nusselt number

Nu„ - hw -Dh/k-(T„/T£ )

0 - 55

, (20)

which includes the (small) effect of variable thermophysical properties

between the wall and the fluid. Nu^ was also correlated with Re.

3.4 Uncertainty analysis

Uncertainties for the calculated quantities were obtained by Taylor

series error propagation as described by ASME [1986]

.

This technique

generally produces the same level of confidence in a calculated result as the

level of confidence in the measurements which contribute to the result [Kline

and McClintock, 1953]

.

A summary of the uncertainties in the data analysis

parameters and in the calculated quantities is listed in table 4. Actual

values at the experimental points are included in table 3. The largest

contributor to the uncertainties in Tf , h, and Nu was the flow distribution

uncertainty (i.e., whether or not the flow had split evenly along the specimen

width) , particularly near the exit of the specimen. Using an analysis similar

to Olson [1990] in which transverse temperature measurements were used to

predict the local gas flow, we predicted the flow distribution varied by no

more than 2 percent across the width of the specimen, except close to the side

edges. However, since the wall- to -fluid temperature difference was small (5

to 10 K for low heat flux and high helium flow)

,

the small uncertainty in the

flow distribution still produced a large uncertainty in h and Nu.

12
4. Results of experiments

4.1 Friction factor

The pressure drop in the 18° pin- fin specimen was much greater than in

either the tube or channel specimens. For example, for the pin- fin specimen

the pressure drop was 1296 kPa (188 psi) at m = 31.1 kg/h and P0 = 3.4 MPa.

For similar flow conditions, the pressure drop in the tube specimen was 75 kPa

(m = 31.0 kg/h, P0 = 3.4 MPa), and in the channel specimen it was 51 kPa (m = 30.6 kg/h, P0 = 3.5 MPa). The variation of the friction factor with Reynolds

number was determined in experiment 1. Figure 6 shows the variation in f with

Re along with a least-squares correlation of the data (for Re > 2500) . These

data are correlated with

f = 0 . 8561 -Re -0,2160

. (21)

The standard deviation of the difference between the measured and correlated

values is 0.92 percent. If the points for Re > 1500 are included in the

correlation, the function is

f - 0 . 9193 -Re'0 2241

. (22)

The standard deviation of the difference between the measured and correlated

values is 1.09 percent. Data points for Re < 1500 were not included because

we believed the flow was laminar or in transition. The uncertainty in our

measured values of f is believed to be 22 to 23 percent for Re > 450. The

largest source of uncertainty for f was the uncertainty in the height of the

pins, which we estimated as 0.025 mm. This could not be confirmed without

sectioning the specimen, which would render it unusable for future tests. If

the uncertainty in the height of the pins were half as much, or 0.013 mm, then

the uncertainty in f would be 12 to 13 percent.

We can compare our measurements of friction factor to the literature

results, making some assumptions about minimum flow area and number of rows

which is needed for those correlations. For example, Metzger et al . [1982]

used the form of eq (5) and found, for 10 3 < Re < 10A and staggered circular

pins

,

fM = 0. 317-Re"0 - 132

. (23)

If the angle of the pins to the flow direction for our specimen were 30°

instead of 18°, then there would be 87 rows in the flow direction. If we then

use as the minimum flow area the open area along a row of pins, at Re = 8000,

we calculate a pressure drop that is 23 percent lower using the Metzger

correlation than what we measure. This is probably a reasonable agreement

because both N and Vmax have to be considered approximations, due to the

differences in geometry between our specimen and the literature results.

Metzger et al . indicate that the exponent of the Re term changes to -0.318 for

10 A < Re < 10 5

, which makes our exponent somewhat midway between what they

report.

We used the friction factor correlation developed for the tests without

13
heat transfer to predict the pressure drop when the specimen was heated.

Figure 7 compares the error between the predicted pressure drop and the

measured pressure drop, plotted as a function of helium flow rate. For Re >

2500 we used eq (21) for f; for 666 < Re < 2500 we used eq (22) for f. For Re

< 666, we assumed f ~ 1/Re, which is the functional form for laminar flow in a

tube or channel. The constant of proportionality was chosen so that f would

match the measured value at Re = 450. The error between the measured and

predicted pressure drop was less than 10 percent for most of the points, which

was within the uncertainty of the measured friction factor.

4.2 Temperature distributions and heat transfer

In experiments 2 to 6 we heated the specimen to determine the heat

transfer performance. A typical plot of temperatures in the helium gas and

along the specimen is shown in figure 8. The data are for the lowest flow

rate (11.4 kg/h) of experiment 5, which corresponded to the largest inlet-tooutlet temperature rise in the helium at that heat flux rate. The measured

specimen temperatures along the y centerline (y/W = 0.08 for the hot side, y/W

= 0.00 for the insulated side), are shown from the inlet to the outlet. The

calculated gas temperature is also plotted (eq 12) for the locations of an

insulated- side thermocouple. The gas temperature increased approximately

linearly from the inlet to the outlet. The heated- side temperatures were 16

to 18 K higher than the insulated- side temperatures over most of the specimen.

Specimen temperatures on both sides increased steadily from the inlet to the

outlet, except that the temperature decreased near the outlet.

The temperature difference between the heated and insulated sides

correlates well with the incident normal heat flux. As the heat flux

increases, this temperature difference increases almost linearly. Higher

coolant flow reduces the temperature difference, because higher flows reduce

specimen temperatures and therefore increase the nickel thermal conductivity.

Because the temperature increased and the pressure decreased from the

inlet to the outlet, other fluid properties changed significantly also. Both

thermal conductivity and dynamic viscosity increase with temperature, so they

increased from the inlet to the outlet. Fluid density decreased from the

inlet to the outlet, due to the increase in temperature and the decrease in

pressure. Because the density decreased, fluid velocity increased from the

inlet to the outlet; for the conditions shown in the figure, the specimen

inlet velocity was 22 m/s and the specimen outlet velocity was 61 m/s.

Temperatures at locations perpendicular to the flow direction (yvariation) for the conditions of figure 8 are shown in figure 9. Here, at

each x- location we have plotted temperature on the insulated side as a

function of y-position. Temperatures were much more uniform in the ydirection for the pin- fin specimen than for either the channel or tube

specimen. The lowest temperatures were closest to the +y edge of the

specimen; at x/L = 0.83, the temperature at y/W = 0.41 was 19 K lower than the

temperature at y/W =0.00. We believe temperatures were more uniform in the

pin- fin specimen when compared to the tube and channel specimens because the

flow was more evenly distributed along the specimen width. Except near the +y

edge of the specimen, the measured temperature variations in the y- direction

14
can be explained by nonuniformities of < 2 percent in the flow. The high

pressure drop in the pin- fin specimen will cause the inlet and outlet

distribution manifolds to produce more uniform flow. Also, because there are

no barriers to transverse flow for the pin- fin as there were for the tube and

channel specimens, the flow can readjust if it encounters a local

nonuniformity in flow area (either blockage or unbonded pins) . The local flow

rate was not adjusted to reflect nonuniformities in wall temperature (as was

done for the channel specimen in Olson [1990]), since in most cases the

nonuniformities in temperature were on the same order as the uncertainties in

the wall and gas temperatures

In figure 10 we show the heat transfer coefficient and wall- to-fluid

temperature difference for the same conditions as those for figure 8

(experiment 5, 11.4 kg/h helium flow). Shown are points along y/W = 0.00,

from the inlet to the outlet, h was calculated directly from the temperature

difference, with the appropriate heat flux (eq 8); to first order the trends

in Tw -Tf and h are mirrored. Except near x/L — 0 and 1, the temperature

difference was roughly constant over the entire length of the specimen. We

believe the cause of the drop-off near the end walls was heat conduction

through the specimen wall to the inlet and outlet manifolds . The length of

this conduction region was much shorter for the pin- fin specimen when compared

to the channel or tube specimens for 2 reasons: (1) the total thickness of the

specimen was less; (2) the heat transfer coefficient and internal wall area

were greater. Using the same technique for estimating the conduction region

as described in Olson and Glover [1990]

,

we predict the region extends from

x/L = 0 to 0.07, and from x/L = 0.93 to 1.0. In these regions, h and

therefore Nu cannot be calculated from eq (8)

,

since the heat convected into

the fluid was not the same as that incident on the specimen.

The wall- to-fluid temperature difference was 5 to 6 times lower for the

pin-fin specimen than in the tube or channel specimen, for similar incident

heat flux and helium flow rate. Because of the lower absolute temperature

difference, uncertainties in the wall and fluid temperatures produced higher

relative uncertainties in h, Nu, and Ni^ for the pin-fin specimen.

Figure 11 shows the variation of Re, Ni^, and Nu with x for the same

experimental conditions as above. We have plotted Nu and Ni^ along the entire

heated length, although the values at x/L = 0 and 1 are not accurate due to

conduction effects. The Reynolds number decreased from the inlet to the

outlet, due to the increase in viscosity caused by the temperature increase.

Nu and Ni^ also decreased from the inlet to the outlet, within the 0.07 < x/L

< 0.93 region of accuracy. N^ was only 1.9 to 5.8 percent greater than Nu

for experiment 5, due to the small temperature difference between the wall and

the fluid. (The maximum difference in the properties viscosity and thermal

conductivity between the wall and the fluid was 7 percent, compared to a 26

percent difference in properties for the channel specimen [Olson, 1990]).

The trends in temperature distributions, Re, and Nu with position did not

change qualitatively for the other helium flow rates for experiment 5, nor did

they change for the other heat flux rates tested. Figures 8 to 11 are

representative of the variations for all runs

15
For experiments 2 and 4, the wall temperature reading at x = 12.69 cm and

y

= 1.93 cm was likely in error, since it read lower than the fluid

temperature at that location. We suspect the error was caused by a short in

the reference box.

Figure 12 shows the modified Nusselt number plotted against the Reynolds

number for experiments 3 to 6 , for data points along y/W =0.0 and 0.07 < x/L

< 0.93. The data for experiment 2 were not included since they were virtually

identical to the data from experiment 3. Shown as the dashed line is the

correlation of VanFossen [1982] for turbulent flow past staggered, circular

pins with length- to-diame ter ratios of 1/2 and 2.

Nu = 0. 153-Re0 - 685 (VanFossen [1982]). (24)

The solid line is the correlation for our data for Re > 5000:

Ni^ = 0. 0198-Re0 - 928

, (25)

or in terms of Nu,

Nu = 0 . 0198 • Re 0 - 928

• (Tw/Tf )~ 0 - 55

. (26)

The standard deviation between our data and correlation is 3.7 percent (Re >

5000) . The leading coefficient and exponent on Re were calculated from a

least squares fit of the data. The power on the temperature ratio term was

assumed to be the same as for the tube and channel specimen data, -0.55. The

uncertainty on the measured data ranged from 13.6 to 43.8 percent, with the

highest uncertainty occurring near the specimen outlet for low heat flux and

high helium flow (conditions of the smallest Tw -Tf ) .

Our data agree well with the correlation of VanFossen around Re = 5000,

but are higher than his values for higher Re. The variation of Ni^ with Re is

also greater for our data than for that of VanFossen. Recall, however, that

in the definition of Nl^ we have used the measured, insulated side temperature

as the reference wall temperature. The correlation of VanFossen is based on

the pin temperature at the wall -fluid interface.

When we extrapolate our insulated temperature using eqs (18) and (19) to

calculate h„ based on the temperature of the wall-fluid interface (this

compensates for nonisothermal pin temperatures) , we get the results shown in

figure 13. The correlation for Nu„ is

Nu,, = 0. 0357-Re 0 - 837

. (27)

Also plotted is the correlation of VanFossen. The agreement of N^ to the

VanFossen correlation is much better, particularly at high Re. Although the

exponent on Re is higher for our data, for Re > 5000 the two correlations

agree to within the experimental uncertainty of our measurements.

In the NASP application, this specimen would be operated with Re > 5000.

For Re < 5000, there appears to be some dependence of Ni^ and Nu^ on heat

flux. For all heat fluxes Q/A^ > 44 W/cm2

, the data agree within experimental

16
uncertainty, but the data for Q/\ = 20 W/cm2 seem to be systematically higher

at Re = 3000. This is more evident on a logCNu,,) vs log(Re) plot. We

speculate that the higher heat transfer for the low heat flux test is related

to flow acceleration. The lower heat flux will have less flow acceleration,

since the increases in temperature, density, and velocity with x are less.

Metzger et al. [1986] found that the heat transfer in pin- fins in a converging

channel was reduced. The converging channel will produce flow acceleration.

It is possible that a similar phenomenon is occurring in our test; the

experiments at higher heat flux have greater temperature rise in the flow

direction, greater density changes, hence more flow acceleration and reduced

heat transfer.

5. Summary and conclusions

We tested a novel pin- fin specimen, with a pin angle of 18° to the flow

direction, to measure the friction factor and heat transfer in helium gas.

Experiments were performed in an apparatus which radiatively heated one side

of the specimen at a heat flux of up to 74 W/cm2 (65 Btu/(s • ft2

) ) , and cooled

the specimen with helium gas at 3.5 MPa (500 psi) and Re of 450 to 12 000.

Helium gas temperatures ranged from 284 K (52 °F) to 742 K (877 °F) ; the peak

specimen temperature was 761 K (910 °F) . We report the heat transfer both as

a modified Nusselt number, which should be used for design purposes to predict

the temperature on the insulated side of the specimen, and as a wall Nusselt

number, which we used to compare the performance to past work on pin- fin

configurations. Our measured wall Nusselt number agrees with the correlation

of VanFossen to within experimental uncertainty for Re > 5000. Conduction to

the end manifolds was important in the specimen within 7 percent of where

heating begins and ends. Over most of the specimen, the non-uniformity in

helium flow was less than 2 percent. At Re < 5000 (lower than the range for

NASP) , there appears to be some reduction in heat transfer at higher heat

fluxes, possibly due to increased flow acceleration.

17
6. References

Armstrong, J., and Winstanley, D. , 1987, "A Review of Staggered Array Pin Fin

Heat Transfer for Turbine Cooling Applications," ASME Paper 87-GT-201 .

ASME, 1986, "ASME Performance Test Codes Supplement on Instruments and

Apparatus - Part 1 - Measurement Uncertainty," ANSI/ASME PTC 19.1-1985 .

Kays, W. , and London, A. L. , 1964, Compact Heat Exchangers . McGraw-Hill, Inc.

New York.

Kline, S. J., and McClintock, F. A., 1953, "Describing Uncertainties in

Single -Sample Experiments," Mechanical Engineering . Vol. 75, pp . 3-8.

McCarty, R. D. , 1972, "Thermophysical Properties of Helium-4 from 2 to 1500 K

with Pressures to 1000 Atmospheres," NBS -TN- 631 .

McCarty, R. D., 1973, "Thermodynamic Properties of Helium 4 from 2 to 1500 K

at Pressures to 10 8 Pa," J. Phvs . Chem. Ref. Data . Vol. 2, no. 4, pp . 923-

1042.

Metzger, D. E., Fan, Z. X., and Shepard, W. B., 1982, "Pressure Loss and Heat

Transfer Through Multiple Rows of Short Pin Fins," in Heat Transfer 1982 . U.

Grigull et ai., eds . , Vol. 3, pp . 137-142.

Metzger, D. E., Shepard., W. B., and Haley, S. W. , 1986, "Row Resolved Heat

Transfer Variations in Pin- Fin Arrays Including Effects of Non-Uniform Arrays

and Flow Convergence," ASME Paper 86-GT-132 .

Olson, D. A., 1990, "Heat Transfer in a Compact Heat Exchanger Containing

Rectangular Channels and Using Helium Gas," NISTIR 3959 .

Olson, D. A., 1989, "Apparatus for Measuring High-Flux Heat Transfer in

Radiatively Heated Compact Exchangers," NISTIR 89-3926 .

Olson, D. A., and Glover, M. P., 1990, "Heat Transfer in a Compact Tubular

Heat Exchanger With Helium Gas at 3.5 MPa," NISTIR 3941 .

Rohsenow, W. M. , and Choi, H. , 1961, Heat. Mass, and Momentum Transfer . Prentice-Hall, Inc., Englewood Cliffs.

Rohsenow, W. M. , and Hartnett, J. P., 1973, Handbook of Heat Transfer . McGraw

Hill, Inc., New York.

Scotti, S. J., Martin, C. J., and Lucas, S. H. , 1988, "Active Cooling Design

for Scramjet Engines Using Optimization Methods," NASA TM-100581 .

Shore, C. P., 1986, "Review of Convectively Cooled Structures for Hypersonic

Flight," NASA TM- 87740 .

VanFossen, G. J., 1982, "Heat-Transfer Coefficients for Staggered Arrays of

Short Pin Fins," J. of Engineering for Power . Vol. 104, pp. 268-274.

18
APPENDIX A. Calculation of open volume, wetted- wall area, and flow area

for pin- fin specimens

A.l. Open volume

The open volume was found by determining the open flow volume around each

pin, then multiplying by the number of pins. We added the volume of a narrow

channel next to each side edge, of width 0.64 mm and height 0.51 mm, which

NASA Langley milled into the piece to prevent accumulation of braze.

The open volume per pin was found by referencing to figure (A.l). Each

pin is considered to occupy a hexagon of the normal area, where the width

between sides of the hexagon is S = 2.03 mm. If the pin solid were not

present, for a separation between plates, t, of 0.51 mm the volume would be

Vo.no.p - (3^/2) -S2 -t . (A.l)

To determine the volume of the solid pin, we assumed the pin diameter varied

from d at the point of the braze to S at the channel height t. With z as the

vertical coordinate as in the drawing, the diameter varied with z as

dp = S - 2 (

2 -z2

) 1/2

. (A. 2)

Performing the integration and substituting a = S - 2t, we find the solid

volume of the pin as

Vs ,p - 7Tt/4-[S 2 -( )r/4)-S-t+(8/3)-t2

] . (A. 3)

The total open volume per pin is

Vw o,p = Vv o,no.p

- Vs,p

= (3 1/2/2) • S

2 • t - 7rt/4- [

2

- (tt/4) -S-t+(8/3) -t2

]

. (A. 4)

The total number of pins was found by dividing the normal area per pin

by the total normal area, recognizing that there will be partial pins along

all four edges. We found n = 3203. The total open volume was therefore n

times VQ plus the volume of the two channels along the edges. Substituting

values for S and t we find

VQ = 3.856 cm3

. (A. 5)

A. 2. Wetted-wall area

The wetted-wall area, A*, was found by calculating the wetted-wall area

per pin, A„ p

, then multiplying by the number of pins, n. As in the

calculation of the open volume, we added the wetted-wall area of the two

channels next to the side edges. The wetted-wall area per pin was composed of

the wall area on the top channel, the wall area on the bottom channel, and the

wall area on the side of the pins. The wall area on the side of the pins was

found by integration, with reference again to figure A.l.

19
Vp = S

2

* (3 1/2/2 -tt/4) + [(3 1/2/2)-S2 -(vV0-d2

] + *t • (irS/2-2t) , (A. 6)

where the terms on the right hand side of the equation are, respectively, the

wall area on the top channel, the wall area on the bottom channel, and the

wall area on the side of the pins.

Multiplying eq (A. 6) by n and adding the wall area of the two side

channels, we find

Aw = 215.8 cm2

. (A. 7)

A. 3. Flow area

The flow area was found by assuming the open volume is distributed evenly

through the length of the specimen. It is an average flow area, neither the

minimum or maximum. It is simply the open volume divided by the length, or

Af = V0/L, = 0.2530 cm2

. (A. 8)

20
Table 1. Uncertainties in experimental measurements and gas properties

at a 95 percent confidence interval

Measurement or

Property Technique

Major Source

of Uncertainty

Magnitude of

Uncertainty

Gas Flow Rate Thermal Mass

Flow Meter

Meter Calibration ±1%

Heat Flux Calibration of

Furnace

Heat Flow Meter ±4%

Gas Inlet and

Outlet Temperatures

Platinum Resistance ThermometerRadiation ±0.5 K

Gas Pressure Pressure Transducer

Calibration ±0.25%

Gas Differential

Pressure

Pressure Transducer

Calibration greater of

±0.5% or

±1.4 kPa

Specimen

Temperature

Type N Thermocouple

Wire Calibration,

Installation

greater of

±0.4% of T(C)

or ±1.1 K

Gas Density Thermodynamic

Function

Function Accuracy ±0.1%

Gas Enthalpy Thermodynamic

Function

Function Accuracy ±0.2%

Gas Specific Heat Thermodynamic

Function

Function Accuracy ±5%

Gas Viscosity Thermodynamic

Function

Function Accuracy ±10%

Gas Thermal

Conductivity

Thermodynamic

Function

Function Accuracy ±3%

21
Table 2

.

Summary of geometrical parameters and experimental conditions

for 18° pin-fin specimen

Angle of Pins to Flow Direction =18°

Pin Height, t = 0.508 mm

Pin Spacing, S = 2.032 mm

Pin Diameter at Braze, d = 1.016 mm

Specimen Hydraulic Diameter, Dh = 0.7149 mm

Specimen Heated Length, L = 15.24 cm

Specimen Width, W = 7.85 cm

Specimen Heated Normal Area, A^ = 119.6 cm2 Specimen Wetted Wall Area, A„ = 215.8 cm2 Flow Normal Area, Af = 0.2530 cm2

Expt

.

#

Date

Inlet

Pressure

(kPa)

Heater

Voltage

(%)

Normal

Heat Flux

(W/cm2

)

Helium

Flow Rate

(kg/h)

Reynolds

Number

1 9/18/90 3435 0.0 0.0 1.1-31.1 450-12 300

2 9/19/90 3570 24.8 20.2 4.1-15.4 900- 6 100

3 11/20/90 3500 25.5 20.4 3.7-28.3 800-11 400

4 9/19/90 3440 50.2 44.2 10.3-27.0 2400-10 800

5 11/21/90 3505 75.2 63.1 11.4-27.8 2400-11 300

6 11/23/90 3525 93.8 73.8 15.0-25.6 3300-10 400

22
Table 3 Data tables for all experiments

18° P inf in Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:21:10

TA TB M P0 P0-P1 V f f Uf

K K kg/h kPa kPa X X

295.13 294.57 1.12 3465.4 3.66 0.00 0.31749 44.28

Hot -side Temperatures:

X Y Tw X Y Tw cm cm K cm cm K 1.332 0.485 294.81 2.549 -1.330 294.93

2.597 0.526 294.88 5.033 -1.444 294.95

2.681 0.923 294.89 7.571 -1.375 294.92

5.107 0.426 294.90 10.071 -1.476 294.90

7.626 0.498 294.87 2.465 -2.649 294.97

7.710 0.895 294.87 7.657 -2.616 294.94

10.111 0.396 294.88 12.699 -2.643 294.87

12.651 0.478 294.84 7.540 2.687 294.86

12.734 0.875 294.88 7.623 3.085 294.85

13.931 0.527 294.84

Insulated-Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw Wtf Wre

cm cm K < kPa m/s K 1C X

-0.038 -0.229 294.97 295.13 3465.4 2.22 445 0.665 1.10 0.50 10.69

1.293 -0.226 294.97 295.08 3465.1 2.22 445 0.665 1.10 0.50 10.69 2.527 -0.132 294.95 295.04 3464.8 2.22 445 0.665 1.10 0.50 10.69

3.802 0.056 294.94 294.99 3464.4 2.22 445 0.665 1.10 0.50 10.69

4.976 -0.008 294.90 294.95 3464.2 2.22 445 0.665 1.10 0.50 10.69

6.314 0.028 294.91 294.90 3463.8 2.22 445 0.665 1.10 0.50 10.69

7.607 0.033 294.93 294.85 3463.5 2.22 445 0.665 1.10 0.50 10.69

8.913 -0.013 294.89 294.80 3463.2 2.22 445 0.665 1.10 0.50 10.69

10.185 0.020 294.90 294.76 3462.9 2.22 445 0.665 1.10 0.50 10.69

11.453 0.066 294.87 294.71 3462.6 2.22 445 0.665 1.10 0.50 10.69

12.723 -0.033 294.88 294.66 3462.3 2.22 445 0.665 1.10 0.50 10.69

13.993 0.025 294.87 294.62 3462.0 2.22 445 0.665 1.10 0.50 10.69

15.240 -0.058 294.82 294.57 3461.7 2.22 445 0.665 1.10 0.50 10.69

2.565 -1.880 294.97 295.03 3464.7 2.22 445 0.665 1.10 0.50 10.69

5.032 -1.892 294.97 294.94 3464.1 2.22 445 0.665 1.10 0.50 10.69

7.620 -1.938 294.94 294.85 3463.5 2.22 445 0.665 1.10 0.50 10.69

10.185 -1.951 294.92 294.76 3462.9 2.22 445 0.665 1.10 0.50 10.69

12.700 -1.913 294.91 294.66 3462.3 2.22 445 0.665 1.10 0.50 10.69

2.494 1.925 294.91 295.04 3464.8 2.22 445 0.665 1.10 0.50 10.69

5.098 1.900 294.90 294.94 3464.1 2.22 445 0.665 1.10 0.50 10.69

7.620 1.852 294.92 294.85 3463.5 2.22 445 0.665 1.10 0.50 10.69

10.160 1.956 294.88 294.76 3462.9 2.22 445 0.665 1.10 0.50 10.69

12.692 1.930 293.46 294.66 3462.3 2.22 445 0.665 1.10 0.50 10.69

2.540 -3.211 294.99 295.04 3464.8 2.22 445 0.665 1.10 0.50 10.69

7.633 -3.213 294.94 294.85 3463.5 2.22 445 0.665 1.10 0.50 10.69

12.720 -3.211 294.90 294.66 3462.3 2.22 445 0.665 1.10 0.50 10.69

2.499 3.221 294.88 295.04 3464.8 2.22 445 0.665 1.10 0.50 10.69

7.620 3.454 294.88 294.85 3463.5 2.22 445 0.665 1.10 0.50 10.69

12.700 3.180 294.86 294.66 3462.3 2.22 445 0.665 1.10 0.50 10.69

23
Table 3 (continued) 18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:26:38

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.03 295.36 3.81 3445.2 24.26 0.00 0.18077 22.82

Hot -side Temperatures:

X Y Tw X Y Tw

cm cm K cm cm K 1.332 0.485 295.33 2.549 -1.330 295.92

2.597 0.526 295.83 5.033 -1.444 295.93

2.681 0.923 295.84 7.571 -1.375 295.93

5.107 0.426 295.86 10.071 -1.476 295.89

7.626 0.498 295.82 2.465 -2.649 295.95

7.710 0.895 295.83 7.657 -2.616 295.91

10.111 0.396 295 . 78 12.699 -2.643 295.89

12.651 0.478 295 . 78 7.540 2.687 295.79

12.734 0.875 295.83 7.623 3.085 295.77

13.931 0.527 295.81

Insulated-Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw Wtf Ure

cm cm < K kPa m/s K X X

-0.038 -0.229 295.96 296.03 3445.3 7.59 1505 0.665 1.10 0.50 10.69

1.293 -0.226 295.95 295.97 3443.2 7.59 1505 0.665 1.10 0.50 10.69 2.527 -0.132 295.95 295.92 3441.2 7.59 1505 0.665 1.10 0.50 10.69

3.802 0.056 295.96 295.86 3439.2 7.60 1506 0.665 1.10 0.50 10.69 4.976 -0.008 295.92 295.81 3437.3 7.60 1506 0.665 1.10 0.50 10.69

6.314 0.028 295.94 295.75 3435 .

1

7.60 1506 0.665 1.10 0.50 10.69

7.607 0.033 295.92 295.69 3433.0 7.61 1506 0.665 1.10 0.50 10.69

8.913 -0.013 295.92 295.63 3430.9 7.61 1506 0.665 1.10 0.50 10.69

10.185 0.020 295.90 295.58 3428.9 7.61 1506 0.665 1.10 0.50 10.69

11.453 0.066 295.91 295.52 3426.8 7.62 1507 0.665 1.10 0.50 10.69

12.723 -0.033 295.89 295.47 3424.8 7.62 1507 0.665 1.10 0.50 10.69

13.993 0.025 295.91 295.41 3422.8 7.62 1507 0.665 1.10 0.50 10.69

15.240 -0.058 295.89 295.36 3420.7 7.63 1507 0.665 1.10 0.50 10.69

2.565 -1.880 295.99 295.91 3441.1 7.59 1505 0.665 1.10 0.50 10.69

5.032 -1.892 295.98 295.80 3437.2 7.60 1506 0.665 1.10 0.50 10.69

7.620 -1.938 296.00 295.69 3433.0 7.61 1506 0.665 1.10 0.50 10.69

10.185 -1.951 295.98 295.58 3428.9 7.61 1506 0.665 1.10 0.50 10.69

12.700 -1.913 295.94 295.47 3424.8 7.62 1507 0.665 1.10 0.50 10.69

2.494 1.925 295.91 295.92 3441.3 7.59 1505 0.665 1.10 0.50 10.69

5.098 1.900 295.89 295.80 3437.1 7.60 1506 0.665 1.10 0.50 10.69

7.620 1.852 295.88 295.69 3433.0 7.61 1506 0.665 1.10 0.50 10.69

10.160 1.956 295.89 295.58 3428.9 7.61 1506 0.665 1.10 0.50 10.69

12.692 1.930 293.96 295.47 3424.8 7.62 1507 0.665 1.10 0.50 10.69

2.540 -3.211 296.03 295.91 3441.2 7.59 1505 0.665 1.10 0.50 10.69

7.633 -3.213 296.01 295.69 3433.0 7.61 1506 0.665 1.10 0.50 10.69

12.720 -3.211 295.98 295.47 3424.8 7.62 1507 0.665 1.10 0.50 10.69

2.499 3.221 295.82 295.92 3441.2 7.59 1505 0.665 1.10 0.50 10.69

7.620 3.454 295.84 295.69 3433.0 7.61 1506 0.665 1.10 0.50 10.69

12.700 3.1180 295.83 295.47 3424.8 7.62 1507 0.665 1.10 0.50 10.69

24
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:32:00

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.71 296.35 6.44 3441.9 61.07 0.00 0.15782 22.19

Hot -side Temperatures:

X Y Tw X Y Tw cm cm X cm cm X 1.332 0.485 295.67 2.549 -1.330 296.63

2.597 0.526 296.58 5.033 -1.444 296.62

2.681 0.923 296.55 7.571 -1.375 296.63

5.107 0.426 296.57 10.071 -1.476 296.61 7.626 0.498 296.55 2.465 -2.649 296.64

7.710 0.895 296.55 7.657 -2.616 296.63

10.111 0.396 296.56 12.699 -2.643 296.61

12.651 0.478 296.58 7.540 2.687 296.50

12.734 0.875 296.57 7.623 3.085 296.47

13.931 0.527 296.56

Insulated-Side Temperatures and Calculated Data: —Uncertaint:ies--

X Y Tw Tf P V RE PR Wtw Utf Ure

cm cm K K kPa m/s X X X

-0.038 -0.229 296.65 296.70 3442.3 12.86 2540 0.665 1.10 0.50 10.69

1.293 -0.226 296.65 296.67 3436.9 12.88 2540 0.665 1.10 0.50 10.69 2.527 -0.132 296.61 296.64 3431.9 12.90 2540 0.665 1.10 0.50 10.69

3.802 0.056 296.63 296.61 3426.7 12.92 2540 0.665 1.10 0.50 10.69 4.976 -0.008 296.61 296.58 3422.0 12.94 2541 0.665 1.10 0.50 10.69

6.314 0.028 296.64 296.55 3416.6 12.95 2541 0.665 1.10 0.50 10.69 7.607 0.033 296.62 296.52 3411.3 12.97 2541 0.665 1.10 0.50 10.69

8.913 -0.013 296.61 296.48 3406.0 12.99 2541 0.665 1.10 0.50 10.69

10.185 0.020 296.62 296.45 3400.9 13.01 2541 0.665 1.10 0.50 10.69

11.453 0.066 296.61 296.42 3395.8 13.03 2542 0.665 1.10 0.50 10.69

12.723 -0.033 296.58 296.39 3390.6 13.05 2542 0.665 1.10 0.50 10.69

13.993 0.025 296.60 296.36 3385.5 13.06 2542 0.665 1.10 0.50 10.69

15.240 -0.058 296.63 296.33 3380.4 13.08 2542 0.665 1.10 0.50 10.69

2.565 -1.880 296.65 296.64 3431.8 12.90 2540 0.665 1.10 0.50 10.69

5.032 -1.892 296.69 296.58 3421.8 12.94 2541 0.665 1.10 0.50 10.69

7.620 -1.938 296.63 296.52 3411.3 12.97 2541 0.665 1.10 0.50 10.69

10.185 -1.951 296.65 296.45 3400.9 13.01 2541 0.665 1.10 0.50 10.69

12.700 -1.913 296.65 296.39 3390.7 13.05 2542 0.665 1.10 0.50 10.69

2.494 1.925 296.56 296.64 3432.0 12.90 2540 0.665 1.10 0.50 10.69

5.098 1.900 296.56 296.58 3421.5 12.94 2541 0.665 1.10 0.50 10.69

7.620 1.852 296.57 296.52 3411.3 12.97 2541 0.665 1.10 0.50 10.69

10.160 1.956 296.55 296.45 3401.0 13.01 2541 0.665 1.10 0.50 10.69

12.692 1.930 294.34 296.39 3390.7 13.04 2542 0.665 1.10 0.50 10.69

2.540 -3.211 296.67 296.64 3431.9 12.90 2540 0.665 1.10 0.50 10.69

7.633 -3.213 296.64 296.51 3411.2 12.97 2541 0.665 1.10 0.50 10.69

12.720 -3.211 296.63 296.39 3390.6 13.05 2542 0.665 1.10 0.50 10.69

2.499 3.221 296.49 296.64 3432.0 12.90 2540 0.665 1.10 0.50 10.69

7.620 3.454 296.49 296.52 3411.3 12.97 2541 0.665 1.10 0.50 10.69

12.700 3.180 296.49 296.39 3390.7 13.05 2542 0.665 1.10 0.50 10.69

25
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:37:30

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.61 296.64 9.92 3433.7 132.59 0.00 0.14239 22.10

Hot-side Temperatures:

X Y Tw X Y Tw cm cm K cm cm K 1.332 0.485 295.51 2.549 -1.330 296.56

2.597 0.526 296.53 5.033 -1.444 296.56

2.681 0.923 296.54 7.571 -1.375 296.56

5.107 0.426 296.54 10.071 -1.476 296.55

7.626 0.498 296.53 2.465 -2.649 296.54

7.710 0.895 296.55 7.657 -2.616 296.57

10.111 0.396 296.54 12.699 -2.643 296.57

12.651 0.478 296.55 7.540 2.687 296.51

12.734 0.875 296.57 7.623 3.085 296.52

13.931 0.527 296.55

Insulated-Side Temperatures and Calculated Data: —Uncertainties

X Y Tw Tf P V RE PR Utw Wtf Wre

cm cm K K kPa m/s K K X

-0.038 -0.229 296.54 296.58 3434.4 19.86 3914 0.665 1.10 0.50 10.69

1.293 -0.226 296.56 296.58 3422.7 19.92 3914 0.665 1.10 0.50 10.69 2.527 -0.132 296.54 296.58 3411.9 19.99 3914 0.665 1.10 0.50 10.69

3.802 0.056 296.53 296.58 3400.7 20.05 3914 0.665 1.10 0.50 10.69 4.976 -0.008 296.50 296.58 3390.3 20.11 3915 0.665 1.10 0.50 10.69

6.314 0.028 296.56 296.58 3378.6 20.18 3915 0.665 1.10 0.50 10.69

7.607 0.033 296.56 296.59 3367.2 20.25 3915 0.665 1.10 0.50 10.69

8.913 -0.013 296.57 296.59 3355.7 20.32 3915 0.665 1.10 0.50 10.69

10.185 0.020 296.55 296.59 3344.5 20.38 3915 0.665 1.10 0.50 10.69

11.453 0.066 296.57 296.59 3333.4 20.45 3915 0.665 1.10 0.50 10.69

12.723 -0.033 296.56 296.59 3322.2 20.52 3915 0.665 1.10 0.50 10.69

13.993 0.025 296.57 296.59 3311.0 20.59 3915 0.665 1.10 0.50 10.69

15.240 -0.058 296.61 296.60 3300.1 20.66 3915 0.665 1.10 0.50 10.69

2.565 -1.880 296.50 296.58 3411.5 19.99 3914 0.665 1.10 0.50 10.69

5.032 -1.892 296.54 296.58 3389.8 20.11 3915 0.665 1.10 0.50 10.69

7.620 -1.938 296.54 296.59 3367.1 20.25 3915 0.665 1.10 0.50 10.69

10.185 -1.951 296.57 296.59 3344.5 20.38 3915 0.665 1.10 0.50 10.69

12.700 -1.913 296.57 296.59 3322.4 20.52 3915 0.665 1.10 0.50 10.69

2.494 1.925 296.51 296.58 3412.2 19.99 3914 0.665 1.10 0.50 10.69

5.098 1.900 296.50 296.58 3389.3 20.12 3915 0.665 1.10 0.50 10.69

7.620 1.852 296.50 296.59 3367.1 20.25 3915 0.665 1.10 0.50 10.69

10.160 1.956 296.52 296.59 3344.7 20.38 3915 0.665 1.10 0.50 10.69

12.692 1.930 294.43 296.59 3322.5 20.52 3915 0.665 1.10 0.50 10.69

2.540 -3.211 296.50 296.58 3411.8 19.99 3914 0.665 1.10 0.50 10.69

7.633 -3.213 296.51 296.59 3367.0 20.25 3915 0.665 1.10 0.50 10.69

12.720 -3.211 296.56 296.59 3322.2 20.52 3915 0.665 1.10 0.50 10.69

2.499 3.221 296.39 296.58 3412.1 19.99 3914 0.665 1.10 0.50 10.69

7.620 3.454 296.48 296.59 3367.1 20.25 3915 0.665 1.10 0.50 10.69

12.700 3.180 296.53 296.59 3322.4 20.52 3915 0.665 1.10 0.50 10.69

26
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:45:51

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.19 296.42 15.11 3416.3 294.17 0.00 0.13214 22.11

Hot-side Temperatures:

X Y Tw X Y Tw

cm cm K cm cm K 1.332 0.485 295.27 2.549 -1.330 296.17

2.597 0.526 296.23 5.033 -1.444 296.16

2.681 0.923 296.19 7.571 -1.375 296.19

5.107 0.426 296.26 10.071 -1.476 296.22

7.626 0.498 296.28 2.465 -2.649 296.23

7.710 0.895 296.27 7.657 -2.616 296.26

10.111 0.396 296.30 12.699 -2.643 296.29

12.651 0.478 296.30 7.540 2.687 296.20

12.734 0.875 296.32 7.623 3.085 296.27

13.931 0.527 296.32

Insulated-Side Temperatures and Calculated Data: -Uncertainties

X Y Tw Tf P V RE PR Utw Wtf Ure

cm cm K K kPa m/s K X X

-0.038 -0.229 296.22 296.12 3418.0 30.35 5970 0.665 1.10 0.50 10.69

1.293 -0.226 296.24 296.14 3392.0 30.58 5970 0.665 1.10 0.50 10.69 2.527 -0.132 296.26 296.15 3367.9 30.80 5970 0.665 1.10 0.50 10.69

3.802 0.056 296.31 296.17 3343.1 31.03 5970 0.665 1.10 0.50 10.69 4.976 -0.008 296.30 296.18 3320.2 31.24 5970 0.665 1.10 0.50 10.69

6.314 0.028 296.31 296.20 3294.1 31.48 5970 0.665 1.10 0.50 10.69 7.607 0.033 296.34 296.21 3268.8 31.72 5970 0.665 1.10 0.50 10.69

8.913 -0.013 296.35 296.23 3243.4 31.97 5970 0.665 1.10 0.50 10.69

10.185 0.020 296.36 296.24 3218.5 32.22 5970 0.665 1.10 0.50 10.69

11.453 0.066 296.37 296.26 3193.8 32.46 5970 0.665 1.10 0.50 10.69

12.723 -0.033 296.37 296.27 3169.0 32.72 5970 0.665 1.10 0.50 10.69

13.993 0.025 296.36 296.28 3144.2 32.97 5971 0.665 1.10 0.50 10.69

15.240 -0.058 296.42 296.30 3119.9 33.22 5971 0.665 1.10 0.50 10.69

2.565 -1.880 296.20 296.15 3367.2 30.81 5970 0.665 1.10 0.50 10.69

5.032 -1.892 296.17 296.18 3319.1 31.25 5970 0.665 1.10 0.50 10.69

7.620 -1.938 296.21 296.21 3268.6 31.73 5970 0.665 1.10 0.50 10.69

10.185 -1.951 296.26 296.24 3218.5 32.22 5970 0.665 1.10 0.50 10.69

12.700 -1.913 296.29 296.27 3169.5 32.71 5970 0.665 1.10 0.50 10.69

2.494 1.925 296.20 296.15 3368.6 30.79 5970 0.665 1.10 0.50 10.69

5.098 1.900 296.23 296.18 3317.8 31.26 5970 0.665 1.10 0.50 10.69

7.620 1.852 296.23 296.21 3268.6 31.73 5970 0.665 1.10 0.50 10.69

10.160 1.956 296.24 296.24 3219.0 32.21 5970 0.665 1.10 0.50 10.69

12.692 1.930 294.42 296.27 3169.6 32.71 5970 0.665 1.10 0.50 10.69

2.540 -3.211 296.27 296.15 3367.7 30.80 5970 0.665 1.10 0.50 10.69

7.633 -3.213 296.34 296.21 3268.3 31.73 5970 0.665 1.10 0.50 10.69

12.720 -3.211 296.37 296.27 3169.1 32.71 5970 0.665 1.10 0.50 10.69

2.499 3.221 296.22 296.15 3368.5 30.79 5970 0.665 1.10 0.50 10.69

7.620 3.454 296.30 296.21 3268.6 31.73 5970 0.665 1.10 0.50 10.69

12.700 3.180 296.35 296.27 3169.5 32.71 5970 0.665 1.10 0.50 10.69

27
18° Table 3 (continued) P inf in Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:50:50

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.43 296.81 20.02 3407.8 492.73 0.00 0.12159 22.16

Hot-side Temperatures:

X Y Tw X Y Tw

cm cm K cm cm K 1.332 0.485 295.30 2.549 -1.330 296.44

2.597 0.526 296.40 5.033 -1.444 296.45

2.681 0.923 296.42 7.571 -1.375 296.50

5.107 0.426 296.44 10.071 -1.476 296.53

7.626 0.498 296.48 2.465 -2.649 296.40

7.710 0.895 296.48 7.657 -2.616 296.51

10.111 0.396 296.49 12.699 -2.643 296.57

12.651 0.478 296.55 7.540 2.687 296.45

12.734 0.875 296.58 7.623 3.085 296.44

13.931 0.527 296.59

Insula ted- Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw Wtf Wre

cm cm K K kPa m/s K K X

-0.038 -0.229 296.40 296.31 3410.7 40.31 7904 0.665 1.10 0.50 10.69

1.293 -0.226 296.39 296.34 3367.2 40.83 7904 0.665 1.10 0.50 10.69 2.527 -0.132 296.43 296.36 3326.8 41.32 7904 0.665 1.10 0.50 10.69

3.802 0.056 296.45 296.38 3285.2 41.84 7905 0.665 1.10 0.50 10.69 4.976 -0.008 296.46 296.40 3246.8 42.33 7905 0.665 1.10 0.50 10.69

6.314 0.028 296.48 296.42 3203.1 42.90 7905 0.665 1.10 0.50 10.69

7.607 0.033 296.49 296.44 3160.8 43.47 7905 0.665 1.10 0.50 10.69

8.913 -0.013 296.53 296.46 3118.2 44.06 7906 0.665 1.10 0.50 10.69

10.185 0.020 296.53 296.48 3076.6 44.65 7906 0.665 1.10 0.50 10.69

11.453 0.066 296.57 296.50 3035 .

1

45.25 7906 0.665 1.10 0.50 10.69

12.723 -0.033 296.57 296.52 2993.6 45.87 7906 0.665 1.10 0.50 10.69

13.993 0.025 296.59 296.54 2952.1 46.51 7906 0.665 1.10 0.50 10.69

15.240 -0.058 296.63 296.56 2911.4 47.15 7907 0.665 1.10 0.50 10.69

2.565 -1.880 296.40 296.36 3325.6 41.33 7904 0.665 1.10 0.50 10.69

5.032 -1.892 296.46 296.40 3245.0 42.35 7905 0.665 1.10 0.50 10.69

7.620 -1.938 296.50 296.44 3160.4 43.47 7905 0.665 1.10 0.50 10.69

10.185 -1.951 296.56 296.48 3076.6 44.65 7906 0.665 1.10 0.50 10.69

12.700 -1.913 296.58 296.52 2994.4 45.86 7906 0.665 1.10 0.50 10.69

2.494 1.925 296.42 296.36 3327.9 41.31 7904 0.665 1.10 0.50 10.69 5.098 1 .900 296.45 296.40 3242.8 42.38 7905 0.665 1.10 0.50 10.69

7.620 1.852 296.50 296.44 3160.4 43.47 7905 0.665 1.10 0.50 10.69

10.160 1.956 296.53 296.48 3077.4 44.63 7906 0.665 1.10 0.50 10.69

12.692 1.930 294.51 296.52 2994.7 45.86 7906 0.665 1.10 0.50 10.69

2.540 -3.211 296.42 296.36 3326.4 41.32 7904 0.665 1.10 0.50 10.69

7.633 -3.213 296.48 296.44 3160.0 43.48 7905 0.665 1.10 0.50 10.69

12.720 -3.211 296.58 296.52 2993.7 45.87 7906 0.665 1.10 0.50 10.69

2.499 3.221 296.38 296.36 3327.8 41.31 7904 0.665 1.10 0.50 10.69

7.620 3.454 296.45 296.44 3160.4 43.47 7905 0.665 1.10 0.50 10.69

12.700 3.180 296.56 296.52 2994.4 45.86 7906 0.665 1.10 0.50 10.69

28
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 14:56:18

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

296.23 296.87 24.60 3415.1 748.61 0.00 0.11718 22.26

Hot -side Temperatures:

X Y Tw X Y Tw

cm cm X cm cm K 1.332 0.485 295.18 2.549 -1.330 296.23

2.597 0.526 296.18 5.033 -1.444 296.26

2.681 0.923 296.20 7.571 -1.375 296.32

5.107 0.426 296.19 10.071 -1.476 296.37

7.626 0.498 296.30 2.465 -2.649 296.20

7.710 0.895 296.31 7.657 -2.616 296.28

10.111 0.396 296.37 12.699 -2.643 296.41

12.651 0.478 296.43 7.540 2.687 296.27

12.734 0.875 296.42 7.623 3.085 296.27

13.931 0.527 296.44

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf P V RE PR Utw Utf Ure

cm cm X X kPa m/s X X X

-0.038 -0.229 296.14 296.05 3419.4 49.37 9718 0.665 1.10 0.50 10.69

1.293 -0.226 296.15 296.09 3353.3 50.33 9718 0.665 1.10 0.50 10.69 2.527 -0.132 296.16 296.12 3292.1 51.26 9718 0.665 1.10 0.50 10.69

3.802 0.056 296.22 296.16 3228.8 52.26 9719 0.665 1.10 0.50 10.69 4.976 -0.008 296.21 296.19 3170.5 53.21 9719 0.665 1.10 0.50 10.69

6.314 0.028 296.23 296.22 3104.0 54.33 9719 0.665 1.10 0.50 10.69

7.607 0.033 296.27 296.26 3039.8 55.47 9720 0.665 1.10 0.50 10.69

8.913 -0.013 296.30 296.29 2975.0 56.67 9720 0.665 1.10 0.50 10.69

10.185 0.020 296.33 296.32 2911.8 57.89 9721 0.665 1.10 0.50 10.69

11.453 0.066 296.36 296.35 2848.9 59.15 9721 0.665 1.10 0.50 10.69

12.723 -0.033 296.39 296.38 2785.8 60.48 9722 0.666 1.10 0.50 10.69

13.993 0.025 296.42 296.40 2722.8 61.87 9722 0.666 1.10 0.50 10.69

15.240 -0.058 296.49 296.43 2660.9 63.30 9723 0.666 1.10 0.50 10.69

2.565 -1.880 296.15 296.13 3290.2 51.29 9718 0.665 1.10 0.50 10.69

5.032 -1.892 296.20 296.19 3167.7 53.25 9719 0.665 1.10 0.50 10.69

7.620 -1.938 296.25 296.26 3039.2 55.48 9720 0.665 1.10 0.50 10.69

10.185 -1.951 296.35 296.32 2911.8 57.89 9721 0.665 1.10 0.50 10.69

12.700 -1.913 296.42 296.38 2787.0 60.46 9722 0.666 1.10 0.50 10.69

2.494 1.925 296.18 296.12 3293.7 51.23 9718 0.665 1.10 0.50 10.69 5.098 1.900 296.22 296.19 3164.4 53.31 9719 0.665 1.10 0.50 10.69

7.620 1.852 296.28 296.26 3039.2 55.48 9720 0.665 1.10 0.50 10.69

10.160 1.956 296.34 296.32 2913.1 57.86 9721 0.665 1.10 0.50 10.69

12.692 1.930 294.48 296.38 2787.4 60.45 9722 0.666 1.10 0.50 10.69

2.540 -3.211 296.13 296.13 3291.4 51.27 9718 0.665 1.10 0.50 10.69

7.633 -3.213 296.27 296.26 3038.5 55.49 9720 0.665 1.10 0.50 10.69

12.720 -3.211 296.37 296.38 2786.0 60.48 9722 0.666 1.10 0.50 10.69

2.499 3.221 296.13 296.12 3293.4 51.24 9718 0.665 1.10 0.50 10.69

7.620 3.454 296.25 296.26 3039.2 55.48 9720 0.665 1.10 0.50 10.69

12.700 3.180 296.37 296.38 2787.0 60.46 9722 0.666 1.10 0.50 10.69

29
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 15:03:38

TA TB M P0 P0-P1 Vf f Uf

K K kg/h kPa kPa X X

295.50 296.61 31.13 3404.8 1296.07 0.01 0.11300 22.63

Hot-side Temperatures:

X Y Tw X Y Tw

cm cm K cm cm K 1.332 0.485 294.95 2.549 -1.330 295.46

2.597 0.526 295.46 5.033 -1.444 295.52

2.681 0.923 295.48 7.571 -1.375 295.62

5.107 0.426 295.54 10.071 -1.476 295.72

7.626 0.498 295.62 2.465 -2.649 295.46

7.710 0.895 295.62 7.657 -2.616 295.60

10.111 0.396 295 . 70 12.699 -2.643 295.73

12.651 0.478 295.74 7.540 2.687 295.59

12.734 0.875 295.77 7.623 3.085 295.59

13.931 0.527 295.80

Insulated-Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw utf Wre

cm cm K K kPa m/s K K X

-0.038 -0.229 295.36 295.22 3412.2 62.44 12322 0.665 1.10 0.50 10.69

1.293 -0.226 295.40 295.28 3297.7 64.58 12323 0.665 1.10 0.50 10.69 2.527 -0.132 295.45 295.32 3191.7 66.71 12324 0.665 1.10 0.51 10.69

3.802 0.056 295.48 295.37 3082.1 69.05 12325 0.665 1.10 0.51 10.69 4.976 -0.008 295.50 295.41 2981.2 71.37 12326 0.665 1.10 0.51 10.69

6.314 0.028 295.56 295.45 2866.1 74.20 12328 0.665 1.10 0.51 10.69 7.607 0.033 295.58 295.48 2755.0 77.16 12329 0.666 1.10 0.51 10.69

8.913 -0.013 295.63 295.51 2642.7 80.40 12331 0.666 1.10 0.51 10.69

10.185 0.020 295.65 295.53 2533.4 83.84 12333 0.666 1.10 0.51 10.69

11.453 0.066 295 . 70 295.55 2424.4 87.57 12335 0.666 1.10 0.52 10.69

12.723 -0.033 295.73 295.55 2315.2 91.65 12337 0.666 1.10 0.52 10.69

13.993 0.025 295.75 295.55 2206.1 96.13 12340 0.666 1.10 0.52 10.69

15.240 -0.058 295.79 295.53 2098.9 100.99 12342 0.666 1.10 0.53 10.69

2.565 -1.880 295.42 295.33 3188.4 66.77 12324 0.665 1.10 0.51 10.69

5.032 -1.892 295.49 295.41 2976.3 71.48 12326 0.665 1.10 0.51 10.69

7.620 -1.938 295.60 295.48 2753.9 77.19 12329 0.666 1.10 0.51 10.69

10.185 -1.951 295.69 295.53 2533.4 83.84 12333 0.666 1.10 0.51 10.69

12.700 -1.913 295.73 295.55 2317.2 91.57 12337 0.666 1.10 0.52 10.69

2.494 1.925 295.44 295.32 3194.5 66.65 12324 0.665 1.10 0.51 10.69 5.098 1 .900 295.52 295.41 2970.7 71.62 12326 0.665 1.10 0.51 10.69

7.620 1.852 295.56 295.48 2753.9 77.19 12329 0.666 1.10 0.51 10.69

10.160 1.956 295.65 295.53 2535.6 83.77 12333 0.666 1.10 0.51 10.69

12.692 1.930 293.94 295.55 2317.9 91.55 12337 0.666 1.10 0.52 10.69

2.540 -3.211 295.38 295.32 3190.6 66.73 12324 0.665 1.10 0.51 10.69

7.633 -3.213 295.55 295.48 2752.8 77.22 12329 0.666 1.10 0.51 10.69

12.720 -3.211 295.66 295.55 2315.5 91.64 12337 0.666 1.10 0.52 10.69

2.499 3.221 295.37 295.32 3194.1 66.66 12324 0.665 1.10 0.51 10.69

7.620 3.454 295.56 295.48 2753.9 77.19 12329 0.666 1.10 0.51 10.69

12.700 3.180 295.73 295.55 2317.2 91.57 12337 0.666 1.10 0.52 10.69

30
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 15:16:05

TA TB M P0 P0-P1 Vf f Wf

K K kg/h kPa kPa X X

294.91 295.31 18.08 3444.3 394.76 0.00 0.12347 22.14

Hot -side Temperatures:

X r Tw X Y Tw cm cm K cm cm K 1.332 0.485 294.86 2.549 -1.330 294.91 2.597 0.526 294.93 5.033 -1.444 294.96

2.681 0.923 294.92 7.571 -1.375 294.96

5.107 0.426 294.98 10.071 -1.476 295.01 7.626 0.498 295.01 2.465 -2.649 294.92

7.710 0.895 295.02 7.657 -2.616 294.99

10.111 0.396 295.05 12.699 -2.643 295.05

12.651 0.478 295.06 7.540 2.687 294.99

12.734 0.875 295.08 7.623 3.085 295.01

13.931 0.527 295.09

Insulated-Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw Wtf Ure

cm cm K K kPa m/s K K X

-0.038 -0.229 294.90 294.82 3446.6 35.85 7160 0.665 1.10 0.50 10.69

1.293 -0.226 294.92 294.85 3411.7 36.21 7160 0.665 1.10 0.50 10.69 2.527 -0.132 294.95 294.87 3379.4 36.56 7160 0.665 1.10 0.50 10.69

3.802 0.056 294.94 294.89 3346.0 36.92 7160 0.665 1.10 0.50 10.69

4.976 -0.008 294.96 294.92 3315.3 37.26 7160 0.665 1.10 0.50 10.69

6.314 0.028 294.99 294.95 3280.3 37.65 7160 0.665 1.10 0.50 10.69 7.607 0.033 294.99 294.97 3246.4 38.04 7160 0.665 1.10 0.50 10.69

8.913 -0.013 295.01 295.00 3212.2 38.44 7160 0.665 1.10 0.50 10.69

10.185 0.020 295.03 295.02 3178.9 38.84 7160 0.665 1.10 0.50 10.69

11.453 0.066 295.07 295.05 3145.7 39.25 7160 0.665 1.10 0.50 10.69

12.723 -0.033 295.06 295.07 3112.5 39.67 7160 0.665 1.10 0.50 10.69

13.993 0.025 295.09 295.10 3079.2 40.09 7160 0.665 1.10 0.50 10.69

15.240 -0.058 295.12 295.12 3046.6 40.52 7160 0.665 1.10 0.50 10.69

2.565 -1.880 294.89 294.87 3378.4 36.57 7160 0.665 1.10 0.50 10.69

5.032 -1.892 294.95 294.92 3313.8 37.27 7160 0.665 1.10 0.50 10.69

7.620 -1.938 294.99 294.97 3246.1 38.05 7160 0.665 1.10 0.50 10.69

10.185 -1.951 294.99 295.02 3178.9 38.84 7160 0.665 1.10 0.50 10.69

12.700 -1.913 295.05 295.07 3113.1 39.66 7160 0.665 1.10 0.50 10.69

2.494 1.925 294.90 294.87 3380.3 36.55 7160 0.665 1.10 0.50 10.69

5.098 1.900 294.92 294.92 3312.1 37.29 7160 0.665 1.10 0.50 10.69

7.620 1.852 294.98 294.97 3246.1 38.05 7160 0.665 1.10 0.50 10.69

10.160 1.956 295.00 295.02 3179.6 38.84 7160 0.665 1.10 0.50 10.69

12.692 1.930 293.60 295.07 3113.3 39.66 7160 0.665 1.10 0.50 10.69

2.540 -3.211 294.89 294.87 3379.1 36.56 7160 0.665 1.10 0.50 10.69

7.633 -3.213 294.97 294.97 3245.7 38.05 7160 0.665 1.10 0.50 10.69

12.720 -3.211 295.08 295.07 3112.6 39.67 7160 0.665 1.10 0.50 10.69

2.499 3.221 294.90 294.87 3380.1 36.55 7160 0.665 1.10 0.50 10.69

7.620 3.454 294.99 294.97 3246.1 38.05 7160 0.665 1.10 0.50 10.69

12.700 3.180 295.04 295.07 3113.1 39.66 7160 0.665 1.10 0.50 10.69

31
Table 3 (continued)

18° Pinfin Specimen

Experiment: 1 Date: 18 September 1990

Time: 15:22:35

TA TB K PO P0-P1 Vf f Uf

K K kg/h kPa kPa X X

294.74 294.89 7.45 3422.7 79.42 0.01 0.15295 22.15

Hot -side Temperatures:

X Y Tw X Y Tw cm cm K cm cm X 1.332 0.485 294.90 2.549 -1.330 294.81 2.597 0.526 294.80 5.033 -1.444 294.85

2.681 0.923 294.83 7.571 -1.375 294.82

5.107 0.426 294.79 10.071 -1.476 294.84

7.626 0.498 294.82 2.465 -2.649 294.83

7.710 0.895 294.81 7.657 -2.616 294.83

10.111 0.396 294.84 12.699 -2.643 294.85

12.651 0.478 294.85 7.540 2.687 294.86

12.734 0.875 294.86 7.623 3.085 294.86

13.931 0.527 294.86

Insulated-Side Temperatures and Calculated Data: —Uncertainties--

X Y Tw Tf P V RE PR Utw Wtf Wre

cm cm K K kPa m/s K K X

-0.038 -0.229 294.83 294.73 3423.1 14.87 2951 0.665 1.10 0.50 10.69

1.293 -0.226 294.82 294.74 3416.1 14.90 2951 0.665 1.10 0.50 10.69 2.527 -0.132 294.82 294.75 3409.6 14.93 2951 0.665 1.10 0.50 10.69

3.802 0.056 294.83 294.76 3402.9 14.96 2951 0.665 1.10 0.50 10.69

4.976 -0.008 294.82 294.77 3396.7 14.98 2951 0.665 1.10 0.50 10.69

6.314 0.028 294.86 294 . 78 3389.7 15.01 2951 0.665 1.10 0.50 10.69

7.607 0.033 294.83 294.80 3382.9 15.05 2951 0.665 1.10 0.50 10.69 8.913 -0.013 294.84 294.81 3376.0 15.07 2951 0.665 1.10 0.50 10.69

10.185 0.020 294.86 294.82 3369.3 15.10 2951 0.665 1.10 0.50 10.69

11.453 0.066 294.85 294. S3 3362.6 15.14 2951 0.665 1.10 0.50 10.69

12.723 -0.033 294.85 294.84 3355.9 15.17 2951 0.665 1.10 0.50 10.69

13.993 0.025 294.87 294.85 3349.2 15.20 2951 0.665 1.10 0.50 10.69

15.240 -0.058 294.85 294.86 3342.7 15.23 2951 0.665 1.10 0.50 10.69

2.565 -1.880 294.82 294.75 3409.4 14.93 2951 0.665 1.10 0.50 10.69

5.032 -1.892 294.84 294.77 3396.4 14.98 2951 0.665 1.10 0.50 10.69

7.620 -1.938 294.85 294.80 3382.8 15.05 2951 0.665 1.10 0.50 10.69

10.185 -1.951 294.84 294.82 3369.3 15.10 2951 0.665 1.10 0.50 10.69

12.700 -1.913 294.86 294.84 3356.0 15.16 2951 0.665 1.10 0.50 10.69

2.494 1.925 294.86 294.75 3409.8 14.93 2951 0.665 1.10 0.50 10.69

5.098 1 .900 294.83 294.77 3396.1 14.99 2951 0.665 1.10 0.50 10.69

7.620 1.852 294.84 294.80 3382.8 15.05 2951 0.665 1.10 0.50 10.69

10.160 1.956 294.87 294.82 3369.4 15.10 2951 0.665 1.10 0.50 10.69

12.692 1.930 293.57 294.84 3356.1 15.16 2951 0.665 1.10 0.50 10.69

2.540 -3.211 294.82 294.75 3409.5 14.93 2951 0.665 1.10 0.50 10.69

7.633 -3.213 294.84 294.80 3382.7 15.05 2951 0.665 1.10 0.50 10.69

12.720 -3.211 294.88 294.84 3355.9 15.17 2951 0.665 1.10 0.50 10.69

2.499 3.221 294.85 294.75 3409.8 14.93 2951 0.665 1.10 0.50 10.69

7.620 3.454 294.85 294.80 3382.8 15.05 2951 0.665 1.10 0.50 10.69

12.700 3.180 294.88 294.84 3356.0 15.16 2951 0.665 1.10 0.50 10.69

32
Table 3 (continued)

18° Pinfin Specimen

Experiment: 2 Date: 19 September 1990

Time: 11:32:24

TA T8 M P0 P0- PI Vf Qt Uqt

K K kg/h kPa kPa X U X

293.56 686.41 4.09 3588.3 50. 47 24 .83 2317.0 1.04

Insulated-!Side Hot-Side Temperatures: PUT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 363.71 2.549 -1.330 395.14 -0.038 0.038 316.87

2.597 0.526 396.58 5.033 -1.444 458.96 3.993 -0.224 427.57

2.681 0.923 400.71 7.571 -1.375 531.59 11.648 -0.241 627.28

5.107 0.426 463.58 10.071 -1.476 600.51 15.077 -1.430 703.78

7.626 0.498 529.86 2.465 -2.649 390.68

7.710 0.895 534.71 7.657 -2.616 533.51

10.111 0.396 599.86 12.699 -2.643 667.91

12.651 0.478 663.80 7.540 2.687 523.53

12.734 0.875 665.77 7.623 3.085 524.02

13.931 0.527 700.23

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Ure Wh Wnu cm cm K K K kPa m/s W/(m* K) K K X 7. 7. -0.038 -0.229 314.94 293.55 293.56 3588.6 7.76 1625 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 357.92 328.00 328.01 3584.1 8.67 1508 0.665 3921 16.87 17.70 16.67 1.10 3.05 10.69 12.39 13.91 2.527 -0.132 391.54 361.08 361.09 3580.0 9.54 1412 0.665 3494 14.09 14.73 13.94 1.10 3.28 10.69 12.98 14.44 3.802 0.056 423.72 393.03 393.04 3575.7 10.38 1333 0.665 3393 12.91 13.46 12.73 1.10 3.91 10.69 14.65 15.96 4.976 -0.008 455.78 422.72 422.73 3571.8 11.17 1268 0.666 3229 11.69 12.18 11.54 1.10 4.66 10.69 15.77 16.99 6.314 0.028 492.46 457.29 457.30 3567.3 12.09 1201 0.666 3074 10.54 10.98 10.41 1.10 5.56 10.69 17.28 18.40 7.607 0.033 527.09 490.82 490.83 3563.0 12.98 1144 0.666 2976 9.72 10.11 9.59 1.10 6.46 10.69 19.11 20.13 8.913 -0.013 562.72 524.63 524.64 3558.6 13.88 1092 0.666 2827 8.82 9.17 8.70 1.16 6.65 10.69 18.78 19.82 10.185 0.020 597.08 557.31 557.33 3554.3 14.75 1047 0.666 2666 7.97 8.28 7.87 1.30 6.95 10.69 18.85 19.88 11.453 0.066 629.01 589.08 589.10 3550.1 15.60 1008 0.666 2577 7.42 7.69 7.32 1.42 7.34 10.69 19.76 20.75 12.723 -0.033 662.83 620.52 620.54 3545.9 16.45 972 0.666 2485 6.90 7.15 6.82 1.56 7.86 10.69 19.97 20.94 13.993 0.025 696.95 654.19 654.21 3541.6 17.35 937 0.666 2708 7.24 7.50 7.12 1.70 8.57 10.69 21.32 22.24 15.240 -0.058 712.66 686.38 686.40 3537.4 18.22 906 0.666 3054 7.90 8.06 7.62 1.76 9.01 10.69 37.45 37.98

2.565 -1.880 389.25 362.05 362.06 3579.8 9.57 1410 0.665 3904 15.71 16.35 15.38 1.10 3.29 10.69 14.23 15.57 5.032 -1.892 456.44 424.16 424.17 3571.6 11.21 1265 0.666 3310 11.95 12.44 11.78 1.10 4.70 10.69 16.19 17.38 7.620 -1.938 527.94 491.16 491.17 3562.9 12.99 1143 0.666 2935 9.58 9.97 9.46 1.10 6.47 10.69 18.90 19.93 10.185 -1.951 597.60 557.31 557.33 3554.3 14.75 1047 0.666 2632 7.87 8.18 7.78 1.30 6.95 10.69 18.63 19.67 12.700 -1.913 663.12 619.94 619.96 3545.9 16.43 972 0.666 2432 6.75 7.00 6.69 1.56 7.85 10.69 19.58 20.58 2.494 1.925 387.93 360.24 360.25 3580.1 9.52 1415 0.665 3850 15.54 16.19 15.24 1.10 3.27 10.69 13.94 15.31 5.098 1.900 458.08 425.85 425.86 3571.4 11.25 1262 0.666 3319 11.96 12.45 11.78 1.10 4.74 10.69 16.34 17.52 7.620 1.852 525.31 491.16 491.17 3562.9 12.99 1143 0.666 3161 10.32 10.71 10.13 1.10 6.47 10.69 20.20 21.17

10.160 1.956 589.70 556.67 556.69 3554.4 14.73 1048 0.666 3213 9.62 9.93 9.36 1.27 6.94 10.69 22.27 23.15 12.692 1.930 424.65 619.74 619.76 3546.0 16.42 973 0.666 -538 -1.49 -1.21 7.61 1.10 7.84 10.69 7.50 9.81 2.540 -3.211 388.82 361.42 361.42 3579.9 9.55 1412 0.665 3880 15.63 16.27 15.32 1.10 3.28 10.69 14.11 15.46 7.633 -3.213 527.15 491.49 491.51 3562.9 12.99 1143 0.666 3028 9.88 10.27 9.73 1.10 6.47 10.69 19.44 20.44

12.720 -3.211 660.30 620.45 620.47 3545.9 16.44 972 0.666 2638 7.32 7.57 7.20 1.55 7.86 10.69 21.07 22.00 2.499 3.221 385.54 360.37 360.38 3580.1 9.52 1414 0.665 4234 17.09 17.74 16.62 1.10 3.27 10.69 15.07 16.34 7.620 3.454 515.14 491.16 491.17 3562.9 12.99 1143 0.666 4502 14.70 15.09 14.00 1.10 6.47 10.69 28.07 28.78

12.700 3.180 642.16 619.94 619.96 3545.9 16.43 972 0.666 4730 13.13 13.39 12.31 1.48 7.85 10.69 36.53 37.07

33
Table 3 (continued) 18° Pinfin Specimen

Experiment: 2 Oate: 19 September 1990

Time: 11:44:21

TA TB M

K K kg/h 292.65 405.70 15.42

PO P0-P1 Vf kPa kPa X

3547.7 360.85 24.81

Qt Wqt U X

2506.0 1.20

Insulated- Side

Hot-Side Temperatures: PRT Temperatures:

X Y Tw X Y Tw X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 317.37 2.549 -1.330 324.63 -0.038 0.038 299.24

2.597 0.526 325.47 5.033 -1.444 341.81 3.993 -0.224 330.49

2.681 0.923 326.95 7.571 -1.375 362.10 11.648 -0.241 384.68

5.107 0.426 343.84 10.071 -1.476 381.00 15.077 -1.430 406.96

7.626 0.498 359.36 2.465 -2.649 322.43

7.710 0.895 363.41 7.657 -2.616 363.27

10.111 0.396 381.02 12.699 -2.643 399.76

12.651 0.478 397.74 7.540 2.687 360.76

12.734 0.875 399.96 7.623 3.085 361.10

13.931 0.527 409.06

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Wh Unu

cm cm K K K kPa m/s W/(mJ K) < K % % 7. -0.038 -0.229 298.42 292.60 292.67 3549.8 29.48 6136 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 311.39 302.50 302.58 3517.9 30.73 6002 0.665 14406 65.46 66.51 56.00 1.10 0.98 10.69 17.78 18.87 2.527 -0.132 320.45 312.01 312.09 3488.4 31.94 5879 0.665 13765 61.27 62.18 52.62 1.10 1.02 10.69 19.06 20.08 3.802 0.056 329.02 321.19 321.28 3457.9 33.15 5765 0.665 14539 63.47 64.32 54.01 1.10 1.18 10.69 21.80 22.70 4.976 -0.008 337.73 329.72 329.82 3429.8 34.29 5663 0.665 14583 62.55 63.38 53.16 1.10 1.38 10.69 23.20 24.05 6.314 0.028 348.00 339.65 339.76 3397.8 35.64 5550 0.665 14185 59.64 60.44 50.83 1.10 1.63 10.69 24.69 25.49 7.607 0.033 357.37 349.29 349.40 3366.8 36.97 5446 0.665 14654 60.45 61.22 51.22 1.10 1.89 10.69 28.10 28.80 8.913 -0.013 367.05 359.00 359.13 3335.6 38.33 5345 0.666 14705 59.55 60.28 50.36 1.10 1.94 10.69 28.84 29.52

10.185 0.020 376.68 368.39 368.53 3305.1 39.68 5252 0.666 14057 55.94 56.63 47.55 1.10 2.03 10.69 28.95 29.64 11.453 0.066 385.48 377.52 377.67 3274.8 41.02 5165 0.666 14233 55.70 56.34 47.20 1.10 2.14 10.69 31.42 32.05 12.723 -0.033 394 . 79 386.56 386.71 3244.4 42.38 5082 0.666 14078 54.22 54.85 45.97 1.10 2.29 10.69 32.11 32.73 13.993 0.025 404.57 396.23 396.39 3214.0 43.83 4997 0.666 15301 57.94 58.61 48.51 1.10 2.50 10.69 33.92 34.51 15.240 -0.058 408.16 405.48 405.65 3184.1 45.26 4919 0.666 34522 128.69 129.16 92.62 1.10 2.63 10.69 114.23 114.40 2.565 -1.880 319.64 312.28 312.37 3487.5 31.98 5875 0.665 15784 70.21 71.12 59.10 1.10 1.03 10.69 21.64 22.54 5.032 -1.892 338.08 330.13 330.23 3428.4 34.35 5658 0.665 14713 63.05 63.88 53.51 1.10 1.39 10.69 23.47 24.31 7.620 -1.938 357.79 349.39 349.50 3366.5 36.98 5445 0.665 14091 58.12 58.88 49.52 1.10 1.89 10.69 27.10 27.83 10.185 -1.951 377.19 368.39 368.53 3305.1 39.68 5252 0.666 13241 52.69 53.38 45.18 1.10 2.03 10.69 27.35 28.07

12.700 -1.913 395.10 386.39 386.54 3244.9 42.35 5084 0.666 13272 51.13 51.76 43.72 1.10 2.29 10.69 30.35 31 .00 2.494 1.925 319.61 311.76 311.85 3489.2 31.91 5882 0.665 14845 66.11 67.02 56.17 1.10 1.02 10.69 20.33 21.29 5.098 1.900 338.95 330.62 330.72 3426.9 34.42 5653 0.665 14046 60.13 60.96 51.38 1.10 1.41 10.69 22.57 23.44 7.620 1.852 357.83 349.39 349.50 3366.5 36.98 5445 0.665 14021 57.83 58.59 49.31 1.10 1.89 10.69 26.98 27.71 10.160 1.956 375.61 368.21 368.34 3305.7 39.65 5254 0.666 15789 62.85 63.54 52.52 1.10 2.02 10.69 32.32 32.93

12.692 1.930 325.62 386.33 386.48 3245.1 42.34 5084 0.666 -1865 -7.18 -6.54 47.80 1.10 2.29 10.69 7.59 9.87

2.540 -3.211 319.76 312.10 312.19 3488.1 31.96 5877 0.665 15177 67.54 68.45 57.19 1.10 1.03 10.69 20.83 21.77

7.633 -3.213 358.30 349.48 349.60 3366.2 36.99 5444 0.665 13415 55.32 56.08 47.47 1.10 1.89 10.69 25.88 26.64 12.720 -3.211 395.15 386.54 386.69 3244.4 42.37 5082 0.666 13438 51.75 52.38 44.17 1.10 2.29 10.69 30.71 31.36

2.499 3.221 319.25 311.80 311.89 3489.1 31.92 5881 0.665 15659 69.73 70.64 58.77 1.10 1.02 10.69 21.35 22.27

7.620 3.454 354.65 349.39 349.50 3366.5 36.98 5445 0.665 22689 93.58 94.35 73.84 1.10 1.89 10. $9 42.92 43.39

12.700 3.180 389.70 386.39 386.54 3244.9 42.35 5084 0.666 35903 138.31 138.96 99.13 1.10 2.29 10.69 80.55 80.80

34
Table 3 (continued)

18° Pinfin Specimen

Experiment: 3 Oate: 20 November 1990

Time: 10:43:51

TA TB H P0 P0- PI vf at Uqt

K 1C kg/h kPa kPa X U X 299.92 730.42 3.71 3516.2 45. 29 25 .47 2303.0 1.03

Insulated-:Side Hot-Side Temperatures: PUT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 377.05 2.549 -1.330 412.13 -0.038 0.038 325.66

2.597 0.526 413.63 5.033 -1.444 482.83 3.993 -0.224 448.13

2.681 0.923 418.20 7.571 -1.375 563.16 11.648 -0.241 669.35

5.107 0.426 487.73 10.071 -1.476 639.83 15.077 -1.430 750.96

7.626 0.498 561.48 2.465 -2.649 407.39

7.710 0.895 566.30 7.657 -2.616 564.95

10.111 0.396 638.64 12.699 -2.643 712.87

12.651 0.478 708.67 7.540 2.687 553.21

12.734 0.875 710.72 7.623 3.085 553.52

13.931 0.527 747.72

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Ure Uh Wnu

cm cm K K K kPa m/s U/(m' K) K K 7. % %

-0.038 -0.229 323.75 299.92 299.93 3516.5 7.34 1453 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 371.13 337.67 337.68 3512.5 8.26 1341 0.665 3486 14.71 15.49 14.67 1.10 3.33 10.69 12.10 13.65 2.527 -0.132 408.48 373.92 373.93 3508.8 9.14 1251 0.665 3061 12.05 12.65 12.04 1.10 3.59 10.69 12.55 14.05 3.802 0.056 444.05 408.93 408.94 3504.9 9.99 1177 0.666 2947 10.92 11.43 10.88 1.10 4.28 10.69 14.07 15.43 4.976 -0.008 479.42 441.47 441.48 3501.4 10.79 1116 0.666 2795 9.82 10.28 9.79 1.10 5.10 10.69 15.10 16.37 6.314 0.028 519.94 479.35 479.36 3497.4 11.71 1055 0.666 2648 8.79 9.19 8.77 1.10 6.09 10.69 16.47 17.64 7.607 0.033 558.24 516.09 516.10 3493.5 12.61 1002 0.666 2546 8.03 8.38 8.00 1.14 7.08 10.69 18.11 19.18 8.913 -0.013 597.64 553.14 553.15 3489.6 13.53 955 0.666 2406 7.23 7.54 7.21 1.30 7.28 10.69 17.76 18.85 10.185 0.020 635.96 588.95 588.97 3485.7 14.41 914 0.666 2242 6.45 6.73 6.44 1.45 7.61 10.69 17.64 18.73 11.453 0.066 671.30 623.77 623.79 3481.9 15.27 878 0.666 2152 5.95 6.20 5.94 1.59 8.04 10.69 18.37 19.43 12.723 -0.033 708.11 658.22 658.24 3478.1 16.12 846 0.666 2095 5.58 5.81 5.58 1.74 8.61 10.69 18.71 19.75 13.993 0.025 744.88 695.11 695.14 3474.3 17.04 814 0.666 2313 5.93 6.16 5.90 1.89 9.39 10.69 20.18 21.15 15.240 -0.058 761.09 730.39 730.41 3470.6 17.92 787 0.666 2598 6.43 6.58 6.27 1.95 9.87 10.69 35.44 36.00

2.565 -1.880 405.92 374.98 374.99 3508.6 9.16 1249 0.665 3412 13.41 14.01 13.26 1.10 3.60 10.69 13.70 15.09 5.032 -1.892 480.14 443.04 443.05 3501.2 10.82 1114 0.666 2862 10.03 10.48 9.98 1.10 5.14 10.69 15.49 16.73 7.620 -1.938 559.18 516.46 516.47 3493.5 12.62 1002 0.666 2512 7.92 8.27 7.90 1.14 7.09 10.69 17.92 19.00 10.185 -1.951 636.65 588.95 588.97 3485.7 14.41 914 0.666 2210 6.36 6.64 6.36 1.45 7.61 10.69 17.42 18.53 12.700 -1.913 708.24 657.59 657.61 3478.2 16.11 847 0.666 2061 5.49 5.72 5.50 1.74 8.60 10.69 18.44 19.49 2.494 1.925 404.16 373.00 373.01 3508.8 9.11 1253 0.665 3401 13.41 14.02 13.27 1.10 3.58 10.69 13.55 14.95 5.098 1.900 481.63 444.90 444.91 3501.0 10.87 1111 0.666 2895 10.12 10.57 10.06 1.10 5.19 10.69 15.74 16.96 7.620 1.852 555.75 516.46 516.47 3493.5 12.62 1002 0.666 2732 8.61 8.96 8.53 1.13 7.09 10.69 19.30 20.31 10.160 1.956 627.22 588.25 588.27 3485.8 14.39 915 0.666 2707 7.80 8.08 7.68 1.42 7.60 10.69 20.82 21.76 12.692 1.930 698.10 657.36 657.39 3478.2 16.10 847 0.666 2561 6.83 7.06 6.73 1.70 8.59 10.69 22.42 23.29

2.540 -3.211 405.36 374.29 374.29 3508.7 9.15 1250 0.665 3401 13.38 13.98 13.24 1.10 3.59 10.69 13.63 15.02 7.633 -3.213 557.92 516.83 516.84 3493.4 12.63 1001 0.666 2611 8.23 8.58 8.18 1.14 7.09 10.69 18.55 19.60 12.720 -3.211 704.98 658.14 658.16 3478.1 16.12 846 0.666 2231 5.94 6.17 5.91 1.73 8.61 10.69 19.78 20.77

2.499 3.221 401.19 373.14 373.15 3508.8 9.12 1253 0.665 3776 14.89 15.50 14.60 1.10 3.58 10.69 14.75 16.04 7.620 3.454 544.25 516.46 516.47 3493.5 12.62 1002 0.666 3862 12.18 12.54 11.72 1.10 7.09 10.69 26.56 27.30

12.700 3.180 684.61 657.59 657.61 3478.2 16.11 847 0.666 3864 10.30 10.53 9.82 1.65 8.60 10.69 33.03 33.63

35
Table 3 (continued)

18° P inf in Specimen

Experiment: 3 Date: 20 November 1990

Time: 10:53:43

TA TB M PO P0- 4 o -> H- Q. > Wqt

K K kg/h kPa kPa X U X

297.85 504.46 8.40 3502.9 147. 71 25 .48 2501.0 1.08

Insulated- Side Hot-Side Temperatures PRT Temperatures:

X r Tw X Y Tw X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 336.94 2.549 -1.330 351.06 -0.038 0.038 309.30

2.597 0.526 352.57 5.033 -1.444 382.23 3.993 -0.224 365.07

2.681 0.923 354.79 7.571 -1.375 418.61 11.648 -0.241 463.41 5.107 0.426 385.66 10.071 -1.476 452.73 15.077 -1.430 502.66

7.626 0.498 416.87 2.465 -2.649 348.13

7.710 0.895 421.06 7.657 -2.616 420.10

10.111 0.396 453.13 12.699 -2.643 486.04

12.651 0.478 484.14 7.540 2.687 415.95

12.734 0.875 486.62 7.623 3.085 416.44

13.931 0.527 503.35

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Wtf Wre Wh Wnu

cm cm K K K kPa m/s U/(m' K) K K X % % -0.038 -0.229 308.00 297. 84 297.86 3503.8 16.56 3305 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 330.53 315.95 315.98 3490.7 17.61 3176 0.665 8701 38.40 39.36 35.04 1.10 1.65 10.69 14.89 16.18 2.527 -0.132 347.01 333.34 333.37 3478.6 18.63 3063 0.665 8417 35.83 36.63 32.68 1.10 1.76 10.69 16.47 17.64 3.802 0.056 362.79 350.14 350.17 3466.1 19.62 2962 0.665 8905 36.67 37.39 33.14 1.10 2.08 10.69 19.70 20.69 4.976 -0.008 378.57 365.75 365.79 3454.6 20.55 2875 0.665 9012 36.03 36.72 32.47 1.10 2.47 10.69 22.06 22.95 6.314 0.028 396.92 383.93 383.97 3441.5 21.63 2781 0.666 9003 34.82 35.46 31.32 1.10 2.94 10.69 25.01 25.79 7.607 0.033 414.06 401.56 401.60 3428.9 22.70 2697 0.666 9346 35.06 35.66 31.32 1.10 3.41 10.69 29.41 30.08 8.913 -0.013 431.63 419.33 419.38 3416.1 23.78 2618 0.666 9489 34.55 35.10 30.75 1.10 3.51 10.69 30.66 31.31 10.185 0.020 449.00 436.52 436.57 3403.6 24.83 2547 0.666 9202 32.59 33.10 29.04 1.10 3.67 10.69 31.41 32.04 11.453 0.066 464.74 453.22 453.28 3391.2 25.86 2482 0.666 9682 33.42 33.88 29.53 1.10 3.87 10.69 35.66 36.21 12.723 -0.033 481.45 469.75 469.81 3378.7 26.89 2421 0.666 9748 32.83 33.28 28.93 1.10 4.15 10.69 37.40 37.93

13.993 0.025 498.78 487.45 487.52 3366.3 27.99 2360 0.666 11096 36.42 36.88 31.52 1.10 4.52 10.69 41.78 42.26

15.240 -0.058 505.84 504.37 504.44 3354.1 29.06 2305 0.666 61886 198.41 198.73 122.00 1.10 4.76 10.69 349.17 349.22

2.565 -1.880 345.35 333.85 333.88 3478.3 18.66 3059 0.665 9988 42.47 43.27 37.95 1.10 1.77 10.69 19.21 20.22 5.032 -1.892 378.59 366.51 366.54 3454.1 20.59 2871 0.665 9572 38.21 38.90 34.19 1.10 2.49 10.69 23.44 24.28 7.620 -1.938 414.20 401.73 401.78 3428.7 22.71 2696 0.666 9375 35.15 35.75 31.39 1.10 3.41 10.69 29.54 30.21 10.185 -1.951 448.92 436.52 436.57 3403.6 24.83 2547 0.666 9262 32.81 33.32 29.21 1.10 3.67 10.69 31.61 32.24 12.700 -1.913 481.26 469.45 469.51 3379.0 26.87 2422 0.666 9637 32.47 32.92 28.65 1.10 4.14 10.69 36.99 37.52 2.494 1.925 345.38 332.90 332.93 3478.9 18.60 3065 0.665 9242 39.38 40.19 35.53 1.10 1.75 10.69 17.79 18.88 5.098 1.900 380.22 367.40 367.43 3453.4 20.65 2866 0.665 9026 35.97 36.66 32.40 1.10 2.51 10.69 22.33 23.21 7.620 1.852 414.11 401.73 401.78 3428.7 22.71 2696 0.666 9446 35.42 36.02 31.61 1.10 3.41 10.69 29.75 30.41 10.160 1.956 446.23 436.18 436.23 3403.8 24.81 2548 0.666 11444 40.56 41.07 35.16 1.10 3.66 10.69 38.74 39.25 12.692 1.930 478.44 469.34 469.40 3379.0 26.86 2423 0.666 12521 42.19 42.64 35.97 1.10 4.14 10.69 47.77 48.19

2.540 -3.211 345.47 333.52 333.55 3478.5 18.64 3061 0.665 9619 40.93 41.73 36.75 1.10 1.76 10.69 18.52 19.57 7.633 -3.213 414.49 401.91 401.95 3428.6 22.72 2696 0.666 9293 34.84 35.44 31.15 1.10 3.41 10.69 29.30 29.97

12.720 -3.211 480.27 469.71 469.77 3378.8 26.89 2421 0.666 10803 36.38 36.83 31.64 1.10 4.15 10.69 41.34 41.82 2.499 3.221 344 . 70 332.97 333.00 3478.9 18.60 3065 0.665 9822 41 .84 42.64 37.47 1.10 1.76 10.69 18.78 19.81 7.620 3.454 408.79 401.73 401.78 3428.7 22.71 2696 0.666 16609 62.28 62.88 51.40 1.10 3.41 10.69 51.53 51.92 12.700 3.180 471.93 469.45 469.51 3379.0 26.87 2422 0.666 46710 157.37 157.83 104.58 1.10 4.14 10.69 176.77 176.88

36
Table 3 (continued)

18° Pinfin Specimen

Experiment: 3 Date: 20 November 1990

Time: 11:01:20

TA TB M P0 P0- PI Vf Qt Uqt

K K kg/h kPa kPa X U X

295.41 438.49 12.06 3494.0 262. 64 25 .49 2483.0 1.13

Insulated-!5ide Hot-Side Temperatures PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 325.15 2.549 -i..330 334..42 -0.038 0.038 303. 58 2.597 0.526 335.67 5.033 -i..444 356..01 3.993 -0.224 342. 92

2.681 0.923 337.39 7.571 -i..375 381..60 11.648 -0.241 411. 34 5.107 0.426 358.80 10.071 -i..476 405..47 15.077 -1.430 438. 87

7.626 0.498 379.46 2.465 -2..649 331..96 7.710 0.895 383.45 7.657 -2..616 383..01 10.111 0.396 405.65 12.699 -2..643 428..88 12.651 0.478 426.96 7.540 2..687 379,.93 12.734 0.875 429.35 7.623 3..085 380..39 13.931 0.527 440.90

Insulated- Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Uh Unu

cm cm K K X kPa m/s U/(m* • K) < K % % %

-0.038 -0.229 302.53 295.38 295.42 3495.5 23.62 4769 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 318.70 307.91 307.97 3472.3 24.77 4638 0.665 11710 52.59 53.60 46.27 1.10 1.19 10.69 16.24 17.43 2.527 -0.132 330.24 319.95 320.01 3450.8 25.88 4520 0.665 11146 48.78 49.64 43.06 1.10 1.26 10.69 17.49 18.60 3.802 0.056 341.14 331.58 331.64 3428.6 26.98 4412 0.665 11751 50.21 51.00 43.94 1.10 1.47 10.69 20.33 21.29 4.976 -0.008 352.15 342.39 342.46 3408.2 28.01 4317 0.665 11791 49.30 50.07 43.08 1.10 1.73 10.69 22.04 22.93 6.314 0.028 365.01 354.97 355.04 3384.9 29.22 4212 0.665 11621 47.42 48.15 41.46 1.10 2.05 10.69 24.16 24.97 7.607 0.033 376.85 367.17 367.25 3362.3 30.41 4116 0.666 12048 48.05 48.74 41.75 1.10 2.37 10.69 27.95 28.65 8.913 -0.013 389.09 379.48 379.56 3339.6 31.62 4024 0.666 12107 47.21 47.86 40.92 1.10 2.44 10.69 28.78 29.46

10.185 0.020 401.17 391.37 391.46 3317.4 32.81 3940 0.666 11708 44.70 45.31 38.86 1.10 2.55 10.69 29.30 29.98

11.453 0.066 412.18 402.93 403.03 3295.3 33.99 3863 0.666 12045 45.08 45.65 38.97 1.10 2.69 10.69 32.41 33.02

12.723 -0.033 423.84 414.37 414.48 3273.2 35.18 3789 0.666 12031 44.18 44.73 38.15 1.10 2.89 10.69 33.58 34.17

13.993 0.025 436.14 426.63 426.74 3251.1 36.45 3714 0.666 13189 47.47 48.05 40.45 1.10 3.15 10.69 35.96 36.51 15.240 -0.058 440.72 438.34 438.46 3229.4 37.69 3645 0.666 37926 133.99 134.39 93.93 1.10 3.31 10.69 154.46 154.59 2.565 -1.880 328.93 320.31 320.36 3450.2 25.91 4516 0.665 13278 58.07 58.92 50.07 1.10 1.26 10.69 20.51 21.47

5.032 -1.892 352.13 342.91 342.98 3407.2 28.06 4312 0.665 12504 52.23 53.00 45.28 1.10 1.74 10.69 23.36 24.20 7.620 -1.938 377.01 367.30 367.37 3362.1 30.42 4115 0.666 12008 47.88 48.57 41.62 1.10 2.38 10.69 27.89 28.60

10.185 -1.951 401.36 391.37 391.46 3317.4 32.81 3940 0.666 11480 43.83 44.44 38.20 1.10 2.55 10.69 28.76 29.45 12.700 -1.913 423.94 414.16 414.27 3273.6 35.16 3790 0.666 11634 42.74 43.29 37.07 1.10 2.88 10.69 32.52 33.13 2.494 1.925 329.06 319.65 319.70 3451.4 25.85 4523 0.665 12215 53.50 54.36 46.66 1.10 1.25 10.69 18.90 19.93 5.098 1.900 353.38 343.53 343.60 3406.0 28.11 4307 0.665 11714 48.87 49.64 42.74 1.10 1.76 10.69 22.10 22.99

7.620 1.852 377.08 367.30 367.37 3362.1 30.42 4115 0.666 11917 47.51 48.20 41.33 1.10 2.38 10.69 27.69 28.40

10.160 1.956 399.48 391.14 391.23 3317.9 32.79 3942 0.666 13777 52.62 53.23 44.72 1.10 2.55 10.69 34.22 34.80

12.692 1.930 421.97 414.09 414.19 3273.8 35.15 3791 0.666 14469 53.15 53.70 44.71 1.10 2.88 10.69 40.17 40.66

2.540 -3.211 329.07 320.08 320.13 3450.6 25.89 4518 0.665 12740 55.75 56.61 48.35 1.10 1.26 10.69 19.71 20.70 7.633 -3.213 377.50 367.42 367.50 3361.9 30.43 4114 0.666 11564 46.09 46.78 40.26 1.10 2.38 10.69 26.91 27.65 12.720 -3.211 423.51 414.35 414.45 3273.3 35.18 3789 0.666 12437 45.67 46.22 39.26 1.10 2.88 10.69 34.67 35.25 2.499 3.221 328.78 319.69 319.75 3451.3 25.85 4522 0.665 12643 55.37 56.23 48.07 1.10 1.25 10.69 19.50 20.50 7.620 3.454 373.20 367.30 367.37 3362.1 30.42 4115 0.666 19856 79.17 79.87 63.77 1.10 2.38 10.69 45.38 45.82

12.700 3.180 417.21 414.16 414.27 3273.6 35.16 3790 0.666 38190 140.28 140.85 98.70 1.10 2.88 10.69 104.89 105.08

37
Table 3 (continued)

18° Pinfin Specimen

Experiment: 3 Date: 20 November 1990

Time: 11:10:20

TA T8 H P0 P0- PI Vf Qt Uqt

K K kg/h kPa kPa X W X

292.90 397.99 16.32 3512.4 437.58 25 .50 2464.0 1.22

Insulated-:Side Hot-Side Temperatures : PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 316.53 2.549 -1.330 323.48 -0.038 0.038 299.04

2.597 0.526 324.02 5.033 -1.444 339.42 3.993 -0.224 328.23

2.681 0.923 325.65 7.571 -1.375 358.39 11.648 -0.241 378.92

5.107 0.426 341.23 10.071 -1.476 375.95 15.077 -1.430 399.51 7.626 0.498 355.76 2.465 -2.649 320.99

7.710 0.895 359.56 7.657 -2.616 359.31

10.111 0.396 375.76 12.699 -2.643 393.10

12.651 0.478 391.28 7.540 2.687 357.12

12.734 0.875 393.46 7.623 3.085 357.39

13.931 0.527 401.96

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Ure Uh Wnu

cm cm X < K kPa m/s U/(m» K) K K X % %

-0.038 -0.229 298.20 292.83 292.92 3514.9 31.53 6491 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 310.34 302.04 302.13 3476.2 32.86 6360 0.665 15197 69.14 70.18 58.67 1.10 0.92 10.69 18.52 19.57 2.527 -0.132 318.78 310.87 310.97 3440.4 34.15 6237 0.665 14490 64.66 65.56 55.13 1.10 0.96 10.69 19.77 20.76 3.802 0.056 326.75 319.41 319.51 3403.4 35.45 6124 0.665 15302 67.06 67.90 56.63 1.10 1.11 10.69 22.50 23.37 4.976 -0.008 334.91 327.34 327.45 3369.3 36.67 6024 0.665 15212 65.58 66.41 55.39 1.10 1.29 10.69 23.61 24.44 6.314 0.028 344.51 336.57 336.69 3330.5 38.13 5911 0.665 14708 62.23 63.03 52.77 1.10 1.52 10.69 24.83 25.62 7.607 0.033 353.20 345.52 345.65 3293.0 39.56 5807 0.666 15205 63.20 63.97 53.27 1.10 1.76 10.69 28.15 28.86 8.913 -0.013 362.24 354.55 354.69 3255.1 41.05 5706 0.666 15168 61.96 62.70 52.18 1.10 1.81 10.69 28.70 29.39

10.185 0.020 371.16 363.27 363.43 3218.2 42.52 5612 0.666 14578 58.58 59.28 49.56 1.10 1.89 10.69 28.94 29.62 11.453 0.066 379.33 371.76 371.92 3181.4 44.00 5525 0.666 14772 58.44 59.09 49.28 1.10 1.99 10.69 31.39 32.02 12.723 -0.033 387.95 380.15 380.33 3144.5 45.50 5441 0.666 14659 57.12 57.76 48.18 1.10 2.13 10.69 32.13 32.75

13.993 0.025 397.07 389.14 389.33 3107.7 47.11 5355 0.666 15904 60.99 61.67 50.80 1.10 2.33 10.69 33.82 34.41 15.240 -0.058 400.32 397.73 397.93 3071.5 48.70 5276 0.666 35675 134.79 135.27 96.46 1.10 2.45 10.69 113.13 113.31 2.565 -1.880 318.15 311.13 311.23 3439.3 34.19 6234 0.665 16305 72.72 73.62 60.91 1.10 0.97 10.69 22.08 22.97

5.032 -1.892 335.35 327.72 327.83 3367.7 36.73 6019 0.665 15121 65.13 65.96 55.06 1.10 1.30 10.69 23.55 24.38

7.620 -1.938 353.74 345.61 345.74 3292.6 39.58 5806 0.666 14360 59.68 60.45 50.73 1.10 1.76 10.69 26.69 27.43

10.185 -1.951 371.74 363.27 363.43 3218.2 42.52 5612 0.666 13560 54.49 55.18 46.59 1.10 1.89 10.69 27.02 27.75 12.700 -1.913 388.37 380.00 380.17 3145.2 45.47 5443 0.666 13623 53.09 53.73 45.26 1.10 2.13 10.69 29.96 30.62 2.494 1.925 318.26 310.65 310.74 3441.4 34.12 6240 0.665 15076 67.31 68.21 57.06 1.10 0.96 10.69 20.43 21 .39 5.098 1 .900 336.29 328.17 328.29 3365.8 36.80 6013 0.665 14217 61.18 62.01 52.19 1.10 1.31 10.69 22.32 23.20

7.620 1.852 353.85 345.61 345.74 3292.6 39.58 5806 0.666 14159 58.34 59.61 50.12 1.10 1.76 10.69 26.34 27.09 10.160 1.956 370.29 363.11 363.26 3218.9 42.49 5614 0.666 16040 64.47 65.17 53.77 1.10 1.89 10.69 31.67 32.30

12.692 1.930 386.81 379.94 380.12 3145.4 45.46 5443 0.666 16675 65.00 65.64 53.76 1.10 2.13 10.69 36.40 36.94 2.540 -3.211 317.99 310.96 311.06 3440.0 34.16 6236 0.665 16316 72.80 73.70 60.97 1.10 0.97 10.69 22.05 22.94 7.633 -3.213 353.93 345.70 345.83 3292.2 39.59 5805 0.666 14183 58.94 59.71 50.19 1.10 1.76 10.69 26.39 27.13 12.720 -3.211 388.06 380.13 380.31 3144.6 45.50 5442 0.666 14418 56.18 56.82 47.50 1.10 2.13 10.69 31.62 32.25 2.499 3.221 317.68 310.68 310.78 3441.2 34.12 6240 0.665 16408 73.25 74.15 61.30 1.10 0.96 10.69 22.08 22.97

7.620 3.454 350.57 345.61 345.74 3292.6 39.58 5806 0.666 23773 98.80 99.58 77.34 1.10 1.76 10.69 43.42 43.88

12.700 3.180 383.06 380.00 380.17 3145.2 45.47 5443 0.666 38718 150.90 151.57 106.51 1.10 2.13 10.69 83.45 83.69

38
Table 3 (continued)

18° P inf in Specimen

Experiment: 3 Date: 20 November 1990

Time: 11:21:15

TA TB H P0 P0- pi vf at Wqt

K X kg/h kPa kPa X U X

290.46 370.39 21.45 3474.1 714. 41 25 .53 2454.0 1.35

Insulated- Side

Hot-Side Temperatures: PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm X 1.332 0.485 310.13 2.549 -1.330 314.84 -0.038 0.038 295.28

2.597 0.526 315.73 5.033 -1.444 326.82 3.993 -0.224 317.77

2.681 0.923 316.88 7.571 -1.375 341.50 11.648 -0.241 356.18

5.107 0.426 328.90 10.071 -1.476 354.90 15.077 -1.430 371.95

7.626 0.498 339.00 2.465 -2.649 312.94

7.710 0.895 342.58 7.657 -2.616 342.61

10.111 0.396 354.75 12.699 -2.643 368.24

12.651 0.478 366.15 7.540 2.687 340.41

12.734 0.875 368.19 7.623 3.085 340.96

13.931 0.527 374.57

Insulated- Side Thermocouple Temperatures and Calculated Data: Uncertaint i es

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw utf Wre Uh Wnu

cm cm X K K kPa m/s W/(m' X) X X X X % -0.038 -0.229 294.56 290.35 290.49 3478.2 41.53 8582 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 304.07 297.33 297.49 3415.2 43.28 8449 0.665 18905 86.91 87.99 71.32 1.10 0.76 10.69 21.25 22.17 2.527 -0.132 310.57 304.04 304.21 3356.7 45.00 8324 0.665 17709 80.24 81.18 66.41 1.10 0.78 10.69 22.13 23.02 3.802 0.056 316.68 310.52 310.70 3296.3 46.77 8207 0.665 18435 82.37 83.27 67.67 1.10 0.88 10.69 24.38 25.19 4.976 -0.008 322.83 316.54 316.73 3240.6 48.47 8102 0.665 18537 81.77 82.66 67.08 1.10 1.01 10.69 25.29 26.07 6.314 0.028 330.13 323.54 323.75 3177.3 50.50 7983 0.666 17965 78.10 78.97 64.35 1.10 1.18 10.69 26.05 26.80 7.607 0.033 336.61 330.33 330.56 3116.0 52.54 7872 0.666 18899 81.03 81.87 66.15 1.10 1.35 10.69 29.47 30.14 8.913 -0.013 343.51 337.18 337.43 3054.1 54.69 7764 0.666 18772 79.38 80.20 64.82 1.10 1.39 10.69 29.83 30.49

10.185 0.020 350.31 343.80 344.07 2993.8 56.85 7663 0.666 18001 75.14 75.92 61.71 1.10 1.45 10.69 29.86 30.52

11.453 0.066 356.54 350.23 350.52 2933.8 59.08 7567 0.666 18108 74.65 75.39 61.19 1.10 1.53 10.69 31.99 32.60

12.723 -0.033 363.04 356.59 356.91 2873.6 61.38 7475 0.666 18171 74.00 74.73 60.58 1.10 1.64 10.69 32.87 33.47

13.993 0.025 369.86 363.40 363.74 2813.4 63.86 7380 0.666 20057 80.65 81.43 64.94 1.10 1.79 10.69 34.90 35.47

15.240 -0.058 372.19 369.91 370.28 2754.3 66.37 7291 0.666 44485 176.74 177.34 121.05 1.10 1.88 10.69 115.07 115.24 2.565 -1.880 309.76 304.24 304.41 3354.9 45.05 8321 0.665 21017 95.19 96.14 76.59 1.10 0.78 10.69 26.02 26.78

5.032 -1.892 322.84 316.83 317.02 3238.0 48.55 8097 0.665 19441 85.71 86.60 69.76 1.10 1.02 10.69 26.50 27.24 7.620 -1.938 336.86 330.40 330.63 3115.4 52.56 7871 0.666 18349 78.66 79.50 64.53 1.10 1.35 10.69 28.68 29.36

10.185 -1.951 350.63 343.80 344.07 2993.8 56.85 7663 0.666 17109 71.42 72.20 59.13 1.10 1.45 10.69 28.45 29.14 12.700 -1.913 363.24 356.47 356.79 2874.7 61.34 7477 0.666 17231 70.19 70.92 57.95 1.10 1.64 10.69 31.25 31.88

2.494 1.925 309.80 303.87 304.04 3358.2 44.95 8327 0.665 19596 88.82 89.77 72.32 1.10 0.78 10.69 24.25 25.06 5.098 1.900 323.51 317.17 317.37 3234.9 48.65 8091 0.665 18448 81.27 82.16 66.71 1.10 1.02 10.69 25.28 26.06 7.620 1.852 336.82 330.40 330.63 3115.4 52.56 7871 0.666 18485 79.24 80.08 64.92 1.10 1.35 10.69 28.88 29.56

10.160 1.956 349.35 343.67 343.94 2995.0 56.81 7664 0.666 20746 86.62 87.41 69.48 1.10 1.45 10.69 34.19 34.77

12.692 1.930 361.77 356.43 356.75 2875.1 61.32 7477 0.666 22120 90.11 90.85 71.35 1.10 1.64 10.69 39.79 40.29

2.540 -3.211 309.97 304.11 304.28 3356.1 45.02 8323 0.665 19777 89.59 90.54 72.83 1.10 0.78 10.69 24.54 25.34 7.633 -3.213 337.63 330.47 330.70 3114.8 52.58 7870 0.666 16502 70.73 71.57 59.00 1.10 1.35 10.69 25.94 26.70

12.720 -3.211 363.66 356.58 356.89 2873.7 61.38 7475 0.666 16444 66.97 67.70 55.70 1.10 1.64 10.69 29.87 30.53 2.499 3.221 309.72 303.89 304.07 3358.0 44.96 8327 0.665 19970 90.51 91.46 73.46 1.10 0.78 10.69 24.69 25.48 7.620 3.454 334.61 330.40 330.63 3115.4 52.56 7871 0.666 28764 123.30 124.16 93.33 1.10 1.35 10.69 44.31 44.76

12.700 3.180 359.01 356.47 356.79 2874.7 61.34 7477 0.666 50209 204.53 205.33 136.59 1.10 1.64 10.69 89.37 89.59

39
Table 3 (continued)

18° Pinfin Specimen

Experiment: 3 Date: 20 November 1990

Time: 11:35:24

TA TB

K K 288.93 349.87

M P0

kg/h kPa 28.30 3496.0

P0-P1 Vf kPa X

1269.85 25.51

Qt Uqt

U X

2446.0 1.56

Insulated-Side

Hot-Side Temperatures: PRT Temperatures:

X Y Tw X Y Tw X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 305.16 2.549 -1.330 308.54 -0.038 0.038 292.61 2.597 0.526 309.25 5.033 -1.444 317.52 3.993 -0.224 309.76

2.681 0.923 310.22 7.571 -1.375 328.81 11.648 -0.241 338.86

5.107 0.426 319.32 10.071 -1.476 338.95 15.077 -1.430 350.90

7.626 0.498 326.27 2.465 -2.649 306.79

7.710 0.895 329.62 7.657 -2.616 329.78

10.111 0.396 338.69 12.699 -2.643 349.03

12.651 0.478 346.99 7.540 2.687 327.89

12.734 0.875 348.90 7.623 3.085 328.41

13.931 0.527 353.60

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Uh Wnu

cm cm K K < kPa m/s U/(m' K) X K X % % -0.038 -0.229 292.02 288.74 288.99 3503.2 54.11 11364 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 299.31 294.04 294.31 3391.1 56.88 11231 0.665 24770 114.68 115.81 89.83 1.10 0.65 10.69 26.27 27.02 2.527 -0.132 304.27 299.12 299.42 3287.2 59.64 11106 0.665 23166 106.13 107.13 84.02 1.10 0.65 10.69 27.14 27.86 3.802 0.056 308.82 304.03 304.36 3179.8 62.62 10987 0.665 24620 111.62 112.58 87.33 1.10 0.71 10.69 30.05 30.71 4.976 -0.008 313.52 308.59 308.95 3080.9 65.56 10878 0.666 24662 110.72 111.69 86.56 1.10 0.80 10.69 30.46 31.11 6.314 0.028 319.14 313.89 314.29 2968.2 69.16 10756 0.666 23533 104.48 105.44 82.34 1.10 0.92 10.69 30.24 30.89 7.607 0.033 323.98 319.02 319.47 2859.4 72.92 10640 0.666 25251 110.92 111.87 86.24 1.10 1.05 10.69 34.23 34.81 8.913 -0.013 329.13 324.19 324.69 2749.4 77.01 10526 0.666 25567 111.13 112.06 86.14 1.10 1.08 10.69 35.17 35.73

10.185 0.020 334.21 329.18 329.73 2642.2 81.31 10419 0.666 24977 107.48 108.38 83.61 1.10 1.12 10.69 35.65 36.21 11.453 0.066 338.86 334.02 334.64 2535.4 85.93 10317 0.666 25748 109.73 110.60 84.81 1.10 1.19 10.69 38.89 39.40

12.723 -0.033 343.69 338.80 339.49 2428.5 90.94 10219 0.666 26452 111.68 112.56 85.84 1.10 1.27 10.69 40.57 41.06

13.993 0.025 348.89 343.90 344.69 2321.5 96.51 10117 0.666 29064 121.49 122.46 91.69 1.10 1.38 10.69 42.52 42.99

15.240 -0.058 350.67 348.77 349.65 2216.5 102.46 10022 0.666 82752 342.72 343.75 202.00 1.10 1.46 10.69 179.24 179.35 2.565 -1.880 303.68 299.27 299.57 3284.0 59.73 11102 0.665 27267 124.88 125.89 95.93 1.10 0.65 10.69 31.77 32.40 5.032 -1.892 313.61 308.81 309.17 3076.2 65.70 10873 0.666 25378 113.89 114.86 88.57 1.10 0.81 10.69 31.34 31.97

7.620 -1.938 324.23 319.07 319.52 2858.3 72.96 10639 0.666 24191 106.26 107.20 83.27 1.10 1.05 10.69 32.86 33.47

10.185 -1.951 334.71 329.18 329.73 2642.2 81.31 10419 0.666 22483 96.75 97.64 76.72 1.10 1.12 10.69 32.21 32.83 12.700 -1.913 344.24 338.71 339.40 2430.4 90.85 10221 0.666 22903 96.71 97.58 76.33 1.10 1.27 10.69 35.29 35.86 2.494 1.925 303.66 298.99 299.29 3290.0 59.57 11109 0.665 25741 117.96 118.97 91.61 1.10 0.65 10.69 29.93 30.59 5.098 1.900 314.04 309.07 309.43 3070.7 65.87 10867 0.666 24481 109.80 110.77 85.96 1.10 0.81 10.69 30.31 30.96 7.620 1.852 324.24 319.07 319.52 2858.3 72.96 10639 0.666 24118 105.93 106.87 83.05 1.10 1.05 10.69 32.77 33.37

10.160 1.956 333.66 329.08 329.64 2644.3 81.23 10421 0.666 27841 119.83 120.74 91.33 1.10 1.12 10.69 39.58 40.08

12.692 1.930 342.94 338.68 339.37 2431.1 90.82 10222 0.666 31033 131.05 131.95 97.63 1.10 1.27 10.69 47.47 47.89

2.540 -3.211 303.83 299.17 299.47 3286.1 59.67 11105 0.665 25728 117.86 118.87 91.53 1.10 0.65 10.69 30.01 30.67

7.633 -3.213 324.92 319.12 319.57 2857.2 73.00 10637 0.666 21297 93.54 94.47 74.98 1.10 1.05 10.69 29.09 29.77

12.720 -3.211 344.75 338.79 339.48 2428.7 90.93 10220 0.666 21056 88.90 89.76 71.22 1.10 1.27 10.69 32.53 33.14 2.499 3.221 303.59 299.01 299.31 3289.5 59.58 11108 0.665 26314 120.58 121.59 93.26 1.10 0.65 10.69 30.58 31.22 7.620 3.454 322.57 319.07 319.52 2858.3 72.96 10639 0.666 37362 164.11 165.10 117.95 1.10 1.05 10.69 50.21 50.61 12.700 3.180 340.90 338.71 339.40 2430.4 90.85 10221 0.666 73967 312.34 313.45 190.04 1.10 1.27 10.69 112.27 112.45

40
Table 3 (continued)

18° Pinfin Specimen

Experiment: 4 Date: 19 September 1990

Time: 10:45:03

TA TB M P0 P0- PI Vf at Wqt

K K kg/h kPa kPa X U X

293.00 548.99 14.38 3508.5 388. 78 50 .19 5302.0 1.06

Insulated-!Side Hot-Side Temperatures PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm X cm cm K 1.332 0.485 348.16 2.549 -1.330 364.79 -0.038 0.038 307.57

2.597 0.526 366.99 5.033 -1.444 403.62 3.993 -0.224 378.32

2.681 0.923 370.26 7.571 -1.375 450.63 11.648 -0.241 503.31 5.107 0.426 409.23 10.071 -1.476 494.15 15.077 -1.430 553.28

7.626 0.498 445.97 2.465 -2.649 359.92

7.710 0.895 454.20 7.657 -2.616 453.46

10.111 0.396 494.55 12.699 -2.643 537.41

12.651 0.478 533.22 7.540 2.687 448.37

12.734 0.875 537.76 7.623 3.085 448.98

13.931 0.527 559.73

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Wtw Utf Wre Uh Unu

cm cm X X X kPa m/s U/(m' X) X X % % % -0.038 -0.229 305.97 292.95 293.02 3510.7 27.83 5720 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 335.39 315.38 315.46 3476.4 30.22 5444 0.665 13467 59.51 61.56 52.18 1.10 2.01 10.69 12.99 14.45 2.527 -0.132 355.92 336.92 337.01 3444.6 32.54 5206 0.665 12873 54.41 56.08 47.72 1.10 2.16 10.69 14.27 15.60 3.802 0.056 375.84 357.72 357.82 3411.7 34.85 4998 0.665 13218 53.65 55.13 46.68 1.10 2.56 10.69 16.70 17.86 4.976 -0.008 395.73 377.05 377.17 3381.4 37.03 4822 0.666 13150 51.50 52.89 44.72 1.10 3.05 10.69 18.52 19.57 6.314 0.028 418.69 399.55 399.68 3346.9 39.61 4634 0.666 13015 48.99 50.27 42.46 1.10 3.63 10.69 20.91 21.84 7.607 0.033 440.61 421.38 421.53 3313.6 42.16 4468 0.666 12944 46.98 48.15 40.61 1.10 4.21 10.69 23.66 24.49

8.913 -0.013 462.85 443.38 443.55 3279.9 44.78 4315 0.666 12769 44.75 45.82 38.62 1.10 4.34 10.69 24.01 24.83 10.185 0.020 484.66 464.65 464.84 3247.1 47.38 4177 0.666 12240 41.54 42.51 35.94 1.10 4.53 10.69 24.35 25.15 11.453 0.066 504.87 485.33 485.54 3214.4 49.96 4054 0.666 12178 40.11 40.99 34.60 1.10 4.78 10.69 26.18 26.93

12.723 -0.033 525.98 505.79 506.02 3181.7 52.58 3939 0.666 12049 38.56 39.40 33.23 1.10 5.13 10.69 27.01 27.74 13.993 0.025 548.32 527.70 527.96 3148.9 55.40 3825 0.666 13007 40.43 41.29 34.39 1.10 5.59 10.69 28.63 29.32

15.240 -0.058 557.62 548.64 548.92 3116.8 58.17 3723 0.666 21095 63.81 64.38 49.62 1.14 5.88 10.69 70.10 70.38 2.565 -1.880 353.72 337.55 337.64 3443.6 32.61 5199 0.665 15106 63.77 65.43 54.54 1.10 2.17 10.69 16.37 17.55 5.032 -1.892 397.65 377.98 378.10 3380.0 37.13 4814 0.666 12504 48.88 50.26 42.77 1.10 3.07 10.69 17.81 18.90 7.620 -1.938 440.63 421.60 421.75 3313.3 42.18 4467 0.666 13082 47.47 48.64 40.96 1.10 4.22 10.69 23.92 24.75 10.185 -1.951 484.70 464.65 464.84 3247.1 47.38 4177 0.666 12214 41.45 42.42 35.88 1.10 4.53 10.69 24.30 25.11 12.700 -1.913 525.79 505.41 505.65 3182.3 52.53 3941 0.666 11923 38.18 39.02 32.96 1.10 5.12 10.69 26.74 27.48

2.494 1.925 353.93 336.37 336.46 3445.4 32.48 5212 0.665 13961 59.07 60.75 51.17 1.10 2.15 10.69 15.19 16.45 5.098 1.900 397.95 379.09 379.20 3378.3 37.26 4804 0.666 13057 50.94 52.32 44.27 1.10 3.10 10.69 18.62 19.66 7.620 1.852 440.97 421.60 421.75 3313.3 42.18 4467 0.666 12848 46.62 47.79 40.34 1.10 4.22 10.69 23.53 24.36

10.160 1.956 482.26 464.24 464.43 3247.8 47.33 4180 0.666 13609 46.21 47.19 39.35 1.10 4.53 10.69 26.86 27.59

12.692 1.930 362.54 505.28 505.52 3182.5 52.51 3942 0.666 -1679 -5.38 -4.48 32.78 1.10 5.12 10.69 7.30 9.65 2.540 -3.211 354.27 337.14 337.23 3444.2 32.56 5204 0.665 14270 60.29 61.96 52.04 1.10 2.16 10.69 15.55 16.79 7.633 -3.213 442.15 421.82 421.97 3312.9 42.21 4465 0.666 12234 44.37 45.53 38.68 1.10 4.22 10.69 22.49 23.36 12.720 -3.211 525.91 505.74 505.98 3181.8 52.57 3940 0.666 12065 38.62 39.46 33.28 1.10 5.13 10.69 27.04 27.77 2.499 3.221 353.52 336.45 336.54 3445.3 32.49 5211 0.665 14365 60.77 62.45 52.41 1.10 2.15 10.69 15.56 16.80 7.620 3.454 433.75 421.60 421.75 3313.3 42.18 4467 0.666 20571 74.64 75.82 59.72 1.10 4.22 10.69 36.86 37.40 12.700 3.180 515.03 505.41 505.65 3182.3 52.53 3941 0.666 25584 81.93 82.78 61.93 1.10 5.12 10.69 56.12 56.47

41
Table 3 (continued)

1

8

° P inf in Specimen

Experiment: 4 Date: 19 September 1990

Time: 10:52:53

TA TB H PO P0- PI Vf Qt Uqt

K K kg/h kPa kPa X hi X

292.93 476.24 20.25 3477.4 681. 17 50 .21 5335.0 1.09

Insulated-!Side Hot-Side Temperatures PRT Temperatures:

X Y Tu X Y Tw X Y Tw

cm cm K cm cm K cm cm X 1.332 0.485 335.92 2.549 -1.330 347.03 -0.038 0.038 303.54

2.597 0.526 348.76 5.033 -1.444 374.49 3.993 -0.224 354.30

2.681 0.923 351.28 7.571 -1.375 408.36 11.648 -0.241 442.79

5.107 0.426 378.93 10.071 -1.476 439.55 15.077 -1.430 478.79

7.626 0.498 402.87 2.465 -2.649 342.87

7.710 0.895 410.75 7.657 -2.616 410.97

10.111 0.396 439.38 12.699 -2.643 470.92

12.651 0.478 466.36 7.540 2.687 406.48

12.734 0.875 470.66 7.623 3.085 407.28

13.931 0.527 485.96

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertaint i es

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Wtf Wre Uh Wnu

cm cm K K K kPa m/s U/(m’ K) < K X % %

-0.038 -0.229 302.27 292.83 292.96 3481.2 39.50 8055 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 323.61 308.88 309.03 3421.1 42.34 7774 0.665 18522 83.02 85.18 69.12 1.10 1.47 10.69 13.98 15.35 2.527 -0.132 338.20 324.28 324.45 3365.4 45.14 7522 0.665 17816 77.29 79.10 64.48 1.10 1.57 10.69 15.30 16.55 3.802 0.056 352.34 339.15 339.35 3307.8 47.99 7297 0.665 18445 77.64 79.29 64.19 1.10 1.85 10.69 17.73 18.82 4.976 -0.008 366.44 352.98 353.19 3254.7 50.72 7102 0.666 18542 75.97 77.55 62.64 1.10 2.19 10.69 19.54 20.54 6.314 0.028 382.77 369.06 369.31 3194.3 53.99 6890 0.666 18490 73.51 75.00 60.50 1.10 2.61 10.69 21.92 22.82 7.607 0.033 398.30 384.67 384.94 3135.9 57.28 6698 0.666 18610 71.93 73.32 58.97 1.10 3.02 10.69 24.88 25.67 8.913 -0.013 414.07 400.39 400.70 3076.9 60.72 6517 0.666 18554 69.78 71 .08 57.09 1.10 3.11 10.69 25.46 26.23

10.185 0.020 429.64 415.59 415.94 3019.4 64.18 6352 0.666 17815 65.32 66.53 53.67 1.10 3.25 10.69 25.81 26.57

11.453 0.066 444.12 430.37 430.75 2962.1 67.71 6202 0.666 17720 63.43 64.54 52.01 1.10 3.43 10.69 27.69 28.40

12.723 -0.033 459.28 444.98 445.41 2904.7 71.36 6061 0.666 17455 61.07 62.14 50.10 1.10 3.68 10.69 28.38 29.08

13.993 0.025 475.30 460.63 461.11 2847.4 75.32 5918 0.666 18784 64.17 65.29 51.91 1.10 4.01 10.69 29.92 30.58

15.240 -0.058 481.36 475.58 476.11 2791.0 79.30 5789 0.666 35171 117.54 118.32 83.44 1.10 4.22 10.69 84.04 84.28

2.565 -1.880 336.71 324.73 324.90 3363.6 45.23 7515 0.665 20706 89.75 91.56 72.91 1.10 1.58 10.69 17.46 18.57 5.032 -1.892 386.15 353.64 353.86 3252.2 50.85 7093 0.666 7618 31.17 32.71 29.38 1.10 2.21 10.69 9.87 11.72 7.620 -1.938 398.71 384.82 385.10 3135.3 57.31 6696 0.666 18252 70.53 71.92 58.02 1.10 3.03 10.69 24.46 25.26

10.185 -1.951 430.32 415.59 415.94 3019.4 64.18 6352 0.666 16970 62.22 63.42 51.55 1.10 3.25 10.69 24.66 25.46 12.700 -1.913 459.71 444.71 445.14 2905.8 71 .29 6063 0.666 16591 58.07 59.14 48.05 1.10 3.67 10.69 27.05 27.78 2.494 1.925 336.60 323.89 324.06 3366.9 45.07 75 29 0.665 19561 84.93 86.75 69.71 1.10 1.57 10.69 16.50 17.66 5.098 1.900 367.81 354.43 354.65 3249.2 51.01 7082 0.666 18709 76.44 78.01 62.92 1.10 2.23 10.69 19.90 20.88 7.620 1.852 398.44 384.82 385.10 3135.3 57.31 6696 0.666 18624 71.96 73.35 58.99 1.10 3.03 10.69 24.92 25.71 10.160 1.956 427.80 415.30 415.64 3020.5 64.12 6355 0.666 20080 73.66 74.87 59.26 1.10 3.25 10.69 28.87 29.55 12.692 1.930 345.84 444.62 445.05 2906.1 71.27 6064 0.666 -2435 -8.52 -7.42 51.61 1.10 3.67 10.69 7.40 9.74 2.540 -3.211 337.24 324.43 324.61 3364.8 45.17 75 20 0.665 19371 84.01 85.82 69.06 1.10 1.57 10.69 16.44 17.61 7.633 -3.213 400.43 384.98 385.26 3134.7 57.35 6694 0.666 16374 63.25 64.63 53.00 1.10 3.03 10.69 22.12 23.00

12.720 -3.211 460.64 444.95 445.38 2904.9 71.35 6061 0.666 15859 55.48 56.55 46.25 1.10 3.67 10.69 25.92 26.68 2.499 3.221 336.47 323.95 324.12 3366.6 45.08 75 28 0.665 19855 86.20 88.02 70.57 1.10 1.57 10.69 16.72 17.87 7.620 3.454 393.35 384.82 385.10 3135.3 57.31 6696 0.666 30119 116.38 117.79 87.05 1.10 3.03 10.69 39.53 40.03

12.700 3.180 451.34 444.71 445.14 2905.8 71.29 6063 0.666 38979 136.43 137.54 95.37 1.10 3.67 10.69 62.12 62.44

42
Table 3 (continued)

18° Pinfin Specimen

Experiment: 4 Date: 19 September 1990

Time: 11:01:03

TA TB M P0 P0-P1 Vf

K K kg/h kPa kPa X

292.83 430.42 27.04 3431.4 1195.22 50.24

Qt Wqt

U X

5328.0 1.14

Hot-Side Temperatures:

X Y Tw cm cm K 1.332 0.485 327.93

2.597 0.526 337.10

2.681 0.923 339.21 5.107 0.426 359.88

7.626 0.498 376.09

7.710 0.895 383.52

10.111 0.396 404.95

12.651 0.478 424.60

12.734 0.875 428.71

13.931 0.527 439.98

X Y Tw cm cm K

2. 549 -i .330 335..70 5. 033 -i .444 356..19

7. 571 -i .375 381..79 10. 071 -i .476 405..29

2. 465 -2 .649 331..96

7. 657 -2 .616 384..15 12. 699 -2 .643 429..17

7. 540 2 .687 380..24 7. 623 3 .085 381..14

Insulated- Side

PRT Temperatures:

X Y Tw cm cm K -0.038 0.038 300.87

3.993 -0.224 339.17

11.648 -0.241 405.29

15.077 -1.430 432.43

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Wtf Ure Uh Wnu

cm cm K K K kPa m/s W/(m» K) K K X % % -0.038 -0.229 299.86 292.65 292.89 3438.2 53.37 10765 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 316.05 304.65 304.93 3332.7 57.25 10482 0.665 24248 109.72 111.96 87.01 1.10 1.14 10.69 15.49 16.73 2.527 -0.132 326.95 316.18 316.49 3234.9 61.15 10223 0.665 23387 103.24 105.16 82.14 1.10 1.21 10.69 16.84 17.99 3.802 0.056 337.53 327.31 327.66 3133.9 65.28 9988 0.666 24257 104.64 106.43 82.50 1.10 1.41 10.69 19.18 20.20 4.976 -0.008 348.09 337.64 338.04 3040.8 69.35 9780 0.666 24427 103.21 104.95 81.15 1.10 1.66 10.69 20.77 21.72 6.314 0.028 360.35 349.66 350.13 2934.7 74.34 9551 0.666 24306 100.31 101.99 78.81 1.10 1.96 10.69 22.88 23.73 7.607 0.033 371.90 361.31 361.85 2832.2 79.54 9341 0.666 24691 99.67 101.27 77.92 1.10 2.27 10.69 25.88 26.64 8.913 -0.013 383.65 373.05 373.66 2728.7 85.17 9140 0.666 24773 97.86 99.38 76.31 1.10 2.34 10.69 26.59 27.33

10.185 0.020 395.24 384.38 385.08 2627.9 91.06 8956 0.666 23999 92.90 94.33 72.73 1.10 2.44 10.69 27.11 27.83 11.453 0.066 406.12 395.38 396.18 2527.4 97.33 8785 0.666 23801 90.39 91.73 70.73 1.10 2.58 10.69 28.91 29.60

12.723 -0.033 417.53 406.25 407.17 2426.7 104.09 8623 0.666 23329 86.98 88.30 68.21 1.10 2.76 10.69 29.39 30.06

13.993 0.025 429.52 417.87 418.92 2326.0 111.64 8458 0.666 25126 91.89 93.29 70.98 1.10 3.01 10.69 30.88 31.52

15.240 -0.058 433.69 428.95 430.16 2227.2 119.62 8308 0.666 52231 187.63 188.77 122.72 1.10 3.17 10.69 95.94 96.15 2.565 -1.880 325.89 316.52 316.83 3231.9 61.27 10216 0.665 26961 118.94 120.86 92.05 1.10 1.21 10.69 19.14 20.16 5.032 -1.892 348.24 338.14 338.55 3036.4 69.55 9770 0.666 25325 106.89 108.64 83.46 1.10 1.67 10.69 21.55 22.46

7.620 -1.938 372.45 361.43 361.96 2831.2 79.59 9339 0.666 23666 95.51 97.10 75.28 1.10 2.28 10.69 24.89 25.68

10.185 -1.951 396.24 384.38 385.08 2627.9 91.06 8956 0.666 21840 84.55 85.97 67.37 1.10 2.44 10.69 24.81 25.60

12.700 -1.913 418.31 406.05 406.96 2428.5 103.97 8626 0.666 21271 79.33 80.64 63.29 1.10 2.76 10.69 26.93 27.66 2.494 1.925 325.68 315.89 316.20 3237.5 61.04 10230 0.665 25863 114.25 116.18 89.17 1.10 1.20 10.69 18.32 19.38 5.098 1.900 349.01 338.73 339.14 3031.1 69.79 9759 0.666 24899 104.97 106.71 82.22 1.10 1.68 10.69 21.32 22.23 7.620 1.852 371.97 361.43 361.96 2831.2 79.59 9339 0.666 24798 100.08 101.67 78.17 1.10 2.28 10.69 26.01 26.77

10.160 1.956 393.97 384.16 384.86 2629.9 90.94 8959 0.666 26759 103.63 105.08 79.43 1.10 2.44 10.69 30.03 30.68

12.692 1.930 334.19 405.98 406.89 2429.1 103.92 8627 0.666 -3318 -12.38 -11.12 71.37 1.10 2.76 10.69 7.53 9.83 2.540 -3.211 326.44 316.29 316.61 3233.9 61.19 10221 0.665 24853 109.69 111.61 86.26 1.10 1.21 10.69 17.77 18.86 7.633 -3.213 374.24 361.55 362.08 2830.2 79.64 9337 0.666 20408 82.35 83.93 66.71 1.10 2.28 10.69 21.70 22.60

12.720 -3.211 419.77 406.23 407.14 2426.9 104.08 8624 0.666 19139 71.36 72.66 58.03 1.10 2.76 10.69 24.38 25.19 2.499 3.221 325.64 315.93 316.24 3237.1 61.06 10229 0.665 26066 115.13 117.06 89.71 1.10 1.21 10.69 18.46 19.51 7.620 3.454 368.25 361.43 361.96 2831.2 79.59 9339 0.666 39475 159.31 160.96 112.89 1.10 2.28 10.69 40.68 41.17

12.700 3.180 411.66 406.05 406.96 2428.5 103.97 8626 0.666 51344 191.49 192.94 126.49 1.10 2.76 10.69 63.49 63.81

43
Table 3 (continued) 18° P inf in Specimen

Experiment: 4 Date: 19 September 1990

Time: 11:13:34

TA TB M PO P0- PI Vf Qt Uqt

< K kg/h kPa kPa X U X

293.07 641.42 10.27 3556.6 236. 97 50 .28 5154.0 1.04

Insulated- Side

Hot-Side Temperatures PRT Temperatures:

X r Tw X Y Tw X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 363.26 2.549 -1.330 387.39 -0.038 0.038 312.73

2.597 0.526 390.05 5.033 -1.444 441.33 3.993 -0.224 409.50

2.681 0.923 394.25 7.571 -1.375 505.20 11.648 -0.241 582.18

5.107 0.426 448.00 10.071 -1.476 564.97 15.077 -1.430 650.82

7.626 0.498 501.31 2.465 -2.649 381.67

7.710 0.895 510.09 7.657 -2.616 508.55

10.111 0.396 566.05 12.699 -2.643 624.91

12.651 0.478 620.99 7.540 2.687 502.21

12.734 0.875 623.39 7.623 3.085 502.76

13.931 0.527 655.69

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Wtw wtf Ure Uh Wnu

cm cm K K K kPa m/s W/(m* K) K K X % % -0.038 -0.229 310.60 293.05 293.08 3557.9 19.62 4083 0.665 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 350.27 323.59 323.63 3537.0 21.75 3820 0.665 9797 42.54 44.43 39.04 1.10 2.71 10.69 12.52 14.03 2.527 -0.132 378.75 352.91 352.96 3517.6 23.82 3602 0.665 9176 37.58 39.07 34.48 1.10 2.91 10.69 13.61 15.00 3.802 0.056 406.29 381.23 381.29 3497.6 25.85 3417 0.666 9261 35.99 37.27 32.80 1.10 3.47 10.69 15.85 17.07 4.976 -0.008 433 . 72 407.55 407.61 3479.1 27.75 3264 0.666 9092 33.75 34.93 30.72 1.10 4.13 10.69 17.53 18.63 6.314 0.028 465.32 438.18 438.26 3458.1 29.99 3105 0.666 8886 31.39 32.44 28.53 1.10 4.93 10.69 19.68 20.67

7.607 0.033 495.40 467.90 467.99 3437.8 32.19 2968 0.666 8760 29.58 30.52 26.81 1.10 5.73 10.69 22.17 23.05 8.913 -0.013 526.04 497.86 497.96 3417.3 34.43 2843 0.666 8530 27.59 28.44 24.98 1.10 5.90 10.69 22.24 23.12

10.185 0.020 555.90 526.83 526.94 3397.3 36.63 2734 0.666 8143 25.33 26.09 22.97 1.13 6.16 10.69 22.51 23.38 11.453 0.066 583.60 554.98 555.11 3377.3 38.79 2637 0.666 8033 24.10 24.78 21.81 1.24 6.50 10.69 24.09 24.91 12.723 -0.033 612.82 582.85 582.99 3357.4 40.96 2549 0.666 7839 22.73 23.37 20.59 1.36 6.97 10.69 24.62 25.42 13.993 0.025 643.78 612.68 612.84 3337.4 43.29 2461 0.666 8323 23.31 23.95 20.95 1.48 7.60 10.69 25.75 26.51 15.240 -0.058 658.05 641.20 641.38 3317.8 45.56 2385 0.666 10699 29.02 29.44 25.01 1.54 7.99 10.69 50.60 50.99 2.565 -1.880 375.82 353.77 353.82 3517.0 23.88 3596 0.665 10731 43.87 45.35 39.38 1.10 2.92 10.69 15.53 16.76 5.032 -1.892 433.39 408.82 408.8

a

3478.3 27.85 3257 0.666 9698 35.93 37.10 32.42 1.10 4.16 10.69 18.66 19.70 7.620 -1.938 495.23 468.20 468.29 3437.6 32.21 2967 0.666 8913 30.08 31.02 27.20 1.10 5.74 10.69 22.56 23.43

10.185 -1.951 555.63 526.83 526.94 3397.3 36.63 2734 0.666 8220 25.57 26.33 23.16 1.13 6.16 10.69 22.71 23.57

12.700 -1.913 612.17 582.33 582.47 3357.7 40.92 2550 0.666 7865 22.82 23.46 20.66 1.36 6.96 10.69 24.69 25.49

2.494 1.925 376.22 352.16 352.21 3518.1 23.77 3607 0.665 9875 40.50 42.00 36.80 1.10 2.90 10.69 14.37 15.70 5.098 1.900 436.99 410.32 410.38 3477.2 27.96 3249 0.666 8940 33.04 34.20 30.13 1.10 4.20 10.69 17.43 18.59 7.620 1.852 496.06 468.20 468.29 3437.6 32.21 2967 0.666 8644 29.17 30.11 26.48 1.10 5.74 10.69 21.93 22.82

10.160 1.956 552.69 526.26 526.38 3397.7 36.58 2736 0.666 8966 27.91 28.67 25.00 1.12 6.15 10.69 24.58 25.38

12.692 1.930 391.31 582.15 582.29 3357.9 40.91 2551 0.666 -1222 -3.55 -2.85 20.09 1.10 6.95 10.69 7.31 9.66 2.540 -3.211 376.43 353.20 353.25 3517.4 23.84 3599 0.665 10203 41.76 43.25 37.76 1.10 2.92 10.69 14.84 16.13 7.633 -3.213 496.60 468.50 468.58 3437.4 32.23 2965 0.666 8570 28.91 29.85 26.28 1.10 5.74 10.69 21.76 22.66 12.720 -3.211 611.27 582.78 582.92 3357.4 40.96 2549 0.666 8248 23.92 24.56 21.52 1.35 6.97 10.69 25.82 26.58 2.499 3.221 375.42 352.27 352.32 3518.1 23.78 3606 0.665 10262 42.08 43.58 38.02 1.10 2.90 10.69 14.84 16.13 7.620 3.454 486.69 468.20 468.29 3437.6 32.21 2967 0.666 13044 44.02 44.97 37.69 1.10 5.74 10.69 32.34 32.95 12.700 3.180 597.86 582.33 582.47 3357.7 40.92 2550 0.666 15175 44.03 44.67 36.21 1.30 6.96 10.69 46.43 46.85
Table 3 (continued)

18° P inf in Specimen

Experiment: 21 November 1990

Date: 5 Time: 09 :48:53

TA TB H P0 P0- PI Vf Qt Uqt

K K kg/h kPa kPa X W X

289.43 742.35 11.40 3512.0 332.44 75 .13 7437.0 1.03

Insulated- Side

Hot-Side Temperatures : PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 383.40 2.549 -1.330 414.00 -0.038 0.038 315.57

2.597 0.526 418.03 5.033 -1.444 483.74 3.993 -0.224 440.79

2.681 0.923 423.92 7.571 -1.375 566.81 11.648 -0.241 664.50

5.107 0.426 493.28 10.071 -1.476 644.25 15.077 -1.430 750.78

7.626 0.498 561 . 78 2.465 -2.649 406.57

7.710 0.895 573.96 7.657 -2.616 572.24

10.111 0.396 646.67 12.699 -2.643 720.67

12.651 0.478 716.13 7.540 2.687 565.14

12.734 0.875 720.05 7.623 3.085 565.11

13.931 0.527 759.47

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Wh Wnu cm cm K K K kPa m/s W/(mJ K) < K X % % -0.038 -0.229 312.89 289.41 289.45 3513.9 21.77 4569 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 364.47 329.11 329.16 3484.6 24.91 4191 0.665 10663 45.79 48.43 42.12 1.10 3.50 10.69 12.01 13.57 2.527 -0.132 401.31 367.23 367.29 3457.4 27.97 3890 0.665 10038 40.02 42.02 36.68 1.10 3.77 10.69 13.14 14.58 3.802 0.056 436.86 404.04 404.13 3429.3 30.98 3644 0.666 10206 38.12 39.79 34.56 1.10 4.50 10.69 15.48 16.72 4.976 -0.008 472.21 438.26 438.35 3403.4 33.82 3446 0.666 10116 35.74 37.24 32.26 1.10 5.36 10.69 17.33 18.45 6.314 0.028 513.09 478.08 478.20 3373.9 37.18 3245 0.666 9945 33.09 34.40 29.75 1.10 6.41 10.69 19.64 20.63 7.607 0.033 551.94 516.72 516.85 3345.4 40.49 3075 0.666 9873 31.13 32.28 27.84 1.12 7.44 10.69 22.33 23.21 8.913 -0.013 591.67 555.66 555.82 3316.6 43.88 2924 0.666 9641 28.90 29.92 25.79 1.27 7.66 10.69 22.53 23.40

10.185 0.020 630.25 593.31 593.50 3288.5 47.23 2794 0.666 9258 26.52 27.42 23.71 1.43 8.00 10.69 22.99 23.84 11.453 0.066 666. 47 629.91 630.13 3260.6 50.54 2679 0.666 9086 24.96 25.75 22.31 1.57 8.45 10.69 24.48 25.29

12.723 -0.033 703.85 666.13 666.37 3232.6 53.88 2577 0.666 9002 23.78 24.51 21.29 1.72 9.05 10.69 25.38 26.16

13.993 0.025 742.85 704.90 705.18 3204.6 57.49 2477 0.666 9863 25.04 25.77 22.19 1.88 9.87 10.69 27.36 28.08

15.240 -0.058 760.41 741.97 742.28 3177.1 61.02 2389 0.666 14207 34.80 35.27 28.98 1.95 10.38 10.69 59.80 60.13

2.565 -1.880 397.22 368.35 368.41 3456.6 28.06 3882 0.665 11826 47.05 49.04 42.02 1.10 3.79 10.69 15.06 16.33 5.032 -1.892 471.65 439.91 440.01 3402.2 33.96 3437 0.666 10835 38.18 39.67 34.10 1.10 5.41 10.69 18.52 19.57 7.620 -1.938 551.42 517.10 517.24 3345.1 40.52 3074 0.666 10135 31.94 33.09 28.45 1.11 7.45 10.69 22.90 23.76

10.185 -1.951 629.71 593.31 593.50 3288.5 47.23 2794 0.666 9397 26.91 27.81 24.00 1.43 8.00 10.69 23.30 24.15 12.700 -1.913 702.67 665.46 665.70 3233.1 53.82 2579 0.666 9114 24.09 24.82 21.53 1.72 9.04 10.69 25.68 26.44 2.494 1.925 398.13 366.26 366.32 3458.1 27.89 3897 0.665 10757 42.96 44.98 38.97 1.10 3.76 10.69 13.82 15.19 5.098 1.900 477.09 441.86 441.96 3400.7 34.12 3427 0.666 9771 34.32 35.80 31.12 1.10 5.46 10.69 17.03 18.16 7.620 1.852 553.71 517.10 517.24 3345.1 40.52 3074 0.666 9500 29.94 31.09 26.92 1.12 7.45 10.69 21.58 22.49

10.160 1.956 627.83 592.58 592.77 3289.1 47.16 2796 0.666 9710 27.83 28.73 24.71 1.42 7.99 10.69 23.99 24.81 12.692 1.930 700.60 665.23 665.47 3233.3 53.80 2579 0.666 9587 25.35 26.08 22.49 1.71 9.03 10.69 26.93 27.66

2.540 -3.211 398.99 367.61 367.68 3457.1 28.00 3887 0.665 10897 43.41 45.41 39.28 1.10 3.78 10.69 14.04 15.40 7.633 -3.213 554.47 517.49 517.63 3344.8 40.55 3072 0.666 9404 29.62 30.77 26.67 1.13 7.45 10.69 21.39 22.30 12.720 -3.211 702.27 666.04 666.28 3232.7 53.88 2577 0.666 9374 24.76 25.49 22.04 1.72 9.05 1C. 69 26.36 27.11 2.499 3.221 397.56 366.40 366.47 3458.0 27.90 3896 0.665 11001 43.92 45.94 39.70 1.10 3.76 10.69 14.07 15.43 7.620 3.454 541.19 517.10 517.24 3345.1 40.52 3074 0.666 14465 45.58 46.74 38.37 1.10 7.45 10.69 32.07 32.68

12.700 3.180 684.90 665.46 665.70 3233.1 53.82 2579 0.666 17553 46.40 47.14 37.30 1.65 9.04 10.69 48.28 48.69

45
Table 3 (continued)

18° Pinfin Specimen

Experiment: 21 November 1990

Oate: 5 Time: 09:57:31

TA T8 M P0 P0- PI Vf Qt Wqt

K K kg/h kPa kPa X U X

288.23 626.66 15.55 3496.2 516. 55 75 .18 7577.0 1.04

Insulated-!Side Hot-Side Temperatures : PUT Temperatures:

X Y Tw X Y Tu X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 363.25 2.549 -1.330 384.59 -0.038 0.038 308.17

2.597 0.526 387.92 5.033 -1.444 435.82 3.993 -0.224 401.19

2.681 0.923 392.67 7.571 -1.375 497.57 11.648 -0.241 564.87

5.107 0.426 443.66 10.071 -1.476 554.25 15.077 -1.430 629.10

7.626 0.498 491.13 2.465 -2.649 378.10

7.710 0.895 502.82 7.657 -2.616 502.33

10.111 0.396 555.52 12.699 -2.643 611.42

12.651 0.478 606.20 7.540 2.687 496.39

12.734 0.875 610.26 7.623 3.085 496.95

13.931 0.527 640.50

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Wtw Wtf Ure Uh Unu

cm cm K K K kPa m/s W/(m! K) K K % % %

-0.038 -0.229 305.96 288.18 288.26 3499.2 29.71 6252 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 344.81 317.83 317.92 3453.6 33.13 5856 0.665 14270 62.74 65.62 55.16 1.10 2.63 10.69 12.20 13.74 2.527 -0.132 371.99 346.30 346.42 3411.3 36.49 5525 0.665 13605 56.45 58.72 49.54 1.10 2.83 10.69 13.43 14.84 3.802 0.056 398.06 373.80 373.93 3367.6 39.85 5244 0.666 14108 55.58 57.54 48.19 1.10 3.37 10.69 15.98 17.18 4.976 -0.008 424.18 399.35 399.50 3327.4 43.05 5012 0.666 14140 53.25 55.05 45.96 1.10 4.01 10.69 17.98 19.06 6.314 0.028 454.46 429.08 429.27 3281.6 46.85 4771 0.666 14035 50.32 51.94 43.26 1.10 4.79 10.69 20.47 21.43 7.607 0.033 482.99 457.93 458.15 3237.3 50.64 4562 0.666 14208 48.70 50.15 41.56 1.10 5.56 10.69 23.66 24.49 8.913 -0.013 512.06 487.01 487.26 3192.5 54.57 4372 0.666 14203 46.66 47.96 39.62 1.10 5.72 10.69 24.32 25.13

10.185 0.020 540.28 515.12 515.41 3148.9 58.48 4206 0.666 13936 44.04 45.21 37.32 1.10 5.98 10.69 25.23 26.01 11.453 0.066 566.52 542.44 542.77 3105.5 62.40 4057 0.666 14168 43.20 44.24 36.34 1.17 6.32 10.69 27.78 28.49 12.723 -0.033 593.87 569.47 569.84 3062.0 66.41 3922 0.666 14310 42.18 43.16 35.31 1.28 6.77 10.69 29.35 30.03

13.993 0.025 622.84 598.41 598.84 3018.5 70.76 3789 0.666 15771 44.91 45.91 36.93 1.40 7.38 10.69 31.87 32.49

15.240 -0.058 635.36 626.08 626.55 2975.8 75.06 3672 0.666 29769 82.14 82.81 59.24 1.45 7.76 10.69 90.55 90.77

2.565 -1.880 368.70 347.14 347.25 3410.0 36.60 5516 0.665 16187 67.05 69.31 57.12 1.10 2.84 10.69 15.53 16.77 5.032 -1.892 423.75 400.58 400.74 3325.5 43.20 5002 0.666 15177 57.03 58.82 48.64 1.10 4.05 10.69 19.25 20.26

7.620 -1.938 482.86 458.22 458.44 3236.8 50.68 4560 0.666 14453 49.52 50.97 42.14 1.10 5.57 10.69 24.07 24.88

10.185 -1.951 540.28 515.12 515.41 3148.9 58.48 4206 0.666 13940 44.06 45.23 37.34 1.10 5.98 10.69 25.24 26.02

12.700 -1.913 593.48 568.97 569.34 3062.8 66.34 3925 0.666 14222 41.95 42.93 35.16 1.28 6.76 10.69 29.18 29.86 2.494 1.925 369.45 345.58 345.69 3412.4 36.41 5532 0.665 14670 60.95 63.23 52.83 1.10 2.82 10.69 14.20 15.54 5.098 1.900 427.74 402.04 402.20 3323.2 43.39 4989 0.666 13694 51.33 53.11 44.52 1.10 4.08 10.69 17.69 18.79 7.620 1.852 484.26 458.22 458.44 3236.8 50.68 4560 0.666 13666 46.83 48.28 40.22 1.10 5.57 10.69 22.85 23.70 10.160 1.956 538.28 514.57 514.86 3149.8 58.40 4209 0.666 14809 46.84 48.02 39.30 1.10 5.97 10.69 26.68 27.42 12.692 1.930 591.50 568.80 569.17 3063.1 66.31 3926 0.666 15366 45.33 46.32 37.49 1.27 6.75 10.69 31.41 32.04 2.540 -3.211 370.18 346.59 346.70 3410.9 36.53 5521 0.665 14804 61.39 63.65 53.12 1.10 2.83 10.69 14.39 15.71 7.633 -3.213 486.01 458.51 458.73 3236.4 50.72 4558 0.666 12937 44.31 45.75 38.40 1.10 5.57 10.69 21.72 22.62 12.720 -3.211 594.10 569.41 569.78 3062.1 66.40 3923 0.666 14133 41.66 42.64 34.95 1.28 6.76 10.69 29.01 29.69 2.499 3.221 369.26 345.69 345.80 3412.3 36.42 5531 0.665 14855 61.71 63.99 53.38 1.10 2.82 10.69 14.35 15.68 7.620 3.454 475.16 458.22 458.44 3236.8 50.68 4560 0.666 21104 72.31 73.77 57.51 1.10 5.57 10.69 34.52 35.09

12.700 3.180 580.31 568.97 569.34 3062.8 66.34 3925 0.666 31300 92.32 93.33 66.38 1.23 6.76 10.69 62.93 63.24

46
Table 3 (continued)

18° P inf in Specimen

Experiment: 21 z o>1 1990

Date: 5 Time: 10 :07:26

TA TB M P0 P0- PI Vf at Wqt

K K kg/h kPa kPa X W X

286.72 558.93 19.34 3504.3 718. 91 75 .24 7573.0 1.05

Insulated- Side

Hot-Side Temperatures PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 350.84 2.549 -1.330 367.48 -0.038 0.038 303.11 2.597 0.526 370.19 5.033 -1.444 408.58 3.993 -0.224 378.47

2.681 0.923 374.32 7.571 -1.375 458.75 11.648 -0.241 509.92

5.107 0.426 415.23 10.071 -1.476 504.56 15.077 -1.430 562.08

7.626 0.498 451.40 2.465 -2.649 361.48

7.710 0.895 462.71 7.657 -2.616 463.10

10.111 0.396 505.06 12.699 -2.643 550.85

12.651 0.478 544.89 7.540 2.687 457.11

12.734 0.875 550.03 7.623 3.085 458.03

13.931 0.527 573.11

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Uh Unu

cm cm K K K kPa m/s U/lm1 K) < K X % %

-0.038 -0.229 301.18 286.65 286.76 3508.4 36.66 7802 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 332.90 310.48 310.62 3444.9 40.37 7398 0.665 17210 76.86 79.86 65.47 1.10 2.13 10.69 12.34 13.87 2.527 -0.132 354.80 333.36 333.53 3386.1 44.03 7051 0.665 16340 69.57 72.00 59.34 1.10 2.29 10.69 13.48 14.89 3.802 0.056 375.74 355.46 355.65 3325.3 47.75 6750 0.666 16937 69.05 71.19 58.24 1.10 2.72 10.69 15.90 17.11 4.976 -0.008 396.76 375.99 376.22 3269.3 51.33 6496 0.666 16977 66.63 68.63 56.00 1.10 3.23 10.69 17.76 18.85 6.314 0.028 421.26 399.89 400.15 3205.5 55.62 6228 0.666 16736 62.98 64.81 52.84 1.10 3.86 10.69 19.98 20.96 7.607 0.033 444.13 423.07 423.37 3143.9 59.94 5992 0.666 16996 61.54 63.21 51.27 1.10 4.48 10.69 23.06 23.91 8.913 -0.013 467.47 446.43 446.78 3081.6 64.48 5775 0.666 17011 59.36 60.88 49.23 1.10 4.61 10.69 23.72 24.55 10.185 0.020 490.30 469.01 469.41 3021.0 69.06 5581 0.666 16591 55.96 57.34 46.40 1.10 4.81 10.69 24.45 25.25 11.453 0.066 511.45 490.96 491.42 2960.5 73.72 5408 0.666 16786 54.86 56.11 45.20 1.10 5.08 10.69 26.71 27.45 12.723 -0.033 533.42 512.67 513.19 2899.9 78.54 5248 0.666 16981 53.86 55.05 44.14 1.10 5.44 10.69 28.16 28.87

13.993 0.025 556.64 535.91 536.50 2839.4 83.81 5089 0.666 18785 57.78 59.00 46.40 1.13 5.94 10.69 30.62 31.26

15.240 -0.058 565.71 558.11 558.78 2779.9 89.11 4948 0.666 37865 113.23 114.07 77.99 1.17 6.24 10.69 92.69 92.91 2.565 -1.880 352.11 334.03 334.20 3384.3 44.15 7041 0.665 19372 82.37 84.79 68.13 1.10 2.30 10.69 15.55 16.78 5.032 -1.892 396.59 376.99 377.21 3266.6 51.50 6485 0.666 18013 70.57 72.57 58.68 1.10 3.26 10.69 18.81 19.84 7.620 -1.938 444.41 423.30 423.61 3143.3 59.99 5990 0.666 16953 61.36 63.02 51.14 1.10 4.48 10.69 23.03 23.88

10.185 -1.951 490.91 469.01 469.41 3021.0 69.06 5581 0.666 16117 54.36 55.74 45.31 1.10 4.81 10.69 23.80 24.62 12.700 -1.913 533.78 512.27 512.79 2901.0 78.45 5251 0.666 16343 51.87 53.06 42.80 1.10 5.43 10.69 27.16 27.89 2.494 1.925 352.56 332.78 332.94 3387.7 43.94 7059 0.665 17756 75.69 78.13 63.63 1.10 2.28 10.69 14.35 15.68 5.098 1.900 399.42 378.16 378.38 3263.5 51.71 6471 0.666 16610 64.93 66.91 54.76 1.10 3.29 10.69 17.62 18.72 7.620 1.852 444.89 423.30 423.61 3143.3 59.99 5990 0.666 16576 59.99 61.65 50.19 1.10 4.48 10.69 22.56 23.43

10.160 1.956 488.32 468.57 468.97 3022.1 68.97 5585 0.666 17923 60.50 61.89 49.49 1.10 4.81 10.69 26.25 27.00

12.692 1.930 531.11 512.13 512.65 2901.4 78.42 5252 0.666 18571 58.95 60.14 47.54 1.10 5.43 10.69 30.67 31.32 2.540 -3.211 353.54 333.59 333.76 3385.5 44.07 7047 0.665 17560 74.73 77.16 62.93 1.10 2.29 10.69 14.30 15.63 7.633 -3.213 447.70 423.54 423.84 3142.6 60.03 5988 0.666 14782 53.48 55.14 45.63 1.10 4.48 10.69 20.32 21 .28 12.720 -3.211 535.22 512.62 513.14 2900.1 78.53 5248 0.666 15552 49.33 50.51 41.05 1.10 5.44 10.69 25.92 26.68 2.499 3.221 352.53 332.87 333.03 3387.4 43.95 7058 0.665 17863 76.13 78.57 63.93 1.10 2.28 10.69 14.43 15.75 7.620 3.454 437.51 423.30 423.61 3143.3 59.99 5990 0.666 25378 91.86 93.54 70.96 1.10 4.48 10.69 33.78 34.37

12.700 3.180 522.13 512.27 512.79 2901.0 78.45 5251 0.666 36708 116.50 117.73 81.64 1.10 5.43 10.69 59.67 60.00

47
Table 3 (continued)

18° Pinfin Specimen

Experiment: 21 November 1990

Date: 5

T ime: 10 : 15:57

TA TB P0 P0- PI Vf Ot Wqt

K K kg/h kPa kPa X U X

285.46 510.45 23.41 3508.5 990. 38 75 .24 7567.0 1.07

Insulated- Side

Hot-Side Temperatures: PRT Temperatures:

X Y Tw X Y Tw X Y Tw cm cm K cm cm K cm cm K 1.332 0.485 341.54 2.549 -1.330 354.80 -0.038 0.038 299.21 2.597 0.526 357.13 5.033 -1.444 388.75 3.993 -0.224 361.81

2.681 0.923 360.83 7.571 -1.375 430.63 11.648 -0.241 470.22

5.107 0.426 394.51 10.071 -1.476 468.65 15.077 -1.430 513.67

7.626 0.498 422.60 2.465 -2.649 349.23

7.710 0.895 433.63 7.657 -2.616 434.49

10.111 0.396 468.50 12.699 -2.643 507.01

12.651 0.478 500.79 7.540 2.687 428.71

12.734 0.875 506.28 7.623 3.085 429.94

13.931 0.527 524.90

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Wtf Ure Wh Wnu

cm cm K K K kPa m/s W/(m' K) K K % % % -0.038 -0.229 297.51 285.34 285.51 3514.1 44.11 9474 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 324.06 305.02 305.22 3426.7 48.28 9065 0.665 20338 91.93 95.04 76.01 1.10 1.78 10.69 12.64 14.13 2.527 -0.132 342.24 323.92 324.15 3345.7 52.44 8705 0.665 19202 83.37 85.93 69.21 1.10 1 .90 10.69 13.68 15.07 3.802 0.056 359.41 342.16 342.43 3261.9 56.75 8387 0.666 20022 83.79 86.09 68.75 1.10 2.25 10.69 16.06 17.26 4.976 -0.008 376.83 359.11 359.42 3184.8 60.94 8116 0.666 20016 81.07 83.25 66.35 1.10 2.68 10.69 17.76 18.85 6.314 0.028 397.19 378.83 379.19 3096.9 66.04 7826 0.666 19614 76.61 78.63 62.73 1.10 3.19 10.69 19.74 20.73 7.607 0.033 416.01 397.95 398.38 3012.0 71.27 7567 0.666 19994 75.52 77.39 61.39 1.10 3.70 10.69 22.76 23.62 8.913 -0.013 435.28 417.22 417.72 2926.2 76.85 7326 0.666 20022 73.22 74.95 59.29 1.10 3.81 10.69 23.40 24.24

10.185 0.020 454.19 435.84 436.41 2842.6 82.58 7109 0.666 19476 69.13 70.72 56.05 1.10 3.98 10.69 24.04 24.86 11.453 0.066 471.77 453.93 454.59 2759.4 88.55 6913 0.666 19554 67.49 68.94 54.47 1.10 4.20 10.69 26.05 26.81 12.723 -0.033 489.91 471.82 472.57 2675.9 94.85 6731 0.666 19800 66.55 67.94 53.44 1.10 4.50 10.69 27.45 28.17

13.993 0.025 509.15 490.95 491.83 2592.5 101.81 6549 0.666 21818 71.34 72.78 56.13 1.10 4.91 10.69 29.65 30.31 15.240 -0.058 516.17 509.23 510.23 2510.6 109.00 6385 0.666 44123 140.68 141.73 94.36 1.10 5.16 10.69 89.86 90.08

2.565 -1.880 340.01 324.47 324.70 3343.2 52.57 8695 0.665 22642 98.19 100.75 79.02 1.10 1.91 10.69 15.71 16.94 5.032 -1.892 376.86 359.92 360.24 3181.1 61.15 8104 0.666 20995 84.90 87.07 68.86 1.10 2.70 10.69 18.61 19.66 7.620 -1.938 416.46 398.14 398.57 3011.1 71.32 7564 0.666 19700 74.38 76.24 60.63 1.10 3.70 10.69 22.48 23.35 10.185 -1.951 455.15 435.84 436.41 2842.6 82.58 7109 0.666 18483 65.60 67.18 53.70 1.10 3.98 10.69 22.90 23.76 12.700 -1.913 490.79 471.49 472.24 2677.5 94.73 6734 0.666 18486 62.16 63.55 50.55 1.10 4.49 10.69 25.73 26.49

2.494 1.925 340.22 323.43 323.67 3347.8 52.33 8713 0.665 21028 91.39 93.97 74.61 1.10 1.90 10.69 14.66 15.96 5.098 1.900 378.90 360.89 361.21 3176.8 61.39 8089 0.666 19739 79.68 81.84 65.37 1.10 2.72 10.69 17.73 18.82 7.620 1.852 416.45 398.14 398.57 3011.1 71.32 7564 0.666 19710 74.42 76.28 60.66 1.10 3.70 10.69 22.49 23.36 10.160 1.956 452.40 435.48 436.05 2844.3 82.46 7113 0.666 21181 75.22 76.81 60.05 1.10 3.97 10.69 25.98 26.73 12.692 1.930 487.78 471.37 472.13 2678.0 94.69 6735 0.666 21890 73.62 75.02 58.01 1.10 4.49 10.69 30.20 30.86

2.540 -3.211 341.27 324.11 324.34 3344.8 52.48 8701 C.665 20499 88.97 91.53 72.97 1.10 1.91 10.69 14.43 15.76 7.633 -3.213 419.73 398.33 398.76 3010.3 71.38 7562 0.666 16810 63.45 65.30 53.22 1.10 3.70 10.69 19.45 20.45 12.720 -3.211 492.66 471.77 472.53 2676.1 94.83 6731 0.666 17052 57.31 58.69 47.28 1.10 4.50 10.69 23.86 24.68 2.499 3.221 340.25 323.51 323.74 3347.5 52.35 8712 0.665 21075 91.58 94.16 74.74 1.10 1.90 10.69 14.69 16.00 7.620 3.454 410.44 398.14 398.57 3011.1 71.32 7564 0.666 29697 112.14 114.03 84.28 1.10 3.70 10.69 33.15 33.75 12.700 3.180 480.28 471.49 472.24 2677.5 94.73 6734 0.666 42628 143.34 144.80 97.86 1.10 4.49 10.69 57.86 58.20

48
Table 3 (continued)

18° P inf in Specimen

Experiment: 21 Noventier• 1990 Date: 5 Time: 10 :25:30

TA T8 M P0 P0- Pi Vf Qt Wqt

K K kg/h kPa kPa X W X

284.05 473.56 27.82 3504.1 1387. 91 75 .30 7558.0 1.09

Insulated-Side

Hot-Side Temperatures: PRT Temperatures:

X Y T w X Y Tw X Y Tw

cm cm K cm cm < cm cm K 1.332 0.485 333.75 2.549 -1.330 344.52 -0.038 0.038 295.73

2.597 0.526 346.53 5.033 -1.444 372.87 3.993 -0.224 348.57

2.681 0.923 349.82 7.571 -1.375 408.42 11.648 -0.241 439.56

5.107 0.426 377.98 10.071 -1.476 440.39 15.077 -1.430 476.21 7.626 0.498 400.05 2.465 -2.649 339.25

7.710 0.895 410.76 7.657 -2.616 411.84

10.111 0.396 439.85 12.699 -2.643 472.91

12.651 0.478 466.43 7.540 2.687 406.38

12.734 0.875 471.99 7.623 3.085 407.88

13.931 0.527 487.17

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw utf Wre Uh Wnu cm cm K < K kPa m/s W/(ml K) K K % % %

-0.038 -0.229 294.23 283.89 284.12 3512.0 52.20 11298 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 316.73 300.44 300.71 3389.5 57.14 10885 0.665 23897 109.13 112.35 87.52 1.10 1.51 10.69 13.16 14.60 2.527 -0.132 332.08 316.32 316.64 3275.9 62.17 10515 0.665 22480 99.20 101.89 80.08 1.10 1.62 10.69 14.14 15.49 3.802 0.056 346.46 331.65 332.03 3158.5 67.52 10184 0.666 23540 100.64 103.09 80.25 1.10 1.91 10.69 16.51 17.68 4.976 -0.008 361.07 345.89 346.33 3050.5 72.84 9898 0.666 23616 98.15 100.50 78.05 1.10 2.26 10.69 18.15 19.22 6.314 0.028 378.27 362.45 362.98 2927.3 79.45 9589 0.666 23064 92.88 95.09 74.00 1.10 2.69 10.69 19.98 20.95 7.607 0.033 393.98 378.49 379.12 2808.3 86.40 9310 0.666 23701 92.69 94.76 73.23 1.10 3.12 10.69 23.09 23.94 8.913 -0.013 410.12 394.65 395.40 2688.1 94.04 9048 0.666 23857 90.69 92.63 71.34 1.10 3.20 10.69 23.84 24.67

10.185 0.020 425.98 410.25 411.13 2571.0 102.12 8811 0.666 23291 86.23 88.03 67.94 1.10 3.35 10.69 24.55 25.35 11.453 0.066 440.83 425.39 426.42 2454.3 110.85 8595 0.666 23298 84.15 85.82 66.08 1.10 3.54 10.69 26.48 27.22

12.723 -0.033 456.07 440.33 441.55 2337.4 120.40 8394 0.666 23610 83.28 84.90 65.08 1.10 3.79 10.69 27.88 28.59

13.993 0.025 472.30 456.29 457.74 2220.5 131.25 8191 0.666 25923 89.23 90.94 68.33 1.10 4.13 10.69 29.97 30.63

15.240 -0.058 477.87 471.49 473.21 2105.7 142.94 8008 0.666 56094 188.78 190.18 120.40 1.10 4.34 10.69 97.00 97.20

2.565 -1 .880 330.22 316.79 317.11 3272.4 62.32 10504 0.665 26414 116.44 119.13 91.03 1.10 1.62 10.69 16.22 17.41 5.032 -1.892 361.25 346.58 347.02 3045.3 73.10 9885 0.666 24488 101.64 103.99 80.24 1.10 2.28 10.69 18.83 19.86 7.620 -1.938 394.58 378.66 379.29 2807.1 86.47 9308 0.666 23020 90.00 92.06 71.51 1.10 3.12 10.69 22.50 23.37

10.185 -1.951 427.18 410.25 411.13 2571.0 102.12 8811 0.666 21542 79.75 81.54 63.79 1.10 3.35 10.69 22.83 23.69

12.700 -1.913 457.12 440.05 441.27 2339.5 120.22 8398 0.666 21608 76.25 77.86 60.62 1.10 3.78 10.69 25.65 26.42 2.494 1.925 330.23 315.92 316.24 3278.9 62.03 10524 0.665 24849 109.75 112.46 86.88 1.10 1.61 10.69 15.29 16.54 5.098 1.900 362.73 347.39 347.84 3039.2 73.42 9870 0.666 23428 97.09 99.43 77.31 1.10 2.30 10.69 18.21 19.27 7.620 1.852 394.21 378.66 379.29 2807.1 86.47 9308 0.666 23582 92.20 94.26 72.91 1.10 3.12 10.69 23.01 23.86

10.160 1.956 424.42 409.95 410.82 2573.3 101.96 8816 0.666 25453 94.28 96.10 73.00 1.10 3.35 10.69 26.65 27.39

12.692 1.930 454.02 439.96 441.17 2340.2 120.15 8399 0.666 26647 94.05 95.69 71.73 1.10 3.78 10.69 31.30 31 .93 2.540 -3.211 331.33 316.48 316.80 3274.7 62.22 10511 0.665 23880 105.34 108.03 84.03 1.10 1.62 10.69 14.87 16.16 7.633 -3.213 397.61 378.82 379.45 2805.9 86.55 9305 0.666 19383 75.76 77.80 62.18 1.10 3.12 10.69 19.24 20.26

12.720 -3.211 459.23 440.29 441 .51 2337.6 120.38 8394 0.666 19343 68.23 69.83 55.38 1.10 3.79 10.69 23.13 23.98 2.499 3.221 330.27 315.98 316.30 3278.5 62.05 10522 0.665 24881 109.88 112.59 86.96 1.10 1.61 10.69 15.31 16.57 7.620 3.454 389.14 378.66 379.29 2807.

86.47 9308 0.666 35724 139.67 141.78 101.26 1.10 3.12 10.69 34.13 34.71 12.700 3.180 447.66 440.05 441.27 2339.5 120.22 8398 0.666 53549 188.97 190.76 122.93 1.10 3.78 10.69 61.93 62.25

49
Table 3 (continued)

18° P inf in Specimen

Experiment: 6 Date: 23 November 1990

Time: 10:47:55

TA TB H PO P0-P1 Vf Qt Wqt

K K kg/h kPa kPa X U X

288.36 690.55 15.03 3540.5 563.65 93 .30 8708.0 1.03

Insulated- Side

Hot-Side Temperatures: PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm < cm cm K 1.332 0.485 378.65 2.549 -1.330 404.21 -0.038 0.038 312.33

2.597 0.526 408.19 5.033 -1.444 465.42 3.993 -0.224 423.51

2.681 0.923 414.19 7.571 -1.375 539.14 11.648 -0.241 619.06

5.107 0.426 474.88 10.071 -1.476 607.04 15.077 -1.430 695.77

7.626 0.498 531.98 2.465 -2.649 396.47

7.710 0.895 545.24 7.657 -2.616 545.20

10.111 0.396 608.76 12.699 -2.643 676.38

12.651 0.478 670.31 7.540 2.687 537.55

12.734 0.875 674.26 7.623 3.085 537.49

13.931 0.527 710.81

insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Wre Uh Wnu

cm cm K K K kPa m/s W/(mJ K) K K X % % -0.038 -0.229 310.01 288.33 288.39 3543.7 28.39 6043 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 356.34 323.57 323.65 3493.9 32.24 5593 0.665 13490 58.59 61.78 52.27 1.10 3.11 10.69 11.77 13.36 2.527 -0.132 388,80 357.40 357.51 3447.8 36.02 5228 0.665 12778 51.89 54.35 46.16 1.10 3.35 10.69 12.90 14.37 3.802 0.056 420.23 390.08 390.21 3400.1 39.81 4925 0.666 13032 49.86 51.94 43.87 1.10 3.99 10.69 15.17 16.44 4.976 -0.008 451.38 420.44 420.60 3356.3 43.42 4678 0.666 13027 47.35 49.24 41.44 1.10 4.76 10.69 17.06 18.20 6.314 0.028 487.13 455.79 455.98 3306.2 47.73 4425 0.666 13038 44.84 46.51 38.99 1.10 5.69 10.69 19.60 20.60 7.607 0.033 521.19 490.07 490.30 3257.9 52.03 4209 0.666 13128 42.94 44.42 37.05 1.10 6.61 10.69 22.55 23.42 8.913 -0.013 555.87 524.62 524.89 3209.1 56.51 4015 0.666 13063 40.76 42.08 35.00 1.13 6.80 10.69 23.10 23.95

10.185 0.020 589.48 558.03 558.34 3161.5 60.97 3846 0.666 12794 38.25 39.42 32.78 1.26 7.11 10.69 24.00 24.82 11.453 0.066 621.17 590.50 590.86 3114.1 65.46 3698 0.666 12759 36.67 37.71 31.31 1.39 7.50 10.69 25.96 26.72

12.723 -0.033 655.02 622.63 623.04 3066.7 70.05 3564 0.666 12351 34.21 35.18 29.32 1.53 8.04 10.69 26.34 27.09

13.993 0.025 690.10 657.02 657.49 3019.2 75.05 3433 0.666 13343 35.59 36.56 30.19 1.67 8.77 10.69 28.03 28.73 15.240 -0.058 704.92 689.89 690.43 2972.6 80.01 3317 0.666 20803 53.63 54.27 41.75 1.73 9.21 10.69 66.07 66.37

2.565 -1.880 384.96 358.39 358.50 3446.4 36.13 5218 0.665 15078 61.11 63.56 52.83 1.10 3.37 10.69 14.78 16.08 5.032 -1.892 450.63 421.91 422.07 3354.2 43.60 4667 0.666 14054 50.97 52.85 44.03 1.10 4.80 10.69 18.34 19.40 7.620 -1.938 520.97 490.41 490.64 3257.4 52.08 4207 0.666 13374 43.72 45.20 37.61 1.10 6.62 10.69 22.97 23.83 10.185 -1.951 589.39 558.03 558.34 3161.5 60.97 3846 0.666 12834 38.37 39.54 32.87 1.26 7.11 10.69 24.07 24.89

12.700 -1.913 653.65 622.03 622.44 3067.5 69.97 3566 0.666 12641 35.04 36.01 29.92 1.52 8.02 10.69 26.92 27.66 2.494 1.925 385.67 356.54 356.65 3449.0 35.92 5237 0.665 13805 56.15 58.63 49.31 1.10 3.34 10.69 13.65 15.04 5.098 1.900 455.27 423.64 423.80 3351.7 43.81 4654 0.666 12774 46.19 48.06 40.53 1.10 4.85 10.69 16.98 18.12 7.620 1.852 522.48 490.41 490.64 3257.4 52.08 4207 0.666 12738 41.65 43.13 36.12 1.10 6.62 10.69 21.96 22.85 10.160 1.956 587.00 557.38 557.69 3162.5 60.88 3850 0.666 13600 40.69 41.87 34.52 1.25 7.10 10.69 25.38 26.15 12.692 1.930 651.77 621.83 622.24 3067.8 69.94 3567 0.666 13351 37.01 37.98 31.31 1.51 8.02 10.69 28.35 29.05 2.540 -3.211 387.26 357.74 357.85 3447.3 36.06 5225 0.665 13587 55.14 57.60 48.54 1.10 3.36 10.69 13.55 14.96 7.633 -3.213 525.36 490.76 490.98 3256.9 52.12 4205 0.666 11798 38.56 40.03 33.86 1.10 6.62 10.69 20.48 21.43 12.720 -3.211 655.30 622.55 622.96 3066.8 70.04 3564 0.666 12214 33.83 34.80 29.05 1.53 8.03 10.69 26.07 26.82 2.499 3.221 385.52 356.67 356.78 3448.9 35.94 5235 0.665 13934 56.66 59.14 49.68 1.10 3.34 10.69 13.76 15.14 7.620 3.454 510.77 490.41 490.64 3257.4 52.08 4207 0.666 20151 65.88 67.37 52.67 1.10 6.62 10.69 33.90 34.48

12.700 3.180 637.66 622.03 622.44 3067.5 69.97 3566 0.666 25936 71.89 72.88 53.63 1.46 8.02 10.69 53.99 54.36

50
Table 3 (continued)

18° Pinfin Specimen

Experiment: 6 Date: 23 November 1990

Time: 10:56:23

TA TB M P0 P0-P1

K K kg/h kPa kPa 287.85 610.19 19.07 3529.1 810.77

Hot-Side Temperatures:

X Y Tw X Y cm cm K cm cm

1.332 0.485 364.59 2.549 -1.330 2.597 0.526 387.44 5.033 -1.444

2.681 0.923 392.60 7.571 -1.375 5.107 0.426 440.80 10.071 -1.476

7.626 0.498 483.64 2.465 -2.649

7.710 0.895 496.62 7.657 -2.616

10.111 0.396 546.46 12.699 -2.643

12.651 0.478 594.06 7.540 2.687

12.734 0.875 598.99 7.623 3.085

13.931 0.527 628.04

Vf Qt Uqt

X W X 93.87 8845.0 1.04

Insulated- Side

PRT Temperatures:

Tw X Y Tw

K cm cm K 383.92 -0.038 0.038 307.39 432.48 3.993 -0.224 396.43

491.85 11.648 -0.241 551.77

545.74 15.077 -1.430 613.38

376.85 497.19

601.09

489.93 490.60

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw wtf Ure Uh Unu

cm cm K K K kPa m/s W/(m! K) K K X X X

-0.038 -0.229 305.44 287.78 287.89 3533.7 36.04 7674 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 342.77 316.00 316.14 3462.1 40.31 7210 0.665 16819 74.23 77.62 63.79 1.10 2.51 10.69 11.92 13.50 2.527 -0.132 368.59 343.10 343.27 3395.8 44.55 6819 0.665 16038 66.97 69.66 57.49 1.10 2.70 10.69 13.10 14.55 3.802 0.056 393.50 369.27 369.47 3327.2 48.87 6486 0.666 16537 65.69 68.03 55.74 1.10 3.21 10.69 15.46 16.70 4.976 -0.008 418.39 393.58 393.82 3264.1 53.04 6209 0.666 16582 63.08 65.24 53.28 1.10 3.82 10.69 17.35 18.46 6.314 0.028 447.01 421.88 422.17 3192.1 58.07 5921 0.666 16612 60.26 62.21 50.61 1.10 4.56 10.69 19.88 20.86 7.607 0.033 474.03 449.33 449.66 3122.6 63.17 5669 0.666 16911 58.75 60.50 48.92 1.10 5.30 10.69 23.05 23.90 8.913 -0.013 501.55 476.99 477.39 3052.4 68.55 5441 0.666 17010 56.71 58.30 46.93 1.10 5.45 10.69 23.83 24.66

10.185 0.020 528.39 503.73 504.19 2984.0 74.00 5239 0.666 16717 53.67 55.10 44.32 1.10 5.69 10.69 24.76 25.55 11.453 0.066 553.42 529.71 530.24 2915.8 79.58 5060 0.666 16946 52.54 53.82 43.07 1.12 6.01 10.69 27.14 27.86

12.723 -0.033 579.54 555.41 556.02 2847.5 85.40 4896 0.666 17062 51.19 52.40 41.77 1.23 6.44 10.69 28.58 29.27

13.993 0.025 607.10 582.91 583.62 2779.2 91.78 4734 0.666 18817 54.59 55.82 43.67 1.34 7.03 10.69 31.05 31.68

15.240 -0.058 618.39 609.20 610.01 2712.2 98.25 4591 0.666 36531 102.77 103.62 70.97 1.38 7.38 10.69 90.62 90.84

2.565 -1.880 365.42 343.90 344.06 3393.7 44.68 6808 0.665 18976 79.11 81.80 65.84 1.10 2.71 10.69 15.06 16.33 5.032 -1.892 417.90 394.76 395.00 3261.1 53.25 6197 0.666 17800 67.57 69.72 56.33 1.10 3.85 10.69 18.57 19.61 7.620 -1.938 474.16 449.60 449.94 3121.9 63.22 5667 0.666 17011 59.07 60.82 49.14 1.10 5.30 10.69 23.21 24.05 10.185 -1.951 528.87 503.73 504.19 2984.0 74.00 5239 0.666 16394 52.63 54.06 43.61 1.10 5.69 10.69 24.31 25.12

12.700 -1.913 579.49 554.93 555.54 2848.7 85.29 4899 0.666 16736 50.24 51.45 41.14 1.23 6.43 10.69 28.06 28.77

2.494 1.925 365.90 342.41 342.58 3397.5 44.44 6828 0.665 17446 72.94 75.65 61.68 1.10 2.69 10.69 13.94 15.31 5.098 1.900 421.27 396.15 396.39 3257.5 53.49 6182 0.666 16406 62.13 64.27 52.55 1.10 3.89 10.69 17.39 18.51 7.620 1.852 474.85 449.60 449.94 3121.9 63.22 5667 0.666 16542 57.44 59.19 48.02 1.10 5.30 10.69 22.62 23.48

10.160 1.956 526.03 503.20 503.66 2985.3 73.89 5243 0.666 18106 58.17 59.61 47.35 1.10 5.69 10.69 26.65 27.39

12.692 1.930 576.75 554.77 555.38 2849.2 85.25 4900 0.666 18738 56.26 57.48 45.12 1.21 6.43 10.69 31.25 31.88

2.540 -3.211 367.49 343.37 343.54 3395.1 44.60 6815 0.665 16947 70.73 73.42 60.12 1.10 2.70 10.69 13.70 15.09 7.633 -3.213 478.54 449.88 450.22 3121.2 63.28 5665 0.666 14548 50.50 52.24 43.18 1.10 5.30 10.69 20.11 21.08

12.720 -3.211 581.73 555.34 555.96 2847.7 85.38 4896 0.666 15564 46.70 47.91 38.74 1.23 6.44 10.69 26.21 26.96 2.499 3.221 365.85 342.52 342.68 3397.3 44.46 6827 0.665 17555 73.39 76.10 61.99 1.10 2.69 10.69 14.02 15.38 7.620 3.454 465.53 449.60 449.94 3121.9 63.22 5667 0.666 26434 91.79 93.56 70.12 1.10 5.30 10.69 35.30 35.86

12.700 3.180 565.76 554.93 555.54 2848.7 85.29 4899 0.666 39228 117.77 119.03 80.72 1.17 6.43 10.69 64.31 64.62

51
18° Table 3 (continued) P inf in Specimen

Experiment: 6 Date: 23 November 1990

Time: 11:03:40

TA TB M P0 P0- PI Vf Qt Wqt

K K kg/h kPa kPa X W X

287.09 558.53 22.74 3515.6 1096. 10 93 .76 8869.,0 1.05

Insulated-:Side Hot-Side Temperatures : PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm K 1.332 0.485 355.13 2.549 -i .330 370..84 -0.038 0.038 303.,78 2.597 0.526 373.86 5.033 -i .444 411..76 3.993 -0.224 379..11 2.681 0.923 378.50 7.571 -i .375 462..18 11.648 -0.241 509. 79 5.107 0.426 418.99 10.071 -i .476 507..84 15.077 -1.430 561..98 7.626 0.498 453.21 2.465 -2 .649 364..21 7.710 0.895 465.90 7.657 -2 .616 467..18 10.111 0.396 507.80 12.699 -2 .643 554..69 12.651 0.478 546.90 7.540 2 .687 460..05 12.734 0.875 552.76 7.623 3 .085 461..03 13.931 0.527 575.78

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Ure Uh Unu

cm cm K K K kPa m/s U/(m* K) K K X X %

-0.038 -0.229 302.10 287.00 287.15 3521.8 42.99 9167 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00

1.293 -0.226 333.77 310.74 310.93 3425.1 47.78 8694 0.665 19670 87.81 91.33 73.35 1.10 2.12 10.69 12.09 13.64 2.527 -0.132 355.57 333.54 333.77 3335.4 52.58 8288 0.665 18685 79.54 82.39 66.55 1.10 2.28 10.69 13.20 14.64 3.802 0.056 376.35 355.55 355.83 3242.7 57.58 7936 0.666 19417 79.17 81.68 65.43 1.10 2.71 10.69 15.57 16.80 4.976 -0.008 397.32 376.00 376.33 3157.3 62.47 7640 0.666 19461 76.40 78.75 62.90 1.10 3.22 10.69 17.37 18.49 6.314 0.028 421.51 399.79 400.19 3060.1 68.46 7326 0.666 19411 73.08 75.24 59.93 1.10 3.84 10.69 19.74 20.73 7.607 0.033 444.21 422.86 423.33 2966.1 74.63 7049 0.666 19790 71.70 73.67 58.32 1.10 4.46 10.69 22.86 23.71 8.913 -0.013 467.33 446.11 446.67 2871.1 81.27 6795 0.666 19948 69.67 71.47 56.33 1.10 4.59 10.69 23.66 24.49

10.185 0.020 490.01 468.57 469.22 2778.7 88.14 6568 0.666 19524 65.92 67.56 53.26 1.10 4.79 10.69 24.48 25.28

11.453 0.066 511.17 490.39 491.15 2686.5 95.34 6365 0.666 19674 64.38 65.87 51.71 1.10 5.06 10.69 26.64 27.38 12.723 -0.033 533.07 511.95 512.85 2594.2 103.02 6178 0.666 19901 63.21 64.63 50.48 1.10 5.42 10.69 28.08 28.78

13.993 0.025 556.16 535.03 536.07 2501.8 111.57 5992 0.666 22060 67.96 69.42 53.08 1.13 5.91 10.69 30.58 31.23

15.240 -0.058 564.95 557.05 558.28 2411.2 120.47 5827 0.666 45984 137.75 138.82 90.71 1.17 6.22 10.69 95.67 95.88

2.565 -1.880 352.86 334.21 334.44 3332.6 52.73 8277 0.665 22065 93.80 96.64 76.01 1.10 2.29 10.69 15.15 16.42 5.032 -1.892 397.16 376.99 377.32 3153.3 62.71 7626 0.666 20602 80.73 83.08 65.74 1.10 3.25 10.69 18.36 19.42 7.620 -1.938 444.72 423.10 423.57 2965.1 74.70 7047 0.666 19533 70.74 72.71 57.68 1.10 4.47 10.69 22.61 23.48

10.185 -1.951 490.95 468.57 469.22 2778.7 88.14 6568 0.666 18673 63.05 64.69 51.37 1.10 4.79 10.69 23.48 24.32 12.700 -1.913 533.58 511.56 512.45 2595.8 102.87 6182 0.666 19018 60.44 61.86 48.69 1.10 5.41 10.69 26.90 27.63 2.494 1.925 353.01 332.96 333.19 3337.8 52.45 8298 0.665 20592 87.76 90.63 72.10 1.10 2.27 10.69 14.20 15.54 5.098 1.900 399.57 378.15 378.49 3148.5 63.00 7610 0.666 19417 75.93 78.27 62.52 1.10 3.28 10.69 17.54 18.64 7.620 1.852 444.70 423.10 423.57 2965.1 74.70 7047 0.666 19547 70.80 72.77 57.72 1.10 4.47 10.69 22.62 23.49

10.160 1.956 487.73 468.13 468.78 2780.5 88.00 6573 0.666 21425 72.39 74.04 57.47 1.10 4.79 10.69 26.67 27.41 12.692 1.930 530.40 511.42 512.31 2596.4 102.82 6183 0.666 22199 70.56 71.99 55.17 1.10 5.41 10.69 31.17 31.80 2.540 -3.211 354.71 333.77 334.00 3334.4 52.63 8284 0.665 19646 83.59 86.44 69.28 1.10 2.28 10.69 13.75 15.13 7.633 -3.213 448.99 423.33 423.80 2964.2 74.76 7044 0.666 16399 59.37 61.32 49.98 1.10 4.47 10.69 19.28 20.29

12.720 -3.211 536.38 511.90 512.79 2594.4 103.00 6179 0.666 17056 54.18 55.59 44.53 1.10 5.42 10.69 24.29 25.09 2.499 3.221 352.96 333.05 333.28 3337.4 52.47 8296 0.665 20721 88.30 91.17 72.46 1.10 2.27 10.69 14.28 15.62 7.620 3.454 436.85 423.10 423.57 2965.1 74.70 7047 0.666 31104 112.65 114.65 83.60 1.10 4.47 10.69 35.17 35.73 12.700 3.180 520.88 511.56 512.45 2595.8 102.87 6182 0.666 47642 151.40 152.91 99.87 1.10 5.41 10.69 65.81 66.11

52
Table 3 (continued)

18° Pinfin Specimen

Experiment: 6

Date: 23 November 1990

Time: 11:11:26

TA TB M P0 P0- PI Vf Qt Wqt

K K kg/h kPa kPa X u X

286.47 528.27 25.64 3511.5 1380. 53 94 .04 8899.0 1.06

Insulated-!Side Hot-Side Temperatures PRT Temperatures:

X Y Tw X Y Tw X Y Tw

cm cm K cm cm K cm cm < 1.332 0.485 349.32 2.549 -1.330 363.03 -0.038 0.038 301.45

2.597 0.526 365.71 5.033 -1.444 399.46 3.993 -0.224 368.70

2.681 0.923 370.07 7.571 -1.375 444.73 11.648 -0.241 484.96

5.107 0.426 406.07 10.071 -1.476 485.46 15.077 -1.430 531.57

7.626 0.498 435.30 2.465 -2.649 356.53

7.710 0.895 447.84 7.657 -2.616 449.32

10.111 0.396 485.06 12.699 -2.643 527.26

12.651 0.478 519.36 7.540 2.687 442.46

12.734 0.875 525.60 7.623 3.085 443.62

13.931 0.527 545.81

Insulated-Side Thermocouple Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU NUm NUw Utw Utf Ure Uh Unu cm cm K K K kPa m/s U/(m2 K) K K X X X -0.038 -0.229 299.97 286.35 286.55 3519.4 48.41 10353 0.664 0 0.00 0.00 0.00 1.10 0.50 10.69 0.00 0.00 1.293 -0.226 328.34 307.48 307.72 3397.5 53.75 9876 0.665 21852 98.25 101.86 80.47 1.10 1.90 10.69 12.24 13.78 2.527 -0.132 347.79 327.76 328.06 3284.5 59.18 9459 0.665 20713 89.23 92.19 73.32 1.10 2.04 10.69 13.31 14.73 3.802 0.056 366.30 347.35 347.70 3167.8 64.94 9095 0.666 21498 89.07 91.71 72.33 1.10 2.41 10.69 15.60 16.83 4.976 -0.008 385.04 365.53 365.95 3060.3 70.66 8785 0.666 21470 85.94 88.43 69.61 1.10 2.87 10.69 17.27 18.39 6.314 0.028 406.73 386.69 387.20 2937.8 77.78 8454 0.666 21247 81.86 84.17 66.18 1.10 3.42 10.69 19.41 20.41 7.607 0.033 426.90 407.19 407.80 2819.4 85.26 8160 0.666 21701 80.72 82.85 64.73 1.10 3.97 10.69 22.44 23.31 8.913 -0.013 447.51 427.84 428.58 2699.8 93.47 7888 0.666 21843 78.54 80.51 62.64 1.10 4.09 10.69 23.19 24.04

10.185 0.020 467.74 447.78 448.65 2583.3 102.15 7645 0.666 21330 74.34 76.15 59.32 1.10 4.27 10.69 23.92 24.74 11.453 0.066 486.61 467.13 468.17 2467.3 111.50 7425 0.666 21437 72.57 74.22 57.61 1.10 4.51 10.69 25.95 26.71 12.723 -0.033 506.05 486.24 487.48 2351.0 121.73 7223 0.666 21748 71.62 73.21 56.52 1.10 4.83 10.69 27.41 28.13 13.993 0.025 526.63 506.66 508.15 2234.7 133.36 7020 0.666 24066 77.03 78.69 59.45 1.10 5.26 10.69 29.74 30.40

15.240 -0.058 534.04 526.11 527.91 2120.5 145.86 6839 0.666 50213 156.58 157.87 101.54 1.10 5.53 10.69 92.96 93.17

2.565 -1.880 345.37 328.36 328.65 3281.0 59.35 9448 0.665 24384 104.92 107.88 83.47 1.10 2.05 10.69 15.24 16.50 5.032 -1.892 384.93 366.41 366.83 3055.1 70.95 8770 0.666 22666 90.58 93.07 72.58 1.10 2.89 10.69 18.20 19.27 7.620 -1.938 427.45 407.40 408.01 2818.2 85.34 8158 0.666 21327 79.30 81.42 63.80 1.10 3.97 10.69 22.11 23.00

10.185 -1.951 468.79 447.78 448.65 2583.3 102.15 7645 0.666 20222 70.48 72.28 56.82 1.10 4.27 10.69 22.77 23.63 12.700 -1.913 506.83 485.89 487.13 2353.1 121.53 7226 0.666 20461 67.41 68.99 53.83 1.10 4.82 10.69 25.88 26.64 2.494 1.925 345.40 327.25 327.54 3287.5 59.03 9470 0.665 22916 98.83 101.81 79.63 1.10 2.03 10.69 14.37 15.70 5.098 1.900 386.84 367.45 367.88 3049.1 71.29 8754 0.666 21659 86.39 88.87 69.83 1.10 2.92 10.69 17.59 18.70 7.620 1.852 427.01 407.40 408.01 2818.2 85.34 8158 0.666 21814 81.11 83.24 64.97 1.10 3.97 10.69 22.58 23.45 10.160 1.956 465.38 447.39 448.27 2585.6 101.98 7650 0.666 23806 83.02 84.84 64.84 1.10 4.26 10.69 26.48 27.23 12.692 1.930 503.19 485.76 487.00 2353.8 121.47 7227 0.666 24895 82.04 83.65 63.02 1.10 4.82 10.69 31.18 31.81 2.540 -3.211 347.01 327.97 328.26 3283.3 59.24 9455 0.665 21773 93.76 96.72 76.29 1.10 2.04 10.69 13.86 15.24 7.633 -3.213 431.41 407.60 408.22 2817.0 85.42 8155 0.666 17873 66.43 68.54 55.25 1.10 3.98 10.69 18.84 19.87 12.720 -3.211 509.63 486.19 487.44 2351.2 121.70 7223 0.666 18186 59.89 61.46 48.89 1.10 4.83 10.69 23.18 24.03 2.499 3.221 345.43 327.33 327.62 3287.1 59.06 9468 0.665 22979 99.08 102.06 79.79 1.10 2.03 10.69 14.41 15.73 7.620 3.454 420.06 407.40 408.01 2818.2 85.34 8158 0.666 34405 127.93 130.10 93.18 1.10 3.97 10.69 34.79 35.36

12.700 3.180 494.91 485.89 487.13 2353.1 121.53 7226 0.666 51826 170.75 172.49 110.96 1.10 4.82 10.69 63.87 64.19

53
Table 4. Uncertainties in data analysis parameters

and calculated quantities

Uncertainty

Parameter

Major Source

of Uncertainty

Magnitude of

Uncertainty

Estimated or

Calculated

Pin Height Measurement 0.025 mm Estimated

Pin Spacing Measurement 0.050 mm Estimated

Length of

Heated Zone

Measurement 1 mm Estimated

Location of

Temperature Probe

Measurement 1 mm Estimated

Local Flow Rate Specimen Uniformity2% Estimated

Fluid Temperature Local Flow Rate 0.5-8. 6 K Calculated

Total Heat Flow Inlet and Outlet

Temperature

1.0-1. 6% Calculated

Fluid Velocity Local Flow Rate 8. 7-8. 8% Calculated

Friction Factor Pin Height,

Pin Spacing

22-23% for

Re > 500

Calculated

Heat Transfer

Coefficient

Local Flow Rate 12.0-43.4%,

0 . 07<x/L<0 . 93

Calculated

Reynolds Number Viscosity Function,

Local Flow Rate

10.7% Calculated

Nusselt Number Local Flow Rate 13.6-43.8%,

0 . 07<x/L<0 . 93

Calculated

54
480 VAC

75 A

Single Phase

Figure 1. Helium flow apparatus.

55
Cooling Air

and Water

Cooling Air

and Water

480 VAC

75 A

Water-cooled

Reflective Wall

Refractory

Insulation

Gas Out

Pressure Tap ' 0 1 x Pressure Tap

Thermocouples

Figure 2. Specimen furnace, showing location of inlet gas temperature (A),

upstream pressure (0)

,

outlet gas temperature (B)

,

and downstream

pressure (1)

.

oo
Heat

1.27 m

Gas

Flow

0.38 mm

2.03 mm

0.51 mm

Perspective View of

Pinfin Specimen

From Bottom

(Exploded View)

Pins

Figure 3. 18° pin-fin specimen.

57
Regions of

Unbonded Pins

0.5

0

- 0.5

(15.11,3.16)

(15.13,0.76)

(15.12,-2.44)

0 0.5

x/L

1.0

Pressure Tap Coordinates

(x,y) in cm

Figure 4. Top view of pin- fin specimen showing locations of unbonded pins

and pressure taps.
Figure 5. Method for attaching thermocouples to the heated side of the

pin- fin specimen.

59
Re

Figure 6. Friction factor (f) as a function of Reynolds number (Re) for

experiment 1, no heating.

60
trror

in

o_

I

i

IO

Q_

30 ~ i—i—i—i—i—i—i—i—i—

h

20 1

10 P

0

-

-10P

n i r

O

o

A

0

Q/

n (W/cm )

- 20.4

- 44.2

63.1

73.8

o

° 0

o

i i r

A A A A

0

o

0

i—i—

20 1

o -

-30

0

J I L I I I I I I I I I I I I L 10

m

20

\\

i ;

30

Figure 7. Percent difference between predicted and measured pressure drop

(Pq-Pj.) as a function of helium flow rate (m) for heat transfer

experiments

61
Figure 8. Wall (Tw ) and gas (Tf ) temperatures as a function of x/L

experiment 5, 11.4 kg/h helium flow, and y/W = 0.0.

62
800 T

700

600 L

500

400 1

300 1

~r~

X/L:

*

0

w

- 0 0 0.67

A A A A

0.50

B- — — — —— — — — — 0.33

G © —© —e—

0.17

©

200 L- [ 1 1 1 J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -0.50 -0.25 0.00 0.25 0.50

Figure 9. Wall temperature (Tw ) as a function of y/W at several x/L

locations; experiment 5, 11.4 kg/h helium flow.

63
X/L

*

CN

E

Figure 10. Wall-to-gas temperature difference (Tw -Tf ) and heat transfer

coefficient (h) as a function of x/L; experiment 5, 11.4 kg/h

helium flow and y/W = 0.0.

64
X/L

Figure 11. Reynolds number (Re), Nusselt number (Nu) , and modified Nusselt

number (Nu^,) as a function of x/L; experiment 5, 11.4 kg/h helium

flow and y/W = 0.0.

65

Nu,

Nu
Figure 12. Modified Nusselt number (NUj,,) as a function of Reynolds number

(Re); heated experiments 3-6 with 0.07 < x/L < 0.93 and

y/W =0.0.

66
Z5

z

V 5000 10000 15000

Re

Figure 13. Wall Nusselt number (Ni^) as a function of Reynolds number (Re);

heated experiment 3-6 with 0.07 < x/L < 0.93 and y/W = 0.0.

67
Figure

Side View,

Perpendicular

to Row of Pins

Flow

Direction Bottom

View

dp

(z) = S - 2(t

2 - z

2

) 1/2

d = S - 2t = 1.02 mm

S = 2.03 mm

t = 0.508 mm

. 1. Definition of pin geometry for calculating open volume,

wetted-wall area, and flow area.

68
BIBLIOGRAPHIC DATA SHEET

2* PERFORMING ORGANIZATION REPORT NUMBER

:rf “2 * c

"

p* ct pi-,in -**' =»>"*« «« «. »«««..

National Aeronautics and Space Administration

jangley Research Center

[ampton, Virginia 23665

UPPLEMENTARY NOTES

TERATURE

(SURVE^MENTION FT HERE.^

SUMMARY OF M0ST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

e have measured the heat transfer and pressure drop characteristic nf eat exchanger in helium eas at 3 S mp* p

aracteristics of a novel, compact

Din-fin” 4 . §a^ at MPa a d Reynolds numbers of 450 to 12 000. This

ire“ thrri

2

;rpTMs

0

to

C

the

e

fl

S

;w

SPannin8

> to 7i IT/ 2

18

j

, The

i s Peclmen was radxatively heated on the top side at heat fluxes

-iction f^cto/an/w ^

0\

the b3Ck Slde ‘ Correla tlons were developed for the

,st studxes of stLgered pin

U

fin.s‘

to those of

>e temperature of the ^all-nuxd Interface!

meaSUr temP6ratures are extrapolated to

ilabiuty

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