1 1 United States Department of Commerce

I XISI National Institute of Standards and Technology

NISTIR 3941

HEAT TRANSFER IN A

COMPACT TUBULAR HEAT EXCHANGER

WITH HELIUM GAS AT 3.5 MPa

Douglas A. Olson

Michael P. Glover

NISTIR 3941

HEAT TRANSFER IN A

COMPACT TUBULAR HEAT EXCHANGER

WITH HELIUM GAS AT 3.5 MPa

Douglas A. Olson

Michael P. Glover

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

June 1990

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 2

2.1. Flow loop 3

2.2. Tube specimen 3

2.3. Instrumentation 4

3. Description of experiments and analysis techniques 5

3.1 Experiments conducted 5

3.2. Friction factor 6

3.3. Heat transfer coefficient 7

3.4. Uncertainty analysis 10

4. Results of experiments 10

4.1 Friction factor 10

4.2 Temperature distributions and heat transfer 12

5. Conclusions 14

6. References 16

in
LIST OF TABLES

Table Page

1 . Uncertainties in experimental measurements and gas properties at a

95% confidence interval 17

2 . Summary of geometrical parameters and experimental conditions for

tube specimen 18

3. Data tables for all experiments 19

4. Uncertainties in data analysis parameters and calculated

quantities 45

IV
LIST OF FIGURES

Figure Page

1. Helium flow loop 46

2. Specimen furnace, showing location of inlet gas temperature and

upstream pressure (A) , and outlet gas temperature and downstream

pressure (B) 47

3. Tube specimen 48

4. Technique for mounting thermocouples on tube specimen 49

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

experiment 1, no heating 50

6. Percent difference between predicted and measured pressure drop

(Pq-Pi) as a function of wall-to-gas temperature ratio (Tw/Tf) for

heat transfer experiments 51

7. Percent difference between predicted and measured pressure drop

(P0 -Pi) as a function of wall-to-gas temperature ratio (Tw/Tf) for

heat transfer experiments, using method of Rohsenow and Choi to

account for variable property effects 52

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

experiment 5, 12.8 kg/h helium flow, and y/W = 0 53

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

experiment 5, 12.8 kg/h helium flow 54

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

coefficient (h) as a function of x/L; experiment 5, 12.8 kg/h helium

flow and y/W = 0 55

11. Reynolds number (Re) and Nusselt number (Nu) as a function of x/L;

experiment 5, 12.8 kg/h helium flow and y/W = 0 56

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

all heated experiments with 0.2 < x/L <0.8 and y/W = 0 57

v

Nomenclature

A = inlet manifold location

O

Af = flow normal area = n7rD^ /4

An = specimen normal area = L-W

Aw = wetted wall area (total wall area exposed to fluid) = n^D^-L

B = outlet manifold location

Cp = specific heat at constant pressure

= specimen hydraulic diameter = tube inner diameter

f = friction factor

^heating = friction factor of an experiment with heat transfer

fno heat = friction factor of an experiment without heat transfer

fq = heat flux distribution function

G = mass flow rate per unit flow normal area = rii/Af = pV

h = heat transfer coefficient

h = enthalpy

k = thermal conductivity

K = pressure loss coefficient

L = heated length of specimen

m = mass flow rate

n = number of tubes

Nu = Nusselt number — h-D^/k

Num = modified Nusselt number = Nu- (Tw/Tf ) ®

P = pressure

Pr = Prandtl number = p • Cp/k

Qm = heat leak to manifolds through insulation

Qm ,i n

- heat leak to inlet manifold

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

= integration of furnace calibration function fq , 0 to x

Qp = total heat transfer to specimen

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

on total wetted-wall area of the specimen

r = recovery factor = Pr^-/^ for turbulent flow

Re = Reynolds number = pVD^/p

Rem = modified Reynolds number = (pfVfDj-^/pf • (i/f/Vm) T = temperature

Taw ~ cooling fluid adiabatic wall temperature

Tf = local bulk fluid temperature

Tra = mean fluid temperature = (Tf+Tw )/2

Tw = specimen wall temperature

V = velocity

Vg = heater voltage

W = width of specimen

Wdh = uncertainty in inner tube diameter

Wf = uncertainty in friction factor

Wfu = uncertainty in tube-to-tube flow uniformity

= uncertainty in heat transfer coefficient

Wj^ = uncertainty in pressure loss coefficient

Wp = uncertainty in heated length of specimen

Wioc = uncertainty in location of wall temperature probe

Wnu = uncertainty in Nusselt number

Wq t = uncertainty in total heat transfer

vii
Wre = uncertainty in Reynolds number

Wt f = uncertainty in fluid temperature

Wtw = uncertainty in wall temperature

Wv = uncertainty in fluid velocity

x = position coordinate parallel to flow direction

y = position coordinate perpendicular to flow direction

= coefficient of thermal expansion

/i = dynamic viscosity

v - kinematic viscosity

p — density

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

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

viii
Heat Transfer in a Compact Tubular Heat Exchanger

With Helium Gas at 3.5 MPa

Douglas A. Olson

Michael P. Glover

Chemical Engineering Science Division

National Institute of Standards and Technology

Boulder, CO 80303-3328

We have constructed a compact heat exchanger consisting of

circular tubes in parallel brazed to a grooved base plate. This

tube specimen heat exchanger was tested in an apparatus which

radiatively heated the specimen on one side at a heat flux of

up to 54 W/cm^, and cooled the specimen with helium gas at 3.5 MPa

and Reynolds numbers of 3000 to 35 000. The measured friction

factor of the tube specimen was lower than that of a circular tube

with fully developed turbulent flow, although our uncertainty was

high due to entrance and exit losses. The measured Nusselt number,

when modified to account for differences in fluid properties

between the wall and the cooling fluid, agreed with past

correlations for fully developed turbulent flow in circular tubes.

Key words: apparatus; compact heat exchanger; circular tube;

convection heat transfer; friction factor; high temperature;

National Aerospace Plane; radiative furnace; turbulent flow;

variable property effects.

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

1
1 . Introduction

Development of a National Aerospace Plane (NASP) , which will fly at

hypersonic speeds, requires novel cooling techniques to manage the

anticipated high heat fluxes on various components (Shore, 1986). The problem

that motivates this work is cooling of the engine struts. 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/cm^ (Scotti et al., 1988).

NASA plans 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 exchanger temperatures. Reynolds numbers are expected to be in the

range 10 000 to 30 000, with the variation due to the flow rate and the

specific design of the flow passage.

In order to test heat exchangers developed by NASA, we have constructed

an apparatus which can provide helium gas flow and a well-characterized heat

flux to a heat exchanger specimen. We have previously described this helium

flow loop apparatus (Olson, 1989) and predicted its operating conditions. In

this work we have constructed a candidate cooling jacket, which is a tubular

heat exchanger specimen. The length and width of the specimen, flow manifold

connections, and instrumentation were identical to those of the specimens to

be constructed by NASA. We have measured the heat transfer and the friction

factor of the tube specimen in the helium flow loop, testing the operating

capabilities of the apparatus. We chose the tube geometry because it has been

studied extensively (e.g., Ede , 1961, Kays and Leung, 1962), and there are

correlations for fully developed turbulent flow in circular tubes which we can

compare to our results. We note that these correlations were developed for

conditions of much lower heat flux, and for geometries which allowed better

access to wall and fluid temperatures, than for our specimen.

2. Description of experimental apparatus

The apparatus was designed to test a subset of the conditions required

for the NASP application. Those conditions are (1) a heating rate of 0-80

W/cm^; (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

chose 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
2.1. Flow loop

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

specimen furnace section in figure 2. This description is based on Olson

(1989). Helium gas at 13.8 MPa (2000 psi) or less was supplied from a tube

trailer outside the laboratory. The tube trailer contained 1100 m^ 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 3.5 MPa

(500 psi) for the experiments described here.

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

manifold which directed it 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

in the inlet and outlet manifold. 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 refractory insulation, 5 cm thick or greater. The insulation

directed and re-radiated the heat from the heater to the specimen. The heater

contained six high- temperature infrared lamps mounted in an aluminum housing.

A phase-angle power controller which used 480 VAC, single phase, and 75 A at

maximum voltage powered the heater. We estimated that the refractory wall

temperature would be 2033 K (3200 °F) at 100% power.

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. Tube Specimen

The tube specimen consisted of 20 small-diameter tubes lying in parallel

on a base plate as shown in figure 3. The gas was directed into the tubes by

the inlet manifold, flowed down the tubes, and was collected in the outlet

manifold. Both the tubes and the base plate were made of commercially pure

nickel (UNS 02200). The tubes had an outer diameter of 2.0 mm and an inner

diameter of 1.0 mm. Adjacent tubes were 3.8 mm on-center, leaving 1.8 mm of

flat between the tubes. The base plate was 7.82 cm wide, 16.5 cm long and

3.2 mm thick. The total thickness of the tubes and base plate was 4.2 mm.

The tubes (19 cm long) were brazed to the base plate using a braze alloy

foil containing 70% gold, 8% palladium, and 22% nickel (AMS-4786, 1310 K

liquidus) . The protruding tubes on each end of the base plate were slipped

into two header pieces, which were 12.7 mm long by 4.8 mm thick and 7.82 cm

wide with holes drilled to match the 20 tubes. The header pieces were brazed

3
to the tubes and base plate using an alloy of 82% gold and 18% nickel (AMS4787, 1223 K liquidus) . The assembled tube specimen was welded to slots in

the inlet and outlet manifolds. Welding the specimen into the manifolds

caused some bowing of the specimen due to the thermal stresses of the welding.

We pressurized the manifold and specimen to 6.9 MPa (1000 psi) prior to

installing the instrumentation, and there were no leaks. We painted the top

side of the specimen (with the protruding tube ridges) 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 (1350 °F)

.

2.3. Instrumentation

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

manifolds, gas pressure in the manifolds, specimen temperatures, and the

aforementioned 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 inserting the specimen. The heat flux

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

function of position over the furnace target and as a function of heater lamp

voltage. The heat flux was constant in the direction perpendicular to flow

(y)

,

and varied by no more than ±15% in the direction parallel to flow (x)

.

Details of the furnace calibration are given in Olson (1989) .

We measured the gas inlet and outlet temperatures with platinum

resistance thermometers (PRTs) , 4.8 mm diameter, inserted in the gas manifolds

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

manifold (location A in fig. 2) with a variable-reluctance pressure

transducer which had a 8.6 MPa full scale output. Difference in pressure

between the specimen inlet and outlet manifolds (A to B) was measured with a

differential pressure transducer, also a variable-reluctance type with a

1.4 MPa 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 25 thermocouples to the

side opposite the radiant heat flux (insulated-side). The heated-side

temperature was measured at 8 locations with type-N thermocouples mounted as

shown in figure 4. Two holes, 0.33 mm diameter, were drilled 1 . 0 mm on-center

in the flat between the tube ridges. The holes were back-drilled to within

0.13 mm of the surface with a 0.57 mm diameter drill. We spot-welded each

wire of the pair 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 2-5 K at a radiant heat flux of 50 W/cm^

.

Temperatures measured with the insulated-side thermocouples were used to

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

4
disturb the specimen temperatures.

Ail thermocouples were connected to an isothermal reference box. We

measured the temperature of the reference box with a platinum resistance

thermometer. Copper conductor wire connected the reference box to the data

scanner. The connector 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 five experiments conducted with the

tube specimen in the helium flow loop 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. All tests were conducted at approximately

3.5 MPa (500 psi) system pressure. In the first experiment, we tested a

range of helium flow rates without heating the specimen to determine the

friction factor. Subsequent tests used heater voltages of 7.4%, 20%, 35%, and

61% of maximum with a helium flow rate of up to 40 kg/h; the heater voltage

established the heat flux level to the specimen. The range in Reynolds number

was 3000 to 35 000, while the range in normal heat flux was 0 to 54 W/cm^

(48 Btu/(s • ft^) ) . The minimum inlet gas temperature was 277 K (39 °F) , while

the maximum gas outlet temperature was 647 K (705 °F) . The maximum specimen

temperature was 743 K (877 °F)

Because of the high heat fluxes incident to the tube specimen, we

carefully followed a procedure to prevent overheating the specimen during

experimental set-up, run, and shut-down. With inadequate helium flow to cool

the specimen, the furnace is capable of heating the specimen beyond the

melting point of the brazing alloy and the nickel; with an internal pressure

of 3.5 MPa this could easily rupture the specimen. We always started helium

flow before turning on the furnace, and we maintained helium flow after the

furnace was turned off. To set an experimental point, we closed valves 1 and

2, set the control pressure on valve 3, and cracked open valve 4 (see fig. 2).

We opened valve 1 , and verified that the tube trailer pressure was at least

5.5 MPa (800 psi). Then, we slowly opened valve 2 to full open to establish

the helium flow. Valve 4 was adjusted to set a flow rate of at least 5 kg/h.

Next, we turned on the furnace heater lamp to a low voltage (10%) while

monitoring temperatures. The lamp was then turned up to the desired setting,

and the helium flow was increased if necessary to provide sufficient cooling.

5
Before taking the first data point, we waited at least 15 minutes with

the heater lamp at steady power to allow the furnace to reach thermal

equilibrium. 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 about 5 minutes to establish thermal

equilibrium before taking data, since a change of flow rate also affected gas

and specimen temperatures. After we finished taking data at one heater

setting, we turned off the heater and reduced the helium flow to 5 kg/h or

less. We turned off the helium flow when the furnace had cooled sufficiently,

usually after about 30 minutes.

An unsteady experimental setting could translate into errors in the

calculated performance parameters. In the data analysis to follow, we have

assumed the settings were sufficiently steady to ignore thermal transients. A

steady setting was established by maintaining constant helium flow, gas

pressure, furnace heating, and gas inlet temperature. Furnace heating, helium

flow, and gas pressure were all held steady to within the uncertainty in the

calibrations of the measurements. The gas inlet temperature varied by the

largest amount, due to gas expansion in the helium trailer as the trailer

pressure decreased. The gas inlet temperature dropped by as much as 0.36

K/min, never dropping lower than 277 K. However, the error this introduced

in both the heat delivered to the specimen and the specimen- to-gas temperature

difference was less than the calibration uncertainty of the sensors.

For the experiments conducted, we analyzed the measured data to determine

the heat transfer coefficient, h, and the friction factor, f. The heat

transfer coefficient was non-dimensionalized as a Nusselt number, Nu, which

was 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 results from an integration of the one-dimensional

momentum equation in the flow direction:

P0 -Pl = G

2 (l/P1 -1/V 0 ) + (2G 2 /Dh

)|(f/,>)dx, (1)

J 0

where P =

G =

Af =

P =

V =

Dh =

n =

0 =

1 =

pressure

;

mass flow rate per unit flow normal area

rii/Af = pV;

flow normal area = n-TrD^/4;

density;

velocity

;

tube inner diameter;

number of tubes;

location where heating begins (x/L = 0)

;

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

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

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

6
frictional effects. We measured pressure in the inlet and outlet manifolds

rather than at 0 and 1, so we estimated and subtracted the entry and exit

losses for the manifold- to -tube junction. Or,

F0 -Pl = PA-PB - XKiPV

2/2, ( 2 ) 1

where the K values for the entrance and exit were estimated based on the local

geometry, and V is the entrance or exit velocity (Rohsenow and Hartnett,

1973).

If the density change is small compared to the absolute density, and the

pressure drop through the specimen is linear, then the integral can be

approximated as a constant and the resulting equation for f is:

The density change criterion was met when there was no heating, but when the

specimen was heated the exit density was as small as half the entrance

density and eq (3) was not valid.

The friction factor was calculated for experiment 1 where flow rate was

varied with no heating. This was equivalent to finding the variation of f

with Re, where the Re is defined as

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

f =

Po- p l

- G

2 (1/P1 -1 /po) (3)

2(G2 /p)-(L/Dh )

with p = (p o + p i)/2.

Re = pVD^/At. (4)

3.3. Heat transfer coefficient

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

Qw ~ h • (Tw Taw )

(5)

Taw = Tf + rV 2 /(2c

p

), ( 6 ) where T

1 1 1 11 1 i| e

turbulent flow.

7
Adiabatic heating was as much as 2 K for the highest flow rate and heating

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

heat transfer to the specimen, Q-q, 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:

^w ~ (Qt/An) ' f

q

* (

A

n/

A

w) * (7)

with Aw = wetted wall area = n^D^-L;

An = specimen heated normal area = L-W.

The function f

q

is on the order of 1, and if the heat flux were constant then

fq is 1 everywhere. The wall temperature used in eq (5) was measured with the

thermocouples on the insulated side of the specimen. We have assumed that

wall conduction was negligible in the flow direction, and thus at each

position the heat incident on the specimen is all convected into the fluid.

In the defining equation of h we assume (1) that the heat flux into the

cooling fluid is uniform at a particular x location (the same at all

circumferential points around a tube) , (2) that the wall temperature is

uniform around the tube, and (3) that the insulated side temperature is the

same as the wall temperature at the tube/fluid interface. Because the

specimen was heated from one side only and heat flowed through the specimen

structure to enter the fluid from the lower portions of the tube, wall

temperatures were not constant. However, since the Biot number (ratio of

wall conduction resistance to fluid convection resistance) was less than 1,

temperature variations in the specimen should be much less than the

temperature difference between the wall and the fluid. A finite-element

conduction analysis using anticipated values of the heat transfer coefficient

indicated that the tube wall temperature varied from 1.2 K greater than to 3.8

K less than the insulated side temperature (for 50 W/cm^ hot side heat flux

and h = 11 200 W/(m^-K)). This compares with a temperature difference between

the wall and bulk fluid of at least 54 K for the same conditions.

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

h= (Ql/Aw)- fq (8 ) (Tw -[T f+(rV2 )/(2c

p )])

The flow-direction energy equation was used to calculate Qq- (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 tube specimen equals the total heat

absorbed by the specimen plus manifolds, minus the heat leak through the

furnace insulation into the manifolds, Qm . It was calculated from the

temperatures of the gas inlet and outlet, the gas pressure drop, and an

estimation of the manifold heat leak. Or

QT = A- (hB“ hA) “ Qm> ( 9 )

where h = enthalpy;

8
A = location in inlet manifold of PRT

B = location in outlet manifold of PRT;

Qm = heat leak to manifolds through insulation.

Heat absorbed by the manifold was typically 2-5% of the total heat flow, which

we measured during a calibration on the furnace before inserting the test

specimen. 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 = V(TB

-TA) + MU-W/PldP. ( 10 )

where (3 = coefficient of thermal expansion.

The pressure term was significant because helium is not an ideal gas at these

temperatures and pressures. The integral was evaluated using the virial

equation of state for the gas (McCarty, 1973). Combining eqs (9) and (10)

yield for Qq>

Qt = m(c

p

-(TB-TA) + f[(l-m/,]dP) - Qm . (11)

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:

T fx ~ tA

+ Qt * Qpy _j_ mc

p

Qm > i n

riiCp

rx

[ ( 1 -/3T )/p ] dP

2c

P

’ ( 12 )

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

position x; = integration of furnace calibration function fq , 0 to x;

Qm>in ~ heat leak to inlet manifold.

We assume in eq (12) that the helium flow has split evenly into all 20 of the

tubes. The fluid temperature requires the velocity at x, given by

Vx = ra/(Afp x ), (13)

and the density is given by the equation of state (McCarty, 1973) as

Pyi ~ ^x( Tfx > Px) • (1^)

We assume the pressure varies linearly between 0 and 1

Px = ?0 - ( P0

" ? 1

)

X/L • (15)

The maximum error in Tf introduced by our assumption of a linear pressure

variation is less than 0.02 K.

9
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 through iteration.

With Tf and V determined 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, Tg:

Nu = h-D^/k,

Pr = /i-Cp/k. (16)

Transport properties were calculated from the functions given in McCarty

(1972). The Nu, Pr , and Re performance parameters assume constant fluid

properties at the location x. Due to the large wall- to- fluid temperature

difference, viscosity and thermal conductivity varied between the wall and the

fluid (variation was greater than 20% for the lowest helium flow at 61% heater

voltage) . We used the temperature ratio method of Rohsenow and Hartnett

(1973) to correlate the data by calculating:

Nura = Nu-(TW/Tf ) 0 - 55

. (17)

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 into the 20

tubes), particularly near the exit of the tubes. Unfortunately, there was no

way to confirm that the flow was evenly split, and the listed uncertainty is

based on transverse temperature measurements in the specimen, which would be

constant if the flow were evenly distributed.

4. Results of experiments

4.1 Friction factor

Experiment 1 (no heating) was conducted to determine the variation of the

friction factor with Reynolds number (eq 3) . Figure 5 shows the variation in

f with Re along with a least- squares correlation of the data (for Re > 5000)

and the Karman-Nikuradse relation for fully developed turbulent flow in a

smooth tube (Rohsenow and Hartnett, 1973). Our data are correlated with:

f = 0.07532-Re" 0 - 2693

. (18)

The standard deviation of the difference between the measured and correlated

10
values is 2.78%. The points for Re < 5000 were not included in the

correlation because the flow was either laminar or transitional.

The measured values were about 18-20% lower than those given by the

accepted smooth tube correlation. Our estimate of the uncertainty in the

measured friction factor was 12-14%, except for the point at Re = 2200, where

the uncertainty was 37.5% due to the large relative uncertainty of the

pressure measurement. For Re > 5000, the entrance and exit losses were

estimated as 22-32% of the pressure drop from point 0 to 1 , and the

uncertainties in the losses are the dominant component of the uncertainty in

f. These losses must be subtracted from the pressure drop measured with the

transducer (eq 2) . To estimate the uncertainty, we have assumed the loss

coefficients have an uncertainty of 0.2 (they can vary from 0 to 1 depending

on the geometry). If the losses were zero, then the measured friction factor

would be about 10% higher than the accepted values. Since we could not

measure the internal flow geometries of the manifolds and entrance/exit

sections after assembly, we may have over-estimated the losses.

We used the friction factor correlation developed for the tests without

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

experiments 2 to 5 , the Reynolds number decreased from the inlet to the

outlet because the temperature increased. We estimated the pressure drop by

calculating f at each location of a measured wall temperature (from eq 18)

then, we used eq (1) in a summation form and added up the total pressure drop

from 0 to 1 . We compared this pressure drop to the measured pressure drop

minus the entrance/exit losses (eq 2) . Figure 6 compares the predicted- tomeasured pressure drop for experiments 3 to 5 , plotted against the ratio of

wall temperature to gas temperature (taken at x/L = 0.5 and y/W =0). No

heating corresponds to Tw/Tf = 1 . This variable was used because it measures

the effect of variable properties in the fluid; to first order, k, p, and p

all vary most strongly with temperature. As the temperature ratio increases,

the differences between the values of the properties at the tube wall and

those in the mixed core increases. The error in the predicted temperature

increased as the temperature ratio increased (the measured pressure drop was

less than the predicted pressure drop) , although most points fell within the

±14% uncertainty band of the friction factor. The trend in the data agrees

with the findings of Rohsenow and Choi (1961), and Rohsenow and Hartnett

(1973), who report that for Tw/Tf > 1 (heating) the friction factor decreases.

We attempted to correct for the gas heating through the method of Rohsenow and

Choi. In this method, the equation for f is taken to be

^heating ~ (Tf/Tm) ' ^no . heat > (19)

with Tm = (Tw+Tf )/2,

and the fno .heat I s found from eq (18) using a modified Reynolds number:

Rem~ (PfvfDh)/4f ‘ (I'fAm) • (20)

Figure 7 shows the result. This correlation condenses the error in the

predicted pressure drop a few percent (the maximum difference decreased from

22% to 17%) , but does not change the trend. We made no further attempt at

11
correlating the effect of the variable properties since the uncertainty in the

friction factor was on the same order as the error in the predicted pressure

drop

.

4.2 Temperature distributions and heat transfer

Experiments 2 to 5 determined the heat transfer performance of the tube

specimen. A typical plot of temperatures in the helium gas and along the tube

is shown in figure 8. The data are from experiment 5 at the lowest flowrate

tested, which corresponded to the largest inlet- to-outlet temperature rise.

The measured specimen temperatures along the y centerline (y/W = 0) , both for

the insulated side and the heated 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 rate of increase was

slightly less near the entrance and exit, due to the drop-off in the heat flux

near the furnace end-walls (see Olson 1989) . The heated-side temperatures

were slightly higher than the insulated-side temperatures, which was expected

since the heat impinged directly on that side of the specimen. Temperatures

on both sides increased steadily from the inlet to the outlet, except that the

temperature decreased near the outlet.

Because the temperature increased 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

primarily to the temperature increase but also to the pressure drop. Because

density decreased, fluid velocity increased from the inlet to the outlet; for

the conditions shown in the figure, the specimen inlet velocity was 40 m/s and

the specimen outlet velocity was 83 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. Only at x/L = 0.5 were the probes positioned entirely

across the specimen. Temperatures were fairly constant over the middle of the

specimen, although they decreased slightly from the negative to positive y

positions. The trace at x/L = 0 showed the most variability. Since this was

the location where shading ended and heating began, uncertainty in the shading

boundary produces the largest uncertainty in heat flux and therefore in

temperature. The temperature at x/L = 0.5 and y/W = -0.46 was 50 K higher

than the temperature at x/L =0.5 and y/W =0.0. We believe maldistribution

of flow (flow in some of the tubes greater or less than that in the others)

was the most likely cause of these variations in temperature. Non-uniform

heat flux distribution in the y direction could also cause these temperature

variations, but we checked the heat flux calibration after running the tests

and found no variation in y direction heat flux beyond experimental

uncertainty

.

A maldistribution of flow could cause a temperature variation in the

following manner. If the flow in a tube were less than the average, the

fluid would heat up more than expected as it flowed down the tube. Also, the

12
lower fluid velocity would produce a smaller heat transfer coefficient, and

the wall- to-fluid temperature difference would have to be greater to

accommodate the heat flux. These two effects would cause higher wall

temperatures for regions with flow lower than average; similarly, regions

with flow higher than average would have lower wall temperatures. We have

assumed a 5% variation from uniform flow in the uncertainty analysis; this

produces uncertainties in Tf, V, Re, h, and Nu. The uncertainties in Tf, h,

and Nu grow with distance down the tube. For figure 9, the 5% uncertainty in

uniform flow distribution explains all the variations in wall temperature

except for the point at x/L = 0.5 and y/W = -0.46, where an 18% flow

maldistribution is required to explain the wall temperature.

The temperature at the hot side probe at x = 7.595 cm and y

= -3.048 cm

was likely in error, although it has been included in the data tables.

Successive temperature readings at the same conditions of flow and heat flux

showed it to vary by 100 K or more. We suspected an intermittent short as the

cause

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

temperature difference for the same conditions as those for figure 8

(experiment 5, 12.8 kg/h helium flow). Shown are points along y/W = 0, again

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. The temperature difference was relatively flat

in the center portion of the specimen, dropping off dramatically near the

furnace end walls (x/L = 0 and 1) . A 15% decrease near the inlet/outlet was

expected due to the heat flux distribution, but the measured decrease was much

greater. We believe the cause of the drop-off was heat conduction through the

specimen wall to the inlet and outlet manifolds. The temperatures of the

manifolds were the same as the inlet/outlet gas temperatures, which were lower

than the specimen wall temperature at x/L = 0 and 1. We estimated the effect

of wall conduction using a 1 -dimensional model of the specimen as a "fin"

(Rohsenow and Choi, 1961) assuming: (1) constant heat flux from 0 < x/L < 1 with zero heat flux for x/L < 0 and x/L > 1; (2) constant fluid temperature

for x/L < 0, increasing linearly from 0 < x/L < 1, and constant for x/L > 1;

and (3) constant heat transfer coefficient. The results showed that in the

initial 20% and final 20% of the heated zone for this specimen, wall

temperatures were significantly influenced by conduction to the manifolds. 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

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

experimental conditions of above. We have plotted Nu along the entire heated

length, although because of conduction effects the values are accurate only

for 0.2 < x/L < 0.8. The Reynolds number decreased from the inlet to the

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

Nu also decreased from the inlet to the outlet, within the 0.2 < x/L < 0.8

region of accuracy.

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

13
they change for the other heat flux rates tested. Figures 8 to 11 are

representative of the variations for all runs.

Figure 12 shows the modified Nusselt number plotted against the Reynolds

number for all experiments for data points at y/W = 0 and 0.2 < x/L < 0.8.

Also plotted are three correlations from the literature given for fully

developed turbulent flow in circular tubes. The difference between the

correlations gives some idea of the uncertainty in using an individual

correlation. Those correlations are:

Dittus-Boelter

(in Rohsenow and Choi, 1961)

Nu = 0.023-Re°- 8 -Pr0 - 4

,

Rohsenow and Hartnett (1973)

Nu = 0.022- Re0 • 8

• Pr° * 6

,

Kays and Leung (1962): Nu = 0 . 0422 • Re 0 • 74 • Pr°

58

. (21)

The correlation of Kays and Leung is a curve-fit of their theoretical analysis

over the range 0.5 < Pr < 0.7 and 104 < Re < 3xl04

. The data scatter of past

investigators about the correlation curve is often ±30% (e.g., see Ede , 1961).

We have shown the correlation for our data for Re > 10 000, which is the fully

turbulent region. This is:

Num = 0 . 0420 • Re0 • 739 • Pr°

6

, (22)

or in terms of Nu,

Nu = 0.0420-Re°- 739 -Pr0 - 6

- (Tw/T f

) "°

55

. (23)

The standard deviation between our data and correlation is 1.5% (Re > 10 000).

We have assumed a 0.6 power variation on Pr, and the leading coefficient was

calculated based on that variation. The Prandtl number was 0.665 for all

experiments. The Reynolds number power and the leading coefficient were

calculated from a leas t- squares fit.

Our data agreed very well with the past correlations, when we accounted

for the effect of variable properties in the temperature ratio as suggested by

Rohsenow and Hartnett (1973) . The temperature ratio for these experiments

varied from 1.06 to 1.41, producing a difference between Nu and Num of 3% to

21% (Num being higher) . Without accounting for the effect of variable

properties in the temperature ratio, our data fell below the accepted

correlations by 20% at the highest temperature ratio. Also, plots of Nu vs Re

for different heat flux rates would not collapse onto a single curve. The

uncertainty in the measured Nu and Num was 6.6% to 13.0%; the lower

uncertainties occurred closer to the inlet, and the higher uncertainties

occurred closer to the outlet (due to the contribution from the uncertainty in

flow distribution)

.

5. Conclusions

We have constructed a thin, compact heat exchanger specimen consisting of

circular tubes in parallel brazed to a grooved base plate. The heat exchanger

was made of commercially pure nickel. This tube specimen was tested in an

14
apparatus which radiative iy heated one side of the specimen at a heat flux of

up to 54 W/cm^ (48 Btu/(s • ft^) ) , and cooled the specimen with helium gas at

3.5 MPa (500 psi) and Re of 3000 to 35 000. Helium gas temperatures ranged

from 277 K (39 °F) to 647 K (705 °F) ; the peak specimen temperature was 743 K

(877 °F) . The apparatus was designed to test candidate cooling jackets for

the engine struts of the National Aerospace Plane. Measurements showed the

friction factor of the tube specimen was lower than that of a circular tube

with fully developed turbulent flow, although the uncertainties in our

measurements was high due to estimations of entrance and exit losses.

Variable property effects appeared to be important in the friction factor.

The measured Nusselt number, when modified to account for the effects of

variable properties, agreed with past correlations for fully developed

turbulent flow in circular tubes. At these temperatures and pressures, there

were no unusual effects due to using helium as a heat transfer fluid.

Conduction to the end manifolds was important in the first 20% and last 20% of

the heated portion of the specimen.

15
6. References

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

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

Ede , A. J., 1961, "The Heat Transfer Coefficient for Flow in a Pipe," Int. J.

of Heat Mass Transfer . Vol. 4, pp . 105-110.

Kays, W. M. , and Leung, E. Y. , 1962, "Heat Transfer in Annular Passages - Hydrodynamically Developed Turbulent Flow with Arbitrarily Prescribed Heat

Flux," Int. J, of Heat Mass Transfer , Vol. 6, pp . 537-557.

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^ Pa," J. Phys . Chem. Ref. Data . Vol. 2, no. 4, pp . 923-

1042.

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

Radiatively Heated Compact Exchangers," NISTIR 89-3926 .

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 . McGrawHill, 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 .

16
Table 1 . Uncertainties in experimental measurements and gas properties

at a 95% confidence interval

Measurement /Proper tv Technique

Major Source

of Uncertaintv

Magnitude

of Uncertaintv

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 TransducerCalibration ±0.25% of

reading

Gas Differential

Pressure

Pressure TransducerCalibration greater of

±0.5% of reading

or ±300 Pa

Specimen Temperature Type-N ThermocoupleWire 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%

17
Table 2. Summary of geometrical parameters and experimental conditions

for tube specimen

Number of Tubes, n = 20

Tube Inner Diameter, = 1.016 mm

Specimen Heated Length, L = 15.24 cm

Specimen Width, W = 7.82 cm

O

Specimen Heated Normal Area, An = 119.2 cm

O

Specimen Wetted Wall Area, Aw = 97.3 cm4

Flow Normal Area, Af = 0.1621 cm2

Expt

.

#

Date

Inlet

Pressure

(kPa)

Heater

Voltage

(%)

Normal Heat

Flux

(W/m2

)

Helium Flow

Rate

(ks/h)

Reynolds

Number

1 2/8/90 3400 0.0 0.0 2.6-40.1 2200-36 000

2 2/13/90 3500 7.4 3.4 5.7 4500-5000

3 3/9/90 3550 20.0 16.1 5.3-39.0 3000-35 000

4 2/16/90 3500 35.0 31.3 8.6-38.8 4700-35 000

5 3/9/90 3550 60.8 53.7 12.8-38.3 6600-34 000

18
Tube Specimen

Date: 8 February 1990

Time: 15:41:00

Table 3. Data tables for all experiments

TA

K 302.51

TB

K 301.85

Mkg/h

2.56

PA PA-PB

kPa kPa 3375.0 1.3

Vf%

0.00

f Uf%

0.00759 37.48

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 302.11

2.515 -0.762 302.12

5.080 -0.381 302.09

7.620 -0.381 302.11

10.185 -0.381 302.10

12.700 -0.381 302.09

13.970 -0.381 302.07

7.595 -3.048 302.15

Insulated-Side Temperatures and Calculated Data:

X Y Tw Tf P V RE PR Utw Wtf Ure

cm cm K K kPa m/s K K %

-0.020 0.191 302.14 302.50 3374.8 8.31 2214 0.665 1.10 0.50 11.58

1.288 0.191 302.16 302.44 3374.7 8.30 2214 0.665 1.10 0.50 11.58

2.586 0.140 302.14 302.39 3374.6 8.30 2214 0.665 1.10 0.50 11.58

3.810 0.165 302.16 302.33 3374.5 8.30 2214 0.665 1.10 0.50 11.58

5.042 0.191 302.16 302.28 3374.5 8.30 2215 0.665 1.10 0.50 11.58

6.350 0.203 302.14 302.23 3374.4 8.30 2215 0.665 1.10 0.50 11.58

7.620 0.191 302.13 302.17 3374.3 8.30 2215 0.665 1.10 0.50 11.58

8.903 0.152 302.14 302.11 3374.3 8.30 2215 0.665 1.10 0.50 11.58

10.160 0.216 302.13 302.06 3374.2 8.29 2216 0.665 1.10 0.50 11.58

11.430 0.191 302.12 302.01 3374.1 8.29 2216 0.665 1.10 0.50 11.58

12.637 0.140 302.10 301.95 3374.1 8.29 2216 0.665 1.10 0.50 11.58

13.912 0.165 302.08 301.90 3374.0 8.29 2217 0.665 1.10 0.50 11.58

15.240 0.165 301.98 301.84 3373.9 8.29 2217 0.665 1.10 0.50 11.58

-0.036 2.083 302.02 302.50 3374.8 8.31 2214 0.665 1.10 0.50 11.58

2.510 2.108 302.07 302.39 3374.6 8.30 2214 0.665 1.10 0.50 11.58

5.105 2.070 302.08 302.28 3374.5 8.30 2215 0.665 1.10 0.50 11.58

7.650 2.096 302.05 302.17 3374.3 8.30 2215 0.665 1.10 0.50 11.58

10.190 2.121 302.08 302.06 3374.2 8.29 2216 0.665 1.10 0.50 11.58

12.700 2.096 302.03 301 .95 3374.1 8.29 2216 0.665 1.10 0.50 11.58

15.215 2.070 301.91 301.84 3373.9 8.29 2217 0.665 1.10 0.50 11.58

0.000 -2.070 302.20 302.50 3374.8 8.31 2214 0.665 1.10 0.50 11.58

7.620 -2.146 302.21 302.17 3374.3 8.30 2215 0.665 1.10 0.50 11.58

15.240 -2.096 302.06 301.84 3373.9 8.29 2217 0.665 1.10 0.50 11.58

7.620 3.620 302.11 302.17 3374.3 8.30 2215 0.665 1.10 0.50 11.58

7.620 -3.620 302.18 302.17 3374.3 8.30 2215 0.665 1.10 0.50 11.58

19
Table 3 (continued)

Tube Specimen

Date: 8 February 1990

Time: 15:46:12

V f f Wf % %

-0.01 0.00773 12.74

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 300.67

2.515 -0.762 300.73

5.080 -0.381 300.76

7.620 -0.381 300.79

10.185 -0.381 300.83

12.700 -0.381 300.84

13.970 -0.381 300.88

7.595 -3.048 300.77

TA

K 300.77

TB

K 301.36

Mkg/h

5.42

PA PA-PB

kPa kPa

3372.5 6.1

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

X Y Tw Tf P V RE PR Wtw wtf Wre

cm cm K K kPa m/s K K 7, -0.020 0.191 300.74 300.74 3371.6 17.49 4701 0.665 1.10 0.50 11.58

1.288 0.191 300.70 300.79 3371.2 17.49 4701 0.665 1.10 0.50 11.58

2.586 0.140 300.72 300.84 3370.9 17.49 4700 0.665 1.10 0.50 11.58

3.810 0.165 300.71 300.89 3370.6 17.50 4700 0.665 1.10 0.50 11.58

5.042 0.191 300.74 300.93 3370.3 17.50 4699 0.665 1.10 0.50 11.58

6.350 0.203 300.72 300.98 3370.0 17.51 4699 0.665 1.10 0.50 11.58

7.620 0.191 300.73 301.03 3369.7 17.51 4698 0.665 1.10 0.50 11.58

8.903 0.152 300.71 301.08 3369.4 17.52 4698 0.665 1.10 0.50 11.58

10.160 0.216 300.74 301.13 3369.0 17.52 4697 0.665 1.10 0.50 11.58

11.430 0.191 300.74 301.18 3368.7 17.52 4697 0.665 1.10 0.50 11.58

12.637 0.140 300.73 301.23 3368.4 17.53 4696 0.665 1.10 0.50 11.58

13.912 0.165 300.77 301.28 3368.1 17.53 4696 0.665 1.10 0.50 11.58

15.240 0.165 300.81 301.33 3367.8 17.54 4695 0.665 1.10 0.50 11.58

-0.036 2.083 300.69 300.74 3371.6 17.49 4701 0.665 1.10 0.50 11.58

2.510 2.108 300.64 300.84 3370.9 17.49 4700 0.665 1.10 0.50 11.58

5.105 2.070 300.67 300.94 3370.3 17.50 4699 0.665 1.10 0.50 11.58

7.650 2.096 300.66 301 .04 3369.7 17.51 4698 0.665 1.10 0.50 11.58

10.190 2.121 300.69 301.13 3369.0 17.52 4697 0.665 1.10 0.50 11.58

12.700 2.096 300.70 301.23 3368.4 17.53 4696 0.665 1.10 0.50 11.58

15.215 2.070 300.76 301.33 3367.8 17.54 4695 0.665 1.10 0.50 11.58

0.000 -2.070 300.57 300.74 3371.6 17.49 4701 0.665 1.10 0.50 11.58

7.620 -2.146 300.58 301.03 3369.7 17.51 4698 0.665 1.10 0.50 11.58

15.240 -2.096 300.76 301 .33 3367.8 17.54 4695 0.665 1.10 0.50 11.58

7.620 3.620 300.67 301.03 3369.7 17.51 4698 0.665 1.10 0.50 11.58

7.620 -3.620 300.57 301 .03 3369.7 17.51 4698 0.665 1.10 0.50 11.58

20
Table 3 (continued)

Tube Specimen

Date: 8 February 1990

Time: 15:51:12

TA TB M PA PA-PB Vf f Uf

K K kg/h kPa kPa % %

296.40 297.63 10.89 3374.4 20.4 0.00 0.00617 11.66

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 296.36

2.515 -0.762 296.40

5.080 -0.381 296.43

7.620 -0.381 296.46

10.185 -0.381 296.49

12.700 -0.381 296.51

13.970 -0.381 296.53

7.595 -3.048 296.35

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 %

-0.020 0.191 296.43 296.29 3371.2 34.61 9536 0.665 1.10 0.50 11.58

1.288 0.191 296.36 296.39 3370.2 34.63 9534 0.665 1.10 0.50 11.58

2.586 0.140 296.37 296.49 3369.2 34.65 9532 0.665 1.10 0.50 11.58

3.810 0.165 296.36 296.59 3368.2 34.67 9530 0.665 1.10 0.50 11.58

5.042 0.191 296.38 296.69 3367.2 34.70 9528 0.665 1.10 0.50 11.58

6.350 0.203 296.37 296.80 3366.2 34.72 9526 0.665 1.10 0.50 11.58

7.620 0.191 296.38 296.90 3365.2 34.74 9523 0.665 1.10 0.50 11.58

8.903 0.152 296.36 297.00 3364.2 34.76 9521 0.665 1.10 0.50 11.58

10.160 0.216 296.35 297.10 3363.2 34.78 9519 0.665 1.10 0.50 11.58

11.430 0.191 296.38 297.21 3362.2 34.81 9517 0.665 1.10 0.50 11.58

12.637 0.140 296.33 297.30 3361.2 34.83 9515 0.665 1.10 0.50 11.58

13.912 0.165 296.36 297.41 3360.2 34.85 9513 0.665 1.10 0.50 11.58

15.240 0.165 296.46 297.51 3359.1 34.87 9511 0.665 1.10 0.50 11.58

-0.036 2.083 296.58 296.29 3371.2 34.61 9536 0.665 1.10 0.50 11.58

2.510 2.108 296.40 296.49 3369.2 34.65 9532 0.665 1.10 0.50 11.58

5.105 2.070 296.37 296.70 3367.2 34.70 9528 0.665 1.10 0.50 11.58

7.650 2.096 296.38 296.90 3365.1 34.74 9523 0.665 1.10 0.50 11.58

10.190 2.121 296.38 297.11 3363 .34.78 9519 0.665 1.10 0.50 11.58

12.700 2.096 296.38 297.31 3361.2 34.83 9515 0.665 1.10 0.50 11.58

15.215 2.070 296.47 297.51 3359.2 34.87 9511 0.665 1.10 0.50 11.58

0.000 -2.070 296.08 296.29 3371.2 34.61 9536 0.665 1.10 0.50 11.58

7.620 -2.146 296.01 296.90 3365.2 34.74 9523 0.665 1.10 0.50 11.58

15.240 -2.096 296.21 297.51 3359.1 34.87 9511 0.665 1.10 0.50 11.58

7.620 3.620 296.48 296.90 3365.2 34.74 9523 0.665 1.10 0.50 11.58

7.620 -3.620 295.98 296.90 3365.2 34.74 9523 0.665 1.10 0.50 11.58

21
Table 3 (continued)

Tube Specimen

Date: 8 February 1990

Time: 15:55:03

TA TB H PA PA-PB Vf f Wf

K K kg/h kPa kPa % %

291.82 292.98 20.03 3373.2 60.4 0.00 0.00520 12.82

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 291.52

2.515 -0.762 291.53

5.080 -0.381 291.55

7.620 -0.381 291.58

10.185 -0.381 291.62

12.700 -0.381 291.63

13.970 -0.381 291.64

7.595 -3.048 291.46

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 %

-0.020 0.191 291.53 291.45 3363.4 62.78 17734 0.665 1.10 0.50 11.58

1.288 0.191 291.48 291.55 3360.4 62.86 17730 0.665 1.10 0.50 11.58

2.586 0.140 291.48 291.64 3357.5 62.93 17726 0.665 1.10 0.50 11.58

3.810 0.165 291.46 291.73 3354.8 63.00 17723 0.665 1.10 0.50 11.58

5.042 0.191 291.43 291.82 3352.0 63.07 17719 0.665 1.10 O’. 50 11.58

6.350 0.203 291.49 291.92 3349.1 63.15 17715 0.665 1.10 0.50 11.58

7.620 0.191 291.44 292.01 3346.2 63.22 17712 0.665 1.10 0.50 11.58

8.903 0.152 291.38 292.11 3343.4 63.29 17708 0.665 1.10 0.50 11.58

10.160 0.216 291.39 292.20 3340.5 63.37 17704 0.665 1.10 0.50 11.58

11.430 0.191 291.38 292.30 3337.7 63.44 17701 0.665 1.10 0.50 11.58

12.637 0.140 291.37 292.38 3335.0 63.51 17697 0.665 1.10 0.50 11.58

13.912 0.165 291.35 292.48 3332.1 63.58 17694 0.665 1.10 0.50 11.58

15.240 0.165 291.40 292.58 3329.2 63.66 17690 0.665 1.10 0.50 11.58

-0.036 2.083 291.73 291.45 3363.4 62.78 17734 0.665 1.10 0.50 11.58

2.510 2.108 291.47 291.64 3357.7 62.93 17727 0.665 1.10 0.50 11.58

5.105 2.070 291.42 291.83 3351.9 63.08 17719 0.665 1.10 0.50 11.58

7.650 2.096 291.43 292.02 3346.2 63.22 17712 0.665 1.10 0.50 11.58

10.190 2.121 291.46 292.20 3340.5 63.37 17704 0.665 1.10 0.50 11.58

12.700 2.096 291.43 292.39 3334.9 63.51 17697 0.665 1.10 0.50 11.58

15.215 2.070 291 .54 292.58 3329.2 63.66 17690 0.665 1.10 0.50 11.58

0.000 -2.070 291.11 291.45 3363.3 62.78 17734 0.665 1.10 0.50 11.58

7.620 -2.146 290.98 292.01 3346.2 63.22 17712 0.665 1.10 0.50 11.58

15.240 -2.096 291.07 292.58 3329.2 63.66 17690 0.665 1 .10 0.50 11.58

7.620 3.620 291.58 292.01 3346.2 63.22 17712 0.665 1.10 0.50 11.58

7.620 -3.620 290.95 292.01 3346.2 63.22 17712 0.665 1.10 0.50 11.58

22
Table 3 (continued)

Tube Specimen

Date: 8 February 1990

Time: 15:59:25

TA TB M PA PA-PB V f f Wf

K K kg/h kPa kPa % %

285.43 286.29 40.06 3374.3 223.0 0.00 0.00457 14.16

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 284.94

2.515 -0.762 284.96

5.080 -0.381 284.95

7.620 -0.381 284.96

10.185 -0.381 284.96

12.700 -0.381 284.96

13.970 -0.381 284.94

7.595 -3.048 284.90

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 %

-0.020 0.191 284.89 283.99 3337.5 123.32 36075 0.664 1.10 0.52 11.58

1.288 0.191 284.86 284.04 3327.0 123.72 36071 0.664 1.10 0.53 11.58

2.586 0.140 284.84 284.10 3316.7 124.13 36067 0.664 1.10 0.53 11.58

3.810 0.165 284.83 284.16 3306.9 124.51 36063 0.664 1.10 0.53 11.58

5.042 0.191 284.83 284.21 3297.1 124.90 36059 0.664 1.10 0.53 11.58

6.350 0.203 284.86 284.27 3286.7 125.31 36055 0.664 1.10 0.53 11.58

7.620 0.191 284.82 284.33 3276.6 125.72 36051 0.664 1.10 0.53 11.58

8.903 0.152 284.74 284.38 3266.3 126.13 36047 0.664 1.10 0.53 11.58

10.160 0.216 284.76 284.44 3256.3 126.54 36043 0.664 1.10 0.53 11.58

11.430 0.191 284.78 284.50 3246.2 126.95 36039 0.664 1.10 0.53 11.58

12.637 0.140 284.73 284.55 3236.5 127.35 36035 0.664 1.10 0.53 11.58

13.912 0.165 284.70 284.61 3226.4 127.77 36031 0.664 1.10 0.53 11.58

15.240 0.165 284.76 284.67 3215.8 128.21 36027 0.664 1.10 0.53 11.58

-0.036 2.083 285.14 283.99 3337.6 123.31 36075 0.664 1.10 0.52 11.58

2.510 2.108 284.79 284.10 3317.3 124.10 36067 0.664 1.10 0.53 11.58

5.105 2.070 284.76 284.21 3296.6 124.92 36059 0.664 1.10 0.53 11.58

7.650 2.096 284.78 284.33 3276.3 125.73 36051 0.664 1.10 0.53 11.58

10.190 2.121 284.76 284.44 3256.1 126.55 36043 0.664 1.10 0.53 11.58

12.700 2.096 284.76 284.55 3236.0 127.37 36035 0.664 1.10 0.53 11.58

15.215 2.070 284.85 284.66 3216.0 128.20 36027 0.664 1.10 0.53 11.58

0.000 -2.070 284.63 283.99 3337.3 123.32 36075 0.664 1.10 0.52 11.58

7.620 -2.146 284.42 284.33 3276.6 125.72 36051 0.664 1.10 0.53 11.58

15.240 -2.096 284.49 284.67 3215.8 128.21 36027 0.664 1.10 0.53 11.58

7.620 3.620 284.93 284.33 3276.6 125.72 36051 0.664 1.10 0.53 11.58

7.620 -3.620 284.43 284.33 3276.6 125.72 36051 0.664 1.10 0.53 11.58

23
Table 3 (continued)

Tube Specimen

Date: 8 February 1990

Time: 16:02:11

TA TB M PA PA-PB Vf f Wf

K K kg/h kPa kPa % %

283.77 284.33 31.02 3401.5 134.8 0.00 0.00485 13.50

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 283.70

2.515 -0.762 283 . 75 5.080 -0.381 283.76

7.620 -0.381 283 . 78 10.185 -0.381 283.80

12.700 -0.381 283.83

13.970 -0.381 283.85

7.595 -3.048 283.81

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 7. -0.020 0.191 283.84 282.93 3379.3 94.00 28007 0.664 1.10 0.51 11.58

1.288 0.191 283.86 282.97 3372.9 94.19 28005 0.664 1.10 0.51 11.58

2.586 0.140 283.84 283.01 3366.5 94.38 28003 0.664 1.10 0.51 11.58

3.810 0.165 283.85 283.05 3360.5 94.56 28000 0.664 1.10 0.51 11.58

5.042 0.191 283.86 283.09 3354.4 94.74 27998 0.664 1.10 0.51 11.58

6.350 0.203 283.88 283.13 3348.0 94.93 27996 0.664 1.10 0.51 11.58

7.620 0.191 283.85 283.17 3341.8 95.12 27994 0.664 1.10 0.51 11.58

8.903 0.152 283.83 283.21 3335.5 95.31 27991 0.664 1.10 0.51 11.58

10.160 0.216 283.87 283.25 3329.3 95.50 27989 0.664 1.10 0.51 11.58

11.430 0.191 283.85 283.29 3323.1 95.69 27987 0.664 1.10 0.51 11.58

12.637 0.140 283.84 283.33 3317.2 95.87 27985 0.664 1.10 0.51 11.58

13.912 0.165 283.87 283.37 3310.9 96.06 27982 0.664 1.10 0.51 11.58

15.240 0.165 283.89 283.42 3304.4 96.26 27980 0.664 1.10 0.51 11.58

-0.036 2.083 284.20 282.93 3379.4 94.00 28007 0.664 1.10 0.51 11.58

2.510 2.108 283.93 283.01 3366.9 94.37 28003 0.664 1.10 0.51 11.58

5.105 2.070 283.94 283.09 3354.1 94.75 27998 0.664 1.10 0.51 11.58

7.650 2.096 283.93 283.17 3341.7 95.12 27994 0.664 1.10 0.51 11.58

10.190 2.121 283.97 283.26 3329.2 95.50 27989 0.664 1.10 0.51 11.58

12.700 2.096 283.98 283.33 3316.9 95.88 27984 0.664 1.10 0.51 11.58

15.215 2.070 284.04 283.41 3304.5 96.25 27980 0.664 1.10 0.51 11.58

0.000 -2.070 283.87 282.93 3379.2 94.00 28007 0.664 1.10 0.51 11.58

7.620 -2.146 283.76 283.17 3341.8 95.12 27994 0.664 1.10 0.51 11.58

15.240 -2.096 283.82 283.42 3304.4 96.26 27980 0.664 1.10 0.51 11.58

7.620 3.620 284.14 283.17 3341.8 95.12 27994 0.664 1.10 0.51 11.58

7.620 -3.620 283.80 283.17 3341.8 95.12 27994 0.664 1.10 0.51 11.58

24
Tube Specimen

Date: 8 February 1990

Time: 16:07:01

Table 3 (continued)

TA TB M PA PA-PB Vf f Wf

K < kg/h kPa kPa X %

285.69 285.62 13.88 3436.4 30.5 0.00 0.00596 11.77

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 285.82

2.515 -0.762 285.86

5.080 -0.381 285.91

7.620 -0.381 285.90

10.185 -0.381 285.92

12.700 -0.381 285.97

13.970 -0.381 285.98

7.595 -3.048 285.97

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

-0.020 0.191 286.00 285.52 3431.6 41.81 12458 0.664 1.10 0.50 11.58

1.288 0.191 286.00 285.51 3430.1 41.83 12458 0.664 1.10 0.50 11.58

2.586 0.140 286.05 285.51 3428.5 41.85 12459 0.664 1.10 0.50 11.58

3.810 0.165 286.05 285.50 3427.1 41.86 12459 0.664 1.10 0.50 11.58

5.042 0.191 286.07 285.50 3425.7 41.88 12459 0.664 1.10 0.50 11.58

6.350 0.203 286.07 285.49 3424.1 41.90 12459 0.664 1.10 0.50 11.58

7.620 0.191 286.08 285.48 3422.6 41.92 12460 0.664 1.10 0.50 11.58

8.903 0.152 286.09 285.48 3421.1 41.93 12460 0.664 1.10 0.50 11.58

10.160 0.216 286.11 285.47 3419.7 41.95 12460 0.664 1.10 0.50 11.58

11.430 0.191 286.12 285.46 3418.2 41.97 12460 0.664 1.10 0.50 11.58

12.637 0.140 286.13 285.46 3416.8 41.98 12460 0.664 1.10 0.50 11.58

13.912 0.165 286.13 285.45 3415.3 42.00 12461 0.664 1.10 0.50 11.58

15.240 0.165 286.12 285.45 3413.7 42.02 12461 0.664 1.10 0.50 11.58

-0.036 2.083 286.24 285.52 3431.6 41.81 12458 0.664 1.10 0.50 11.58

2.510 2.108 286.19 285.51 3428.6 41.85 12459 0.664 1.10 0.50 11.58

5.105 2.070 286.20 285.49 3425.6 41.88 12459 0.664 1.10 0.50 11.58

7.650 2.096 286.19 285.48 3422.6 41.92 12460 0.664 1.10 0.50 11.58

10.190 2.121 286.21 285.47 3419.6 41.95 12460 0.664 1.10 0.50 11.58

12.700 2.096 286.21 285.46 3416.7 41.98 12460 0.664 1.10 0.50 11.58

15.215 2.070 286.19 285.45 3413.7 42.02 12461 0.664 1.10 0.50 11.58

0.000 -2.070 286.25 285.52 3431.6 41.81 12458 0.664 1.10 0.50 11.58

7.620 -2.146 286.26 285.48 3422.6 41.92 12460 0.664 1.10 0.50 11.58

15.240 -2.096 286.23 285.45 3413.7 42.02 12461 0.664 1.10 0.50 11.58

7.620 3.620 286.36 285.48 3422.6 41.92 12460 0.664 1.10 0.50 11.58

7.620 -3.620 286.32 285.48 3422.6 41.92 12460 0.664 1.10 0.50 11.58

25
Table 3 (continued)

Vf f Wf % %

0.00 0.00763 11.93

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 289.21

2.515 -0.762 289.23

5.080 -0.381 289.23

7.620 -0.381 289.23

10.185 -0.381 289.24

12.700 -0.381 289.21

13.970 -0.381 289.19

7.595 -3.048 289.38

Tube Specimen

Date: 8 February 1990

Time: 16:12:41

TA

K 289.36

TB

K 288.43

Mkg/h

6.25

PA kPa

3466.4

PA-PB

kPa

7.4

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

X Y Tw Tf P V RE PR Utu Wtf Wre

cm cm < K kPa m/s K K °/o -0.020 0.191 289.33 289.32 3465.3 18.89 5560 0.664 1.10 0.50 11.58

1.288 0.191 289.35 289.24 3464.9 18.89 5561 0.664 1.10 0.50 11.58

2.586 0.140 289.39 289.17 3464.5 18.88 5562 0.664 1.10 0.50 11.58

3.810 0.165 289.38 289.09 3464 .

1

18.88 5563 0.664 1.10 0.50 11.58

5.042 0.191 289.40 289.02 3463.7 18.88 5564 0.664 1.10 0.50 11.58

6.350 0.203 289.39 288.94 3463.3 18.88 5565 0.664 1.10 0.50 11.58

7.620 0.191 289.42 288.86 3463.0 18.87 5566 0.664 1.10 0.50 11.58

8.903 0.152 289.44 288.78 3462.6 18.87 5567 0.664 1.10 0.50 11.58

10.160 0.216 289.43 288.70 3462.2 18.87 5568 0.664 1.10 0.50 11.58

11.430 0.191 289.44 288.63 3461.8 18.86 5569 0.664 1.10 0.50 11.58

12.637 0.140 289.43 288.55 3461 .4 18.86 5570 0.664 1.10 0.50 11.58

13.912 0.165 289.39 288.48 3461.0 18.86 5571 0.664 1.10 0.50 11.58

15.240 0.165 289.30 288.39 3460.6 18.85 5572 0.664 1.10 0.50 11.58

-0.036 2.083 289.39 289.32 3465.3 18.89 5560 0.664 1.10 0.50 11.58

2.510 2.108 289.44 289.17 3464.5 18.88 5562 0.664 1.10 0.50 11.58

5.105 2.070 289.45 289.01 3463.7 18.88 5564 0.664 1.10 0.50 11.58

7.650 2.096 289.50 288.86 3462.9 18.87 5566 0.664 1.10 0.50 11.58

10.190 2.121 289.48 288.70 3462.2 18.87 5568 0.664 1.10 0.50 11.58

12.700 2.096 289.44 288.55 3461.4 18.86 5570 0.664 1.10 0.50 11.58

15.215 2.070 289.30 288.40 3460.6 18.85 5572 0.664 1.10 0.50 11.58

0.000 -2.070 289.68 289.32 3465.3 18.89 5560 0.664 1.10 0.50 11.58

7.620 -2.146 289.72 288.86 3463.0 18.87 5566 0.664 1.10 0.50 11.58

15.240 -2.096 289.51 288.39 3460.6 18.85 5572 0.664 1.10 0.50 11.58

7.620 3.620 289.56 288.86 3463.0 18.87 5566 0.664 1.10 0.50 11.58

7.620 -3.620 289.80 288.86 3463.0 18.87 5566 0.664 1.10 0.50 11.58

26
Table 3 (continued)

Tube Specimen

Date: 13 February 1990

Time: 16:03:24

TA TB M PA PA-PB V f Qt Wqt

K K kg/h kPa kPa % W %

291.06 343.16 5.71 3487.6 6.8 7.39 407.0 1.82

Hot-side Temperatures:

X Y Tw cm cm K

1 .270 -0 .762 311..47

2 .515 -0 .762 317..90

5 .080 -0 .381 327..64 7 .620 -0 .381 336..18 10 .185 -0 .381 344..82 12 .700 -0 .381 352..27

13 .970 -0 .381 353..44 7 .595 -3 .048 320..69

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Utw Wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(m2 K) K K % % %

-0.020 0.191 302.01 292.44 292.47 3486.6 17.34 5046 0.665 0 0.00 1.10 0.51 11.58 13.53 14.00

1.288 0.191 310.83 296.06 296.08 3486.3 17.56 5006 0.665 2681 17.56 1.10 0.60 11.58 9.91 10.54

2.586 0.140 317.45 300.20 300.23 3485.9 17.80 4960 0.665 2459 15.96 1.10 0.70 11.58 8.95 9.65

3.810 0.165 322.46 304.27 304.29 3485.6 18.04 4915 0.665 2380 15.31 1.10 0.84 11.58 8.96 9.66

5.042 0.191 326.73 308.42 308.44 3485.2 18.28 4870 0.665 2387 15.22 1.10 1.02 11.58 9.44 10.10

6.350 0.203 331.27 312.86 312.88 3484.9 18.54 4823 0.665 2390 15.09 1.10 1.23 11.58 10.10 10.73

7.620 0.191 335.57 317.19 317.22 3484.5 18.80 4779 0.665 2400 15.02 1.10 1.44 11.58 10.93 11.51 8.903 0.152 339.82 321.56 321.59 3484.2 19.05 4734 0.665 2411 14.95 1.10 1.62 11.58 11.72 12.26

10.160 0.216 344.13 325.83 325.86 3483.9 19.30 4692 0.665 2387 14.66 1.10 1.81 11.58 12.50 13.01 11.430 0.191 348.45 330.09 330.12 3483.5 19.55 4651 0.665 2349 14.31 1.10 2.01 11.58 13.35 13.83

12.637 0.140 351.58 334.08 334.11 3483.2 19.79 4613 0.665 2406 14.54 1.10 2.20 11.58 14.88 15.31 13.912 0.165 353.01 338.11 338.15 3482.8 20.03 4576 0.665 2645 15.85 1.10 2.40 11.58 18.48 18.83

15.240 0.165 349.55 341 .83 341 .86 3482.5 20.24 4542 0.665 4128 24.55 1.10 2.58 11.58 37.12 37.29

-0.036 2.083 304.08 292.44 292.47 3486.6 17.34 5046 0.665 0 0.00 1.10 0.51 11.58 11.43 11.98

2.510 2.108 316.25 299.95 299.98 3485.9 17.78 4962 0.665 2597 16.87 1.10 0.69 11.58 9.31 9.98

5.105 2.070 326.24 308.63 308.66 3485.2 18.30 4868 0.665 2484 15.83 1.10 1.03 11.58 9.76 10.40

7.650 2.096 334.94 317.29 317.32 3484.5 18.80 4778 0.665 2500 15.64 1.10 1.45 11.58 11.32 11.88

10.190 2.121 343.85 325.93 325.96 3483.8 19.31 4691 0.665 2437 14.97 1.10 1.81 11.58 12.75 13.25 12.700 2.096 351.70 334.28 334.31 3483.2 19.80 4612 0.665 2413 14.57 1.10 2.21 11.58 14.99 15.42

15.215 2.070 349.90 341.77 341.80 3482.5 20.24 4543 0.665 3943 23.46 1.10 2.58 11.58 35.23 35.42

0.000 -2.070 307.78 292.44 292.47 3486.6 17.34 5046 0.665 2070 13.66 1.10 0.57 11.58 10.46 11.07

7.620 -2.146 336.42 317.19 317.22 3484.5 18.80 4779 0.665 2294 14.35 1.10 1 .44 11.58 10.54 11.14 15.240 -2.096 349.37 341.83 341.86 3482.5 20.24 4542 0.665 4223 25.12 1.10 2.58 11.58 37.95 38.12

7.620 3.620 335.85 317.19 317.22 3484.5 18.80 4779 0.665 2365 14.80 1.10 1.44 11.58 10.80 11.39

7.620 -3.620 338.40 317.19 317.22 3484.5 18.80 4779 0.665 2080 13.01 1.10 1 .44 11.58 9.76 10.40

27
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 10:24:41

TA TB M PA PA-PB Vf Qt Wqt

K K kg/h kPa kPa % U %

295.04 551.91 5.25 3546.4 8.8 19.94 1870.0 1.14

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 396.76

2.515 -0.762 429.34

5.080 -0.381 482.83

7.620 -0.381 528.50

10.185 -0.381 570.10

12.700 -0.381 604.56

13.970 -0.381 609.95

7.595 -3.048 527.34

Insulated-Side Temperatures and Calculated Data:

X Y Tw Tf Taw P V RE cm cm K K K kPa m/s

-0.020 0.191 349.58 300.72 300.74 3545.4 16.12 4554

1.288 0.191 395.28 318.80 318.82 3544.9 17.08 4378

2.586 0.140 429.35 339.51 339.54 3544.4 18.17 4195

3.810 0.165 456.52 359.83 359.86 3544.0 19.24 4032

5.042 0.191 480.29 380.57 380.60 3543.5 20.34 3881 6.350 0.203 504.57 402.76 402.80 3543.0 21.51 3733

7.620 0.191 527.04 424.40 424.45 3542.6 22.65 3601 8.903 0.152 547.78 446.27 446.32 3542.1 23.81 3479

10.160 0.216 567.67 467.58 467.64 3541.7 24.93 3368

11.430 0.191 587.81 488.90 488.96 3541.2 26.06 3266

12.637 0.140 602.39 508.82 508.88 3540.8 27.11 3177

13.912 0.165 608.69 529.01 529.07 3540.3 28.18 3093

15.240 0.165 588.19 547.58 547.65 3539.8 29.16 3019

-0.036 2.083 353.41 300.72 300.74 3545.4 16.12 4554

2.510 2.108 427.02 338.26 338.29 3544.4 18.10 4205

5.105 2.070 481.37 381.63 381.67 3543.5 20.39 3873

7.650 2.096 527.06 424.91 424.96 3542.6 22.68 3598

10.190 2.121 568.19 468.09 468.14 3541.7 24.96 3366

12.700 2.096 603 . 79 509.84 509.90 3540.7 27.17 3173

15.215 2.070 591 .34 547.27 547.34 3539.8 29.15 3021 0.000 -2.070 360.51 300.72 300.74 3545.3 16.12 4554

7.620 -2.146 524.62 424.40 424.45 3542.6 22.65 3601 15.240 -2.096 583.08 547.58 547.65 3539.8 29.16 3019

7.620 3.620 530.73 424.40 424.45 3542.6 22.65 3601 7.620 -3.620 529.24 424.40 424.45 3542.6 22.65 3601

Uncerta i nt i es

PR h NU Utw Wtf Wre Wh Wnu W/(m2 K) K K % % %

0.665 0 0.00 1.10 0.74 11.58 5.35 6.45

0.665 2377 14.82 1.10 1 .93 11.58 5.70 6.74

0.665 2167 12.95 1.10 2.78 11.58 5.66 6.71 0.665 2056 11.81 1.10 3.71 11.58 6.03 7.02

0.665 2012 11.13 1.10 4.74 11.58 6.62 7.54

0.666 1984 10.55 1.10 5.88 11.58 7.37 8.20

0.666 1973 10.13 1.10 7.01 11.58 8.22 8.97

0.666 1990 9.86 1.10 7.91 11.58 9.04 9.73

0.666 2003 9.61 1.18 8.85 11.58 9.98 10.61 0.666 2001 9.32 1.26 9.84 11.58 11.00 11.58

0.666 2066 9.35 1.32 10.79 11.58 12.50 13.01 0.666 2269 10.00 1.34 11 .77 11.58 15.67 16.08

0.666 3594 15.47 1.26 12.67 11.58 32.06 32.26

0.665 0 0.00 1.10 0.74 11.58 5.26 6.38

0.665 2189 13.11 1.10 2.71 11.58 5.65 6.71 0.665 2013 11.11 1.10 4.79 11.58 6.66 7.57

0.666 1983 10.17 1.10 7.03 11.58 8.26 9.01 0.666 2002 9.60 1.18 8.87 11.58 10.00 10.63 0.666 2054 9.29 1.32 10.84 11.58 12.51 13.02 0.666 3334 14.35 1.27 12.66 11.58 29.60 29.82

0.665 2436 15.80 1.10 1 .44 11.58 7.16 8.02

0.666 2021 10.37 1.10 7.01 11.58 8.36 9.10

0.666 4113 17.70 1.24 12.67 11.58 36.50 36.68

0.666 1905 9.77 1.10 7.01 11.58 8.02 8.79

0.666 1932 9.91 1.10 7.01 11.58 8.10 8.86

28
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 10:33:45

TA TB M PA PA-PB Vf Qt Wqt

K K kg/h kPa kPa % W %

290.96 429.78 10.19 3542.6 24.4 19.95 1958.0 1.23

Hot -side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 347.72

2.515 -0.762 364.34

5.080 -0.381 391.73

7.620 -0.381 415.89

10.185 -0.381 437.44

12.700 -0.381 455.85

13.970 -0.381 459.34

7.595 -3.048 415.08

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU W tw Utf Wre Uh Wnu

cm cm K K K kPa m/s W/(m2 K) K K % % %

-0.020 0.191 319.84 293.82 293.90 3539.4 30.60 8966 0.665 0 0.00 1.10 0.58 11.58 6.65 7.57

1.288 0.191 346.39 303.58 303.66 3538.1 31.61 8773 0.665 4452 28.68 1.10 1.11 11.58 6.14 7.12

2.586 0.140 363.89 314.75 314.85 3536.8 32.77 8561 0.665 4154 26.12 1.10 1.54 11.58 6.01 7.01 3.810 0.165 377.47 325.72 325.82 3535.6 33.90 8365 0.665 4027 24.75 1.10 2.03 11.58 6.37 7.32

5.042 0.191 389.56 336.91 337.02 3534.4 35.06 8175 0.665 3996 24.00 1.10 2.58 11.58 6.97 7.85 6.350 0.203 402.35 348.89 349.00 3533.1 36.30 7983 0.665 3961 23.24 1.10 3.19 11.58 7.74 8.54

7.620 0.191 414.23 360.57 360.69 3531.9 37.51 7806 0.665 3958 22.70 1.10 3.80 11.58 8.62 9.35

8.903 0.152 425.23 372.37 372.50 3530.6 38.73 7637 0.665 4008 22.49 1.10 4.28 11.58 9.50 10.16

10.160 0.216 435.57 383.87 384.01 3529.4 39.92 7479 0.666 4068 22.36 1.10 4.79 11.58 10.54 11.14

11.430 0.191 446.33 395.38 395.52 3528.2 41.12 7330 0.666 4076 21 .96 1.10 5.32 11.58 11.62 12.17

12.637 0.140 454.02 406.12 406.27 3527.0 42.23 7196 0.666 4235 22.40 1.10 5.84 11.58 13.27 13.75 13.912 0.165 457.97 417.02 417.18 3525.8 43.36 7066 0.666 4636 24.08 1.10 6.37 11.58 16.59 16.98

15.240 0.165 446.30 427.04 427.20 3524.5 44.41 6952 0.666 7987 40.81 1.10 6.86 11.58 36.92 37.09

-0.036 2.083 322.99 293.82 293.90 3539.4 30.60 8966 0.665 0 0.00 1.10 0.58 11.58 6.30 7.26

2.510 2.108 362.77 314.08 314.17 3536.9 32.70 8574 0.665 4183 26.34 1.10 1.51 11.58 6.00 7.00

5.105 2.070 390.48 337.49 337.59 3534.4 35.12 8166 0.665 3972 23.83 1.10 2.61 11.58 6.99 7.86

7.650 2.096 414.81 360.85 360.96 3531.9 37.53 7802 0.665 3935 22.56 1.10 3.81 11.58 8.61 9.33

10.190 2.121 436.67 384.14 384 . 28 3529.4 39.95 7476 0.666 4003 21.99 1.10 4.80 11.58 10.42 11.03 12.700 2.096 455.75 406.68 406.83 3526.9 42.29 7189 0.666 4125 21 .80 1.10 5.86 11.58 13.05 13.54

15.215 2.070 449.70 426.87 427.04 3524.5 44.39 6954 0.666 6776 34.63 1.10 6.85 11.58 31.25 31 .46 0.000 -2.070 328.52 293.82 293.90 3539.3 30.60 8966 0.665 4402 28.97 1.10 0.88 11.58 7.68 8.48

7.620 -2.146 412.19 360.57 360.69 3531.9 37.51 7806 0.665 4115 23.60 1.10 3.80 11.58 8.88 9.58

15.240 -2.096 442.99 427.04 427.20 3524.5 44.41 6952 0.666 9660 49.36 1.10 6.86 11.58 44.43 44.58

7.620 3.620 418.75 360.57 360.69 3531.9 37.51 7806 0.665 3650 20.94 1.10 3.80 11.58 8.14 8.90

7.620 -3.620 417.47 360.57 360.69 3531 .9 37.51 7806 0.665 3732 21.41 1.10 3.80 11.58 8.27 9.02

29
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 10:41:50

TA TB M PA PA-PB Vf Qt Wqt

K 1C kg/h kPa kPa % W %

286.47 366.54 17.58 3540.2 59.1 19.96 1945.0 1.44

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 323.22

2.515 -0.762 333.12

5.080 -0.381 349.18

7.620 -0.381 363.39

10.185 -0.381 375.86

12.700 -0.381 386.95

13.970 -0.381 389.22

7.595 -3.048 343.89

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf T aw P V RE PR h NU Utw Wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(mJ K) K K % % %

-0.020 0.191 304.35 287.93 288.15 3531.7 51.88 15681 0.664 0 0.00 1.10 0.53 11.58 8.83 9.54

1.288 0.191 321.99 293.54 293.77 3528.7 52.92 15483 0.665 6698 44.10 1.10 0.75 11.58 6.85 7.74

2.586 0.140 332.58 299.97 300.21 3525.7 54.10 15263 0.665 6254 40.62 1.10 0.96 11.58 6.48 7.42

3.810 0.165 340.59 306.27 306.53 3522.9 55.26 15050 0.665 6067 38.86 1.10 1.22 11.58 6.65 7.56

5.042 0.191 347.55 312.71 312.98 3520.1 56.45 14840 0.665 6036 38.12 1.10 1.51 11.58 7.08 7.94

6.350 0.203 354.86 319.60 319.88 3517.1 57.72 14623 0.665 6003 37.36 1.10 1.86 11.58 7.66 8.47

7.620 0.191 361.47 326.32 326.61 3514.1 58.96 14418 0.665 6040 37.07 1.10 2.20 11.58 8.39 9.13

8.903 0.152 367.68 333.10 333.41 3511.2 60.22 14218 0.665 6126 37.08 1.10 2.48 11.58 9.13 9.81 10.160 0.216 373.55 339.72 340.03 3508.3 61.44 14030 0.665 6219 37.14 1.10 2.77 11.58 10.00 10.63 11.430 0.191 380.31 346.33 346.66 3505.4 62.67 13847 0.665 6116 36.06 1.10 3.08 11.58 10.76 11.35 12.637 0.140 385.20 352.51 352.86 3502.6 63.82 13681 0.665 6211 36.18 1.10 3.38 11.58 11.95 12.48

13.912 0.165 387.65 358.78 359.13 3499.7 64.99 13518 0.665 6588 37.92 1.10 3.68 11.58 14.38 14.83 15.240 0.165 378.77 364.54 364.91 3496.6 66.08 13372 0.665 10930 62.23 1.10 3.97 11.58 30.39 30.60

-0.036 2.083 307.55 287.93 288.15 3531.7 51.88 15681 0.664 0 0.00 1.10 0.53 11.58 7.81 8.60

2.510 2.108 331.88 299.58 299.83 3525.9 54.03 15276 0.665 6301 40.95 1.10 0.94 11.58 6.49 7.43

5.105 2.070 347.64 313.04 313.31 3519.9 56.51 14829 0.665 6079 38.37 1.10 1.53 11.58 7.14 7.99

7.650 2.096 361.26 326.48 326.77 3514.1 58.99 14413 0.665 6104 37.45 1.10 2.21 11.58 8.47 9.20

10.190 2.121 373.91 339.87 340.19 3508.2 61 .47 14025 0.665 6179 36.90 1.10 2.78 11.58 9.97 10.61 12.700 2.096 385.71 352.83 353.17 3502.5 63.88 13673 0.665 6163 35.88 1.10 3.39 11.58 11.93 12.46 15.215 2.070 380.85 364.44 364.81 3496.7 66.06 13374 0.665 9514 54.18 1.10 3.96 11.58 26.43 26.67

0.000 -2.070 313.69 287.93 288.15 3531.7 51.88 15681 0.664 5930 39.52 1.10 0.65 11.58 8.24 9.00

7.620 -2.146 360.27 326.32 326.61 3514.1 58.96 14418 0.665 6254 38.38 1.10 2.20 11.58 8.60 9.33

15.240 -2.096 376.68 364.54 364.91 3496.6 66.08 13372 0.665 12867 73.26 1.10 3.97 11.58 35.55 35.73

7.620 3.620 364.87 326.32 326.61 3514.1 58.96 14418 0.665 5503 33.77 1.10 2.20 11.58 7.87 8.66

7.620 -3.620 366.24 326.32 326.61 3514.1 58.96 14418 0.665 5312 32.60 1.10 2.20 11.58 7.69 8.49

30
Tube Specimen

Date: 9 March 1990

Time: 10:48:18

TA TB M PA PA-PB

K K kg/h kPa kPa

283.68 335.13 27.14 3538.6 124.8

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 310.09

2.515 -0.762 316.64

5.080 -0.381 327.26

7.620 -0.381 336.57

10.185 -0.381 344.43

12.700 -0.381 351.51

13.970 -0.381 352.94

7.595 -3.048 323.81

Table 3 (continued)

Vf Qt Uqt

% U %

19.95 1925.0 1.81

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Wtw Wtf Wre Wh Unu

cm cm K K < kPa m/s W/(m2 K) K K % % 7. -0.020 0.191 296.03 284.20 284.72 3519.9 79.34 24418 0.664 0 0.00 1.10 0.51 11.58 11.68 12.22

1.288 0.191 308.80 287.79 288.33 3513.7 80.46 24217 0.664 9137 60.92 1.10 0.60 11.58 7.96 8.74

2.586 0.140 315.79 291.90 292.46 3507.6 81.73 23992 0.665 8587 56.75 1.10 0.70 11.58 7.35 8.19

3.810 0.165 321.05 295.93 296.51 3501.8 82.97 23776 0.665 8338 54.62 1.10 0.84 11.58 7.35 8.19

5.042 0.191 325.61 300.05 300.65 3495.9 84.25 23559 0.665 8274 53.73 1.10 1.01 11.58 7.61 8.42

6.350 0.203 330.48 304.45 305.07 3489.7 85.61 23329 0.665 8183 52.62 1.10 1.22 11.58 7.98 8.76

7.620 0.191 334.82 308.75 309.39 3483.7 86.94 23109 0.665 8195 52.21 1.10 1 .44 11.58 8.51 9.24

8.903 0.152 338.76 313.09 313.75 3477.6 88.30 22893 0.665 8311 52.46 1.10 1.62 11.58 9.10 9.79

10.160 0.216 342.34 317.32 318.00 3471.7 89.62 22686 0.665 8476 53.01 1.10 1.80 11.58 9.86 10.50

11.430 0.191 346.78 321.55 322.25 3465.7 90.95 22483 0.665 8302 51.47 1.10 2.00 11.58 10.44 11.04

12.637 0.140 349.90 325.51 326.22 3459.9 92.20 22298 0.665 8399 51 .64 1.10 2.19 11.58 11.42 11.98

13.912 0.165 351.34 329.51 330.25 3453.9 93.48 22114 0.665 8816 53.76 1.10 2.39 11.58 13.48 13.95 15.240 0.165 344.65 333.20 333.95 3447.6 94.68 21948 0.665 14017 84.84 1.10 2.57 11.58 26.95 27.19

-0.036 2.083 299.04 284.20 284.72 3520.0 79.33 24418 0.664 0 0.00 1.10 0.51 11.58 9.66 10.31 2.510 2.108 315.29 291.65 292.21 3507.9 81.65 24005 0.665 8661 57.27 1.10 0.69 11.58 7.39 8.22

5.105 2.070 325.52 300.26 300.86 3495.6 84.31 23548 0.665 8377 54.38 1.10 1.02 11.58 7.69 8.49

7.650 2.096 334.45 308.85 309.49 3483.6 86.98 23104 0.665 8350 53.18 1.10 1.44 11.58 8.63 9.36

10.190 2.121 342.43 317.42 318.10 3471.5 89.65 22681 0.665 8477 53.01 1.10 1.81 11.58 9.88 10.52

12.700 2.096 350.14 325.71 326.42 3459.6 92.26 22289 0.665 8370 51 .44 1.10 2.20 11.58 11.44 12.00

15.215 2.070 346.27 333.13 333.89 3447.7 94.66 21951 0.665 12200 73.85 1.10 2.57 11.58 23.49 23.77

0.000 -2.070 304.64 284.20 284.72 3519.8 79.34 24418 0.664 7528 50.60 1.10 0.57 11.58 9.10 9.78

7.620 -2.146 333.80 308.75 309.39 3483.7 86.94 23109 0.665 8538 54.39 1.10 1.44 11.58 8.76 9.47

15.240 -2.096 343.12 333.20 333.95 3447.6 94.68 21948 0.665 16361 99.02 1.10 2.57 11.58 31.21 31.42

7.620 3.620 337.88 308.75 309.39 3483.7 86.94 23109 0.665 7316 46.61 1.10 1 .44 11.58 7.88 8.67

7.620 -3.620 339.26 308.75 309.39 3483.7 86.94 23109 0.665 6977 44.45 1.10 1 .44 11.58 7.65 8.45

31
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 10:54:34

TA TB

K K 281.76 317.18

M PA kg/h kPa

39.04 3535.8

PA-PB Vf kPa %

242.8 19.97

Qt Wqt

U %

1901.0 2.37

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 301 .79 2.515 -0.762 306.40

5.080 -0.381 313.99

7.620 -0.381 320.79

10.185 -0.381 325.97

12.700 -0.381 330.61

13.970 -0.381 331.76

7.595 -3.048 312.24

Insulated-Side Temperatures and Calculated Data: Uncertaint i es

X Y Tw Tf T aw P V RE PR h NU Utw Wtf Wre Wh Unu

cm cm K K K kPa m/s W/(m2 K) K K % 7. % -0.020 0.191 290.77 281.30 282.39 3498.8 113.69 35373 0.664 0 0.00 1.10 0.50 11.58 15.16 15.58

1.288 0.191 300.58 283.75 284.87 3486.9 115.04 35172 0.664 11749 79.06 1.10 0.53 11.58 9.43 10.09

2.586 0.140 305.62 286.56 287.70 3475.1 116.54 34946 0.664 11039 73.82 1.10 0.57 11.58 8.55 9.28

3.810 0.165 309.31 289.31 290.48 3464.0 118.01 34727 0.664 10726 71.29 1.10 0.64 11.58 8.39 9.13

5.042 0.191 312.42 292.12 293.32 3452.9 119.52 34506 0.665 10676 70.53 1.10 0.75 11.58 8.53 9.26

6.350 0.203 315.84 295.13 296.36 3441.0 121.14 34275 0.665 10534 69.14 1.10 0.88 11.58 8.74 9.45

7.620 0.191 318.91 298.06 299.32 3429.5 122.72 34052 0.665 10506 68.53 1.10 1.02 11.58 9.10 9.78

8.903 0.152 321.64 301.02 302.32 3417.9 124.33 33829 0.665 10618 68.82 1.10 1.14 11.58 9.55 10.21 10.160 0.216 324.05 303.90 305.23 3406.5 125.92 33613 0.665 10823 69.71 1.10 1.27 11.58 10.19 10.81 11.430 0.191 327.15 306.79 308.15 3394.9 127.52 33399 0.665 10583 67.73 1.10 1 .40 11.58 10.62 11.21 12.637 0.140 329.26 309.48 310.88 3384.0 129.03 33203 0.665 10680 67.95 1.10 1.53 11.58 11.45 12.01 13.912 0.165 330.20 312.21 313.64 3372.4 130.59 33007 0.665 11091 70.15 1.10 1.67 11.58 13.22 13.71 15.240 0.165 324.98 314.72 316.18 3360.4 132.08 32829 0.665 16844 105.98 1.10 1.80 11.58 24.94 25.20

-0.036 2.083 293.62 281.30 282.39 3498.9 113.68 35373 0.664 0 0.00 1.10 0.50 11.58 11 .73 12.27

2.510 2.108 305.27 286.39 287.53 3475.8 116.46 34959 0.664 11127 74.43 1.10 0.56 11.58 8.60 9.33

5.105 2.070 312.52 292.27 293.47 3452.3 119.60 34495 0.665 10705 70.70 1.10 0.75 11.58 8.56 9.29

7.650 2.096 318.95 298.13 299.39 3429.2 122.76 34047 0.665 10523 68.63 1.10 1.02 11.58 9.11 9.80

10.190 2.121 324.39 303.97 305.30 3406.2 125.96 33607 0.665 10668 68.70 1.10 1.27 11.58 10.09 10.71 12.700 2.096 329.77 309.62 311.02 3383.4 129.10 33193 0.665 10447 66.45 1.10 1.54 11.58 11.30 11.86

15.215 2.070 326.50 314.68 316.14 3360.6 132.06 32832 0.665 14396 90.58 1.10 1 .80 11.58 21 .43 21.73

0.000 -2.070 298.83 281.30 282.39 3498.6 113.69 35373 0.664 9002 60.91 1.10 0.53 11.58 10.09 10.71 7.620 -2.146 318.10 298.06 299.32 3429.5 122.72 34052 0.665 10959 71 .48 1.10 1.02 11.58 9.38 10.04 15.240 -2.096 323.67 314.72 316.18 3360.4 132.08 32829 0.665 19772 124.40 1.10 1 .80 11.58 28.98 29.21 7.620 3.620 322.19 298.06 299.32 3429.5 122.72 34052 0.665 8998 58.70 1.10 1.02 11.58 8.19 8.95

7.620 -3.620 322.96 298.06 299.32 3429.5 122.72 34052 0.665 8706 56.79 1.10 1.02 11.58 8.02 8.79

32
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 11:07:53

TA TB

K K 290.15 471.21

M PA kg/h kPa

7.57 3578.0

PA-PB Vf kPa %

15.5 19.97

Qt Wqt

U %

1896.0 1.18

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 363.59

2.515 -0.762 386.33

5.080 -0.381 423.55

7.620 -0.381 455.69

10.185 -0.381 485.05

12.700 -0.381 509.76

13.970 -0.381 514.31

7.595 -3.048 412.97

Insulated-Side Temperatures and Calculated Data: Uncertai nt i es

X Y Tw Tf Taw P V RE PR h NU Utw wtf Wre Wh Unu

cm cm K K K kPa m/s W/(m2 K) K K % °/o 7. -0.020 0.191 328.26 294.07 294.11 3576.0 22.53 6657 0.665 0 0.00 1.10 0.63 11.58 5.92 6.93

1.288 0.191 362.40 306.79 306.84 3575.2 23.49 6471 0.665 3317 21.21 1.10 1.40 11.58 5.86 6.88

2.586 0.140 386.32 321 .37 321.42 3574.4 24.59 6271 0.665 3041 18.85 1.10 1 .98 11.58 5.77 6.80

3.810 0.165 405.11 335.67 335.73 3573.6 25.67 6089 0.665 2904 17.48 1.10 2.63 11.58 6.10 7.09

5.042 0.191 421.50 350.27 350.33 3572.8 26.78 5915 0.665 2858 16.72 1.10 3.35 11.58 6.68 7.59

6.350 0.203 438.40 365.89 365.95 3572.0 27.96 5742 0.665 2826 16.05 1.10 4.14 11.58 7.41 8.24

7.620 0.191 454.09 381.12 381.20 3571.2 29.11 5584 0.665 2816 15.55 1.10 4.94 11.58 8.25 9.00

8.903 0.152 468.60 396.52 396.59 3570.4 30.28 5435 0.666 2843 15.28 1.10 5.57 11.58 9.06 9.75

10.160 0.216 482.58 411.52 411.60 3569.6 31.41 5298 0.666 2863 15.00 1.10 6.24 11.58 9.99 10.62

11.430 0.191 497.14 426.52 426.61 3568.8 32.55 5169 0.666 2844 14.55 1.10 6.93 11.58 10.93 11.51 12.637 0.140 507.97 440.54 440.63 3568.0 33.61 5056 0.666 2909 14.55 1.10 7.60 11.58 12.31 12.82

13.912 0.165 512.97 454.75 454.85 3567.2 34.69 4946 0.666 3152 15.42 1.10 8.29 11.58 15.21 15.64

15.240 0.165 498.20 467.82 467.93 3566.4 35.69 4850 0.666 4880 23.42 1.10 8.93 11.58 30.39 30.61 -0.036 2.083 331.47 294.07 294.11 3576.0 22.53 6657 0.665 0 0.00 1.10 0.63 11.58 5.74 6.77

2.510 2.108 384.50 320.49 320.55 3574.4 24.52 6283 0.665 3079 19.13 1.10 1.94 11.58 5.77 6.80

5.105 2.070 422.18 351.02 351.08 3572.8 26.83 5907 0.665 2862 16.72 1.10 3.38 11.58 6.72 7.62

7.650 2.096 453.93 381.48 381.56 3571.2 29.14 5580 0.665 2836 15.65 1.10 4.95 11.58 8.30 9.05

10.190 2.121 483.08 411.87 411.96 3569.6 31 .44 5295 0.666 2856 14.96 1.10 6.25 11.58 9.99 10.62

12.700 2.096 508.86 441.26 441.36 3568.0 33.67 5050 0.666 2896 14.47 1.10 7.64 11.58 12.33 12.85

15.215 2.070 500.70 467.60 467.71 3566.4 35.67 4852 0.666 4510 21.65 1.10 8.92 11.58 27.97 28.20

0.000 -2.070 338.35 294.07 294.11 3576.0 22.53 6657 0.665 3338 21 .95 1.10 1.07 11.58 7.37 8.20

7.620 -2.146 452.19 381.12 381.20 3571.2 29.11 5584 0.665 2891 15.97 1.10 4.94 11.58 8.40 9.14

15.240 -2.096 494.64 467.82 467.93 3566.4 35.69 4850 0.666 5531 26.54 1.10 8.93 11.58 34.28 34.47

7.620 3.620 457.76 381.12 381.20 3571.2 29.11 5584 0.665 2681 14.81 1.10 4.94 11.58 7.97 8.75

7.620 -3.620 457.65 381.12 381 .20 3571.2 29.11 5584 0.665 2685 14.83 1.10 4.94 11.58 7.98 8.75

33
Table 3 (continued)

Tube Specimen

Date: 16 February 1990

Time: 14:45:04

TA TB

K K 287.91 594.95

M PA kg/h kPa

8.57 3494.1

PA-PB V

f

kPa %

22.2 34.97

Qt Wqt

W %

3629.0 1.14

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 418.81

2.515 -0.762 457.21

5.080 -0.381 517.14

7.620 -0.381 569.60

10.185 -0.381 618.08

12.700 -0.381 658.80

13.970 -0.381 667.85

7.595 -3.048 515.39

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Wtw Wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(m2 K) K < % % %

-0.020 0.191 355.33 295.40 295.45 3491 .4 26.23 7516 0.665 0 0.00 1.10 0.82 11.58 4.81 6.01 1.288 0.191 415.32 317.32 317.39 3490.2 28.15 7163 0.665 3542 22.15 1.10 2.27 11.58 5.54 6.61 2.586 0.140 455.98 341.20 341.28 3489.1 30.24 6819 0.665 3167 18.86 1.10 3.24 11.58 5.58 6.64

3.810 0.165 486.09 364.46 364.54 3488.0 32.28 6519 0.665 3059 17.42 1.10 4.33 11.58 5.91 6.92

5.042 0.191 512.08 388.34 388.44 3486.9 34.38 6242 0.666 3062 16.70 1.10 5.52 11.58 6.45 7.39

6.350 0.203 539.50 414.10 414.21 3485.8 36.64 5973 0.666 3062 15.98 1.10 6.86 11.58 7.15 8.01 7.620 0.191 564.91 439.36 439.49 3484.7 38.85 5735 0.666 3078 15.43 1.17 8.18 11.58 7.98 8.75

8.903 0.152 589.28 464.97 465.12 3483 .

5

41.10 5515 0.666 3116 15.02 1.26 9.23 11.58 8.74 9.46

10.160 0.216 612.49 490.13 490.29 3482.4 43.32 5318 0.666 3177 14.77 1.36 10.34 11.58 9.64 10.29

11.430 0.191 635.90 515.69 515.87 3481.3 45.57 5134 0.666 3262 14.63 1.45 11.53 11.58 10.66 11.25 12.637 0.140 653.51 540.16 540.35 3480.2 47.72 4971 0.666 3466 15.06 1.52 12.71 11.58 12.16 12.68

13.912 0.165 663.19 565.57 565 . 78 3479.1 49.96 4815 0.666 3840 16.16 1.56 13.95 11.58 15.15 15.57

15.240 0.165 637.99 588.98 589.21 3477.9 52.02 4681 0.666 6002 24.55 1 .46 15.08 11.58 31.75 31.95

-0.036 2.083 371.07 295.40 295.45 3491.4 26.23 7516 0.665 0 0.00 1.10 0.82 11.58 4.61 5.85 2.510 2.108 451.27 339.78 339.86 3489.2 30.12 6838 0.665 3255 19.44 1.10 3.19 11.58 5.61 6.67

5.105 2.070 511.52 389.57 389.67 3486.9 34.48 6229 0.666 3109 16.92 1.10 5.59 11.58 6.53 7.46

7.650 2.096 562.91 439.96 440.08 3484.6 38.91 5729 0.666 3144 15.74 1.16 8.20 11.58 8.11 8.87

10.190 2.121 610.35 490.73 490.89 3482.4 43.37 5313 0.666 3251 15.09 1.35 10.37 11.58 9.83 10.47

12.700 2.096 652.23 541.43 541.63 3480.2 47.83 4963 0.666 3544 15.37 1.52 12.77 11.58 12.45 12.96

15.215 2.070 640.69 588.60 588.83 3478.0 51.99 4683 0.666 5695 23.30 1 .47 15.06 11.58 29.90 30.11 0.000 -2.070 393.98 295.40 295.45 3491.4 26.23 7516 0.665 3101 20.34 1.10 1.79 11.58 6.03 7.03

7.620 -2.146 570.27 439.36 439.49 3484.7 38.85 5735 0.666 2952 14.79 1.19 8.18 11.58 7.76 8.55

15.240 -2.096 639.24 588.98 589.21 3477.9 52.02 4681 0.666 5853 23.94 1.46 15.08 11.58 30.99 31 .20 7.620 3.620 571.62 439.36 439.49 3484.7 38.85 5735 0.666 2922 14.64 1.19 8.18 11.58 7.71 8.51 7.620 -3.620 589.02 439.36 439.49 3484.7 38.85 5735 0.666 2582 12.94 1 .26 8.18 11.58 7.13 7.99

34
Table 3 (continued)

Tube Specimen

Date: 16 February 1990

Time: 14:53:29

TA TB M PA PA-PB Vf Qt Wqt

K < kg/h kPa kPa % U %

285.37 502.70 12.50 3494.5 38.4 34.97 3745.0 1.16

Hot -side Temperatures:

X Y Tw cm cm K 1.270 -0.762 381.48

2.515 -0.762 408.07

5.080 -0.381 450.29

7.620 -0.381 487.81

10.185 -0.381 521.44

12.700 -0.381 549.29

13.970 -0.381 556.09

7.595 -3.048 424.13

Insulated-Side Temperatures and Calculated Data: Uncertainties

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

cm cm K K K kPa m/s W/(mJ K) < K % % %

-0.020 0.191 333.66 290.41 290.53 3489.6 37.64 11088 0.664 0 0.00 1.10 0.68 11.58 5.18 6.31 1.288 0.191 378.39 305.92 306.05 3487.6 39.64 10710 0.665 4949 31.72 1.10 1.64 11.58 5.62 6.68

2.586 0.140 407.04 322.81 322.95 3485.7 41.81 10328 0.665 4459 27.57 1.10 2.31 11.58 5.62 6.68

3.810 0.165 427.79 339.25 339.41 3483.9 43.93 9985 0.665 4342 25.96 1.10 3.08 11.58 5.93 6.94

5.042 0.191 445.84 356.14 356.32 3482.0 46.11 9660 0.665 4364 25.24 1.10 3.92 11.58 6.45 7.39

6.350 0.203 465.28 374.35 374.55 3480.1 48.46 9337 0.666 4364 24.40 1.10 4.86 11.58 7.11 7.97

7.620 0.191 483.12 392.22 392.43 3478.2 50.76 9044 0.666 4394 23.80 1.10 5.79 11.58 7.91 8.69

8.903 0.152 500.16 410.33 410.57 3476.2 53.10 8768 0.666 4457 23.41 1.10 6.54 11.58 8.66 9.38

10.160 0.216 516.36 428.11 428.37 3474.4 55.40 8516 0.666 4554 23.23 1.10 7.32 11.58 9.54 10.19

11.430 0.191 532.52 446.19 446.47 3472.5 57.75 8277 0.666 4696 23.28 1.10 8.17 11.58 10.56 11.16

12.637 0.140 544.68 463.49 463 . 79 3470.7 59.99 8063 0.666 5004 24.17 1.10 9.00 11.58 12.06 12.59

13.912 0.165 551.76 481.45 481.78 3468.8 62.32 7854 0.666 5517 25.96 1.11 9.88 11.58 14.95 15.38

15.240 0.165 532.06 498.01 498.36 3466.8 64.48 7672 0.666 8967 41.22 1.10 10.67 11.58 32.52 32.72

-0.036 2.083 348.71 290.41 290.53 3489.6 37.64 11088 0.664 0 0.00 1.10 0.68 11.58 4.78 5.99

2.510 2.108 403.60 321.80 321.95 3485.8 41.68 10350 0.665 4583 28.40 1.10 2.28 11.58 5.65 6.70

5.105 2.070 445.48 357.01 357.19 3481.9 46.22 9644 0.665 4428 25.57 1.10 3.96 11.58 6.52 7.45

7.650 2.096 481.87 392.64 392.86 3478.1 50.82 9037 0.666 4477 24.23 1.10 5.81 11.58 8.03 8.80

10.190 2.121 515.41 428.54 428.80 3474.3 55.46 8510 0.666 4628 23.59 1.10 7.34 11.58 9.67 10.32

12.700 2.096 544.37 464.39 464.69 3470.6 60.11 8052 0.666 5077 24.49 1.10 9.04 11.58 12.27 12.79

15.215 2.070 535.13 497.74 498.09 3466.8 64.44 7675 0.666 8228 37.83 1.10 10.66 11.58 29.66 29.88

0.000 -2.070 369.57 290.41 290.53 3489.5 37.64 11088 0.664 3990 26.45 1.10 1 .31 11.58 6.05 7.04

7.620 -2.146 487.27 392.22 392.43 3478.2 50.76 9044 0.666 4202 22.76 1.10 5.79 11.58 7.68 8.48

15.240 -2.096 533.47 498.01 498.36 3466.8 64.48 7672 0.666 8607 39.56 1.10 10.67 11.58 31.27 31.48

7.620 3.620 490.52 392.22 392.43 3478.2 50.76 9044 0.666 4063 22.01 1.10 5.79 11.58 7.51 8.33

7.620 -3.620 506.00 392.22 392.43 3478.2 50.76 9044 0.666 3509 19.01 1.10 5.79 11.58 6.87 7.76

35
Table 3 (continued)

Tube Specimen

Date: 16 February 1990

Time: 15:01:07

TA TB

K K 281.89 421.92

M PA kg/h kPa

19.63 3496.0

PA-PB Vf kPa %

76.0 34.96

Qt Wqt

U %

3786.0 1.23

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 349.23

2.515 -0.762 366.57

5.080 -0.381 394.40

7.620 -0.381 419.62

10.185 -0.381 441.29

12.700 -0.381 458.82

13.970 -0.381 463.15

7.595 -3.048 379.51

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf T aw P V RE PR h NU Utw Wtf Wre Wh Wnu

cm cm K < < kPa m/s W/(m2 K) K K % 7. %

-0.020 0.191 314.69 284.86 285.15 3485.4 58.09 17640 0.664 0 0.00 1.10 0.58 11.58 5.97 6.97

1.288 0.191 346.48 294.83 295.13 3481.7 60.15 17244 0.665 7049 46.29 1.10 1.11 11.58 5.80 6.83

2.586 0.140 365.55 305.68 306.01 3477.9 62.39 16832 0.665 6365 40.83 1.10 1.52 11.58 5.69 6.74

3.810 0.165 378.92 316.25 316.60 3474.4 64.57 16450 0.665 6225 39.02 1.10 2.00 11.58 5.92 6.93

5.042 0.191 390.78 327.10 327.48 3470.9 66.82 16078 0.665 6239 38.23 1.10 2.54 11.58 6.34 7.29

6.350 0.203 403.70 338.81 339.21 3467.2 69.24 15699 0.665 6208 37.15 1.10 3.14 11.58 6.87 7.76

7.620 0.191 415.19 350.29 350.72 3463.5 71.63 15347 0.665 6248 36.56 1 .10 3.74 11.58 7.55 8.37

8.903 0.152 426.44 361.93 362.39 3459.8 74.05 15009 0.665 6302 36.06 1.10 4.22 11.58 8.16 8.92

10.160 0.216 436.96 373.36 373.85 3456.2 76.43 14694 0.666 6419 35.96 1.10 4.72 11.58 8.90 9.61 11.430 0.191 447.35 384.97 385.49 3452.6 78.86 14389 0.666 6603 36.23 1.10 5.26 11.58 9.78 10.42

12.637 0.140 455.16 396.08 396.64 3449.1 81.18 14111 0.666 6992 37.63 1.10 5.80 11.58 11.03 11.61 13.912 0.165 459.47 407.63 408.22 3445.5 83.60 13836 0.666 7613 40.17 1.10 6.36 11.58 13.45 13.92 15.240 0.165 444.23 418.26 418.88 3441.7 85.85 13593 0.666 12050 62.46 1.10 6.88 11.58 28.27 28.50

-0.036 2.083 328.51 284.86 285.15 3485.5 58.09 17640 0.664 0 0.00 1.10 0.58 11.58 5.12 6.26

2.510 2.108 363.06 305.04 305.36 3478.2 62.25 16856 0.665 6556 42.11 1.10 1.50 11.58 5.74 6.78

5.105 2.070 390.21 327.66 328.04 3470.7 66.93 16059 0.665 6357 38.91 1.10 2.57 11.58 6.42 7.36

7.650 2.096 414.08 350.56 350.99 3463.4 71.68 15339 0.665 6386 37.34 1.10 3.75 11.58 7.67 8.47

10.190 2.121 436.03 373.63 374.12 3456.2 76.49 14686 0.666 6545 36.65 1.10 4.73 11.58 9.05 9.74

12.700 2.096 454.95 396.67 397.22 3449.0 81.30 14097 0.666 7084 38.08 1.10 5.83 11.58 11.21 11.77

15.215 2.070 446.90 418.09 418.71 3441.7 85.81 13597 0.666 10929 56.67 1.10 6.87 11.58 25.54 25.79

0.000 -2.070 347.53 284.86 285.15 3485.4 58.09 17640 0.664 5109 34.29 1.10 0.93 11.58 6.12 7.10

7.620 -2.146 417.68 350.29 350.72 3463.5 71.63 15347 0.665 6016 35.19 1.10 3.74 11.58 7.37 8.20

15.240 -2.096 444.64 418.26 418.88 3441.7 85.85 13593 0.666 11859 61 .47 1.10 6.88 11.58 27.85 28.08

7.620 3.620 422.07 350.29 350.72 3463.5 71.63 15347 0.665 5646 33.03 1.10 3.74 11.58 7.09 7.95 7.620 -3.620 434.92 350.29 350.72 3463.5 71.63 15347 0.665 4784 27.99 1.10 3.74 11.58 6.47 7.41

36
Table 3 (continued)

Tube Specimen

Date: 16 February 1990

Time: 15:07:14

TA TB M PA PA-PB Vf Qt Wqt

K K kg/h kPa kPa % W %

279.20 374.67 28.66 3499.3 139.9 34.98 3761.0 1.36

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 329.38

2.515 -0.762 341.39

5.080 -0.381 360.41

7.620 -0.381 377.98

10.185 -0.381 392.60

12.700 -0.381 404.48

13.970 -0.381 407.93

7.595 -3.048 342.42

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf T aw P V RE PR h MU Utw Wtf Wre Uh Wnu

cm cm K K K kPa m/s W/(m2 K) K K % % %

-0.020 0.191 302.98 280.80 281.39 3478.8 83.76 25996 0.664 0 0.00 1.10 0.54 11.58 7.08 7.94

1.288 0.191 326.83 287.56 288.18 3472.1 85.91 25591 0.664 9304 62.08 1.10 0.83 11.58 6.11 7.10

2.586 0.140 340.61 294.93 295.59 3465.4 88.24 25167 0.665 8362 54.90 1.10 1.08 11.58 5.88 6.89

3.810 0.165 349.19 302.11 302.79 3459.2 90.51 24768 0.665 8305 53.69 1.10 1 .39 11.58 6.05 7.04

5.042 0.191 357.09 309.47 310.20 3452.8 92.84 24369 0.665 8367 53.22 1.10 1.75 11.58 6.39 7.33

6.350 0.203 366.00 317.42 318.18 3446.1 95.37 23954 0.665 8316 52.01 1.10 2.15 11.58 6.82 7.71 7.620 0.191 373.80 325.21 326.01 3439.6 97.85 23564 0.665 8374 51.52 1.10 2.56 11.58 7.40 8.23

8.903 0.152 381.56 333.11 333.95 3433.0 100.38 23184 0.665 8424 51.00 1.10 2.88 11.58 7.92 8.70

10.160 0.216 388.62 340.86 341.75 3426.5 102.87 22824 0.665 8587 51.18 1.10 3.22 11.58 8.57 9.30

11.430 0.191 395.90 348.74 349.68 3420.0 105.41 22472 0.665 8778 51.52 1.10 3.59 11.58 9.30 9.97

12.637 0.140 401.08 356.28 357.26 3413.8 107.85 22147 0.665 9277 53.66 1.10 3.96 11.58 10.41 11.01 13.912 0.165 404.16 364.11 365.14 3407.3 110.39 21821 0.666 9935 56.63 1.10 4.34 11.58 12.42 12.94 15.240 0.165 392.33 371.33 372.40 3400.5 112.77 21531 0.666 15228 85.64 1.10 4.70 11.58 25.10 25.36

-0.036 2.083 317.88 280.80 281 .39 3478.9 83.76 25996 0.664 0 0.00 1.10 0.54 11.58 5.40 6.50

2.510 2.108 338.24 294.49 295.14 3465.8 88.10 25192 0.665 8719 57.30 1.10 1.07 11.58 5.96 6.97

5.105 2.070 356.73 309.85 310.58 3452.5 92.96 24348 0.665 8507 54.07 1.10 1.77 11.58 6.46 7.40

7.650 2.096 373.15 325.39 326.20 3439.4 97.91 23555 0.665 8524 52.42 1.10 2.57 11.58 7.49 8.31 10.190 2.121 388.21 341 .05 341.94 3426.4 102.93 22816 0.665 8698 51 .82 1.10 3.23 11.58 8.66 9.38

12.700 2.096 400.98 356.67 357.65 3413.5 107.97 22131 0.665 9378 54.20 1.10 3.98 11.58 10.54 11.14

15.215 2.070 394.47 371 .21 372.28 3400.6 112.73 21536 0.666 13793 77.59 1.10 4.69 11.58 22.68 22.97

0.000 -2.070 335.46 280.80 281.39 3478.7 83.77 25996 0.664 5856 39.67 1.10 0.73 11.58 6.20 7.17

7.620 -2.146 376.59 325.21 326.01 3439.6 97.85 23564 0.665 7912 48.68 1.10 2.56 11.58 7.15 8.00

15.240 -2.096 393.15 371.33 372.40 3400.5 112.77 21531 0.666 14621 82.23 1.10 4.70 11.58 24.17 24.44

7.620 3.620 380.52 325.21 326.01 3439.6 97.85 23564 0.665 7342 45.17 1.10 2.56 11.58 6.85 7.74

7.620 -3.620 392.42 325.21 326.01 3439.6 97.85 23564 0.665 6026 37.08 1.10 2.56 11.58 6.19 7.17

37
Table 3 (continued)

Tube Specimen

Date: 16 February 1990

Time: 15:13:12

TA TB M PA PA-PB Vf Qt Uqt

K K kg/h kPa kPa % U %

277.18 347.55 38.84 3502.2 237.0 34.98 3750.0 1.53

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 317.09

2.515 -0.762 326.09

5.080 -0.381 340.43

7.620 -0.381 353.91

10.185 -0.381 364.68

12.700 -0.381 373.01

13.970 -0.381 375.53

7.595 -3.048 328.57

Insulated-Side Temperatures and Calculated Data: Uncertai nt i es

X Y Tw Tf Taw P V RE PR h NU Utw Wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(m* K) X K % 7. %

-0.020 0.191 295.65 277.65 278.71 3466.5 112.66 35492 0.664 0 0.00 1.10 0.52 11.58 8.34 9.09

1.288 0.191 314.60 282.60 283.71 3455.3 115.00 35082 0.664 11606 78.30 1.10 0.69 11.58 6.54 7.47

2.586 0.140 325.25 288.00 289.16 3444.2 117.53 34647 0.664 10402 69.34 1.10 0.85 11.58 6.17 7.15 3.810 0.165 331.53 293.26 294.47 3433.8 119.99 34237 0.665 10369 68.33 1.10 1.06 11.58 6.28 7.24

5.042 0.191 337.39 298.65 299.91 3423.2 122.53 33827 0.665 10439 68.01 1.10 1.31 11.58 6.54 7.47

6.350 0.203 344.13 304.47 305.79 3412.1 125.28 33392 0.665 10342 66.52 1.10 1.60 11.58 6.87 7.76

7.620 0.191 349.77 310.17 311.55 3401.2 127.98 32976 0.665 10440 66.33 1.10 1 .90 11.58 7.36 8.20

8.903 0.152 355.38 315.95 317.39 3390.2 130.74 32567 0.665 10526 66.05 1.10 2.13 11.58 7.82 8.61 10.160 0.216 360.58 321.63 323.13 3379.5 133.47 32177 0.665 10717 66.44 1.10 2.39 11.58 8.39 9.13

11.430 0.191 366.03 327.40 328.96 3368.6 136.26 31792 0.665 10916 66.87 1.10 2.66 11.58 9.01 9.70

12.637 0.140 369.69 332.92 334.54 3358.3 138.94 31434 0.665 11533 69.86 1.10 2.93 11.58 10.00 10.63

13.912 0.165 372.14 338.64 340.33 3347.4 141.75 31072 0.665 12156 72.79 1.10 3.21 11.58 11.70 12.24 15.240 0.165 362.49 343.92 345.67 3336.1 144.40 30747 0.665 17999 106.66 1.10 3.47 11.58 22.67 22.96

-0.036 2.083 309.99 277.65 278.71 3466.6 112.66 35492 0.664 0 0.00 1.10 0.52 11.58 5.75 6.79

2.510 2.108 323.11 287.68 288.84 3444.9 117.38 34673 0.664 10934 72.94 1.10 0.84 11.58 6.30 7.26

5.105 2.070 336.85 298.93 300.19 3422.7 122.66 33806 0.665 10682 69.55 1.10 1.33 11.58 6.63 7.55 7.650 2.096 349.09 310.31 311.69 3401.0 128.05 32966 0.665 10670 67.76 1.10 1.90 11.58 7.47 8.29

10.190 2.121 360.32 321.77 323.27 3379.2 133.54 32168 0.665 10832 67.14 1.10 2.39 11.58 8.46 9.20

12.700 2.096 369.74 333.20 334.83 3357.8 139.08 31415 0.665 11603 70.24 1.10 2.94 11.58 10.09 10.71 15.215 2.070 364.24 343.83 345.59 3336.3 144.36 30752 0.665 16367 97.00 1.10 3.47 11.58 20.60 20.91 0.000 -2.070 328.40 277.65 278.71 3466.3 112.67 35492 0.664 6355 43.36 1.10 0.63 11.58 6.28 7.24

7.620 -2.146 352.26 310.17 311.55 3401.2 127.98 32976 0.665 9801 62.27 1.10 1 .90 11.58 7.09 7.96

15.240 -2.096 363.13 343.92 345.67 3336.1 144.40 30747 0.665 17342 102.76 1.10 3.47 11.58 21 .92 22.21 7.620 3.620 356.02 310.17 311.55 3401.2 127.98 32976 0.665 8973 57.00 1.10 1 .90 11.58 6.75 7.65 7.620 -3.620 368.52 310.17 311.55 3401.2 127.98 32976 0.665 7004 44.50 1.10 1.90 11.58 6.01 7.01

38
Tube Specimen

Date: 16 February 1990

Time: 15:26:58

Table 3 (continued)

TA TB

K K 285.13 566.24

M PA kg/h kPa

9.53 3542.9

PA-PB Vf kPa %

26.4 34.99

Qt Wqt

W %

3697.0 1.14

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 406.25

2.515 -0.762 441.54

5.080 -0.381 497.16

7.620 -0.381 545.99

10.185 -0.381 590.51

12.700 -0.381 627.48

13.970 -0.381 636.07

7.595 -3.048 466.52

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Wtw Utf Ure Uh Wnu

cm cm K K K kPa m/s W/(m2 K) K K % % %

-0.020 0.191 346.48 291.85 291.91 3539.7 28.45 8428 0.665 0 0.00 1.10 0.77 11.58 4.90 6.08

1.288 0.191 402.96 311.92 312.00 3538.3 30.38 8061 0.665 3885 24.58 1.10 2.09 11.58 5.55 6.62

2.586 0.140 440.44 333.79 333.88 3536.9 32.49 7699 0.665 3473 20.99 1.10 2.97 11.58 5.58 6.64

3.810 0.165 468.33 355.08 355.18 3535.6 34.54 7382 0.665 3348 19.40 1.10 3.97 11.58 5.89 6.90

5.042 0.191 492.42 376.95 377.06 3534.3 36.65 7087 0.665 3343 18.60 1.10 5.06 11.58 6.40 7.35

6.350 0.203 517.92 400.54 400.67 3532.9 38.92 6799 0.666 3334 17.80 1.10 6.28 11.58 7.07 7.94

7.620 0.191 541.43 423.67 423.81 3531.6 41.15 6542 0.666 3344 17.18 1.10 7.49 11.58 7.85 8.64

8.903 0.152 563.76 447.12 447.28 3530.3 43.42 6303 0.666 3384 16.75 1.16 8.45 11.58 8.59 9.32

10.160 0.216 585.19 470.15 470.33 3528.9 45.65 6089 0.666 3444 16.47 1.25 9.47 11.58 9.45 10.11 11.430 0.191 606.37 493.57 493.76 3527.6 47.91 5887 0.666 3542 16.38 1 .33 10.56 11.58 10.45 11.06

12.637 0.140 622.55 515.97 516.18 3526.3 50.08 5709 0.666 3756 16.85 1 .40 11.64 11.58 11.89 12.42

13.912 0.165 631.63 539.23 539.46 3525.0 52.33 5537 0.666 4135 17.98 1.43 12.78 11.58 14.71 15.15

15.240 0.165 607.35 560.67 56C.92 3523.6 54.41 5389 0.666 6425 27.20 1.34 13.81 11.58 30.61 30.82

-0.036 2.083 360.89 291.85 291 .91 3539.7 28.45 8428 0.665 0 0.00 1.10 0.77 11.58 4.66 5.89

2.510 2.108 436.56 332.49 332.57 3537.0 32.36 7720 0.665 3552 21.53 1.10 2.93 11.58 5.60 6.66

5.105 2.070 492.38 378.08 378.19 3534.3 36.75 7073 0.665 3380 18.77 1.10 5.12 11.58 6.47 7.41 7.650 2.096 539.88 424.22 424.36 3531.6 41.21 6536 0.666 3405 17.48 1.10 7.51 11.58 7.97 8.74

10.190 2.121 583.56 470.70 470.88 3528.9 45.70 6084 0.666 3511 16.78 1.24 9.50 11.58 9.61 10.26

12.700 2.096 621.88 517.13 517.34 3526.3 50.19 5700 0.666 3820 17.10 1.39 11.70 11.58 12.12 12.64

15.215 2.070 610.36 560.32 560.57 3523.6 54.38 5391 0.666 6043 25.59 1.35 13.79 11.58 28.59 28.81 0.000 -2.070 381.93 291.85 291.91 3539.6 28.45 8428 0.665 3458 22.85 1.10 1.65 11.58 6.06 7.05

7.620 -2.146 545.16 423.67 423.81 3531.6 41.15 6542 0.666 3242 16.65 1.10 7.49 11.58 7.69 8.50

15.240 -2.096 607.23 560.67 560.92 3523.6 54.41 5389 0.666 6442 27.27 1.34 13.81 11.58 30.68 30.89

7.620 3.620 548.68 423.67 423.81 3531.6 41.15 6542 0.666 3150 16.18 1.10 7.49 11.58 7.55 8.37

7.620 -3.620 563.20 423.67 423.81 3531.6 41.15 6542 0.666 2822 14.50 1.16 7.49 11.58 7.06 7.93

39
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 11:51:14

Vf Qt Wqt

% W %

60.73 6225.0 1.14

Hot-side Temperatures:

X Y Tw cm cm K

1 ..270 -0 .762 460..10

2..515 -0 .762 504..88

5..080 -0 .381 569..63

7..620 -0 .381 629..98

10..185 -0 .381 685..40

12..700 -0 .381 732..54

13..970 -0 .381 743..21

7..595 -3 .048 525..21

TA TB M PA PA-PB

K K kg/h kPa kPa

290.12 646.68 12.83 3545.6 51.1

Insulated-Side Temperatures and Calculated Data: Uncertai nt i es

X Y Tw Tf Taw P V RE PR h NU Utw Wtf Wre Uh Wnu

cm cm K K K kPa m/s W/(m2 K) K K % % % -0.020 0.191 374.13 301.33 301 .46 3539.5 39.52 11107 0.665 0 0.00 1.10 0.89 11.58 4.66 5.89

1.288 0.191 452.52 326.43 326.59 3536.9 42.78 10522 0.665 4726 28.99 1.10 2.59 11.58 5.39 6.49

2.586 0.140 502.80 353.78 353.96 3534.3 46.34 9962 0.665 4187 24.33 1.10 3.71 11.58 5.38 6.48

3.810 0.165 534.63 380.40 380.61 3531.8 49.81 9481 0.665 4141 22.90 1.10 4.95 11.58 5.68 6.73

5.042 0.191 561.67 407.74 407.98 3529.3 53.37 9040 0.666 4225 22.28 1.15 6.32 11.58 6.19 7.17

6.350 0.203 591.55 437.23 437.51 3526.7 57.22 8617 0.666 4273 21.48 1.27 7.85 11.58 6.86 7.75 7.620 0.191 621.05 466.14 466.46 3524.1 61.00 8244 0.666 4285 20.61 1 .39 9.37 11.58 7.60 8.41 8.903 0.152 648.85 495.46 495.82 3521.5 64.84 7904 0.666 4337 20.00 1.50 10.57 11.58 8.30 9.05

10.160 0.216 674.94 524.25 524.65 3519.0 68.62 7600 0.666 4432 19.66 1.61 11.85 11.58 9.13 9.82

11.430 0.191 703.11 553.51 553.96 3516.4 72.46 7319 0.666 4503 19.23 1.72 13.21 11.58 9.98 10.61 12.637 0.140 723.89 581.51 582.00 3514.0 76.14 7072 0.666 4742 19.57 1.80 14.56 11.58 11.26 11.82 13.912 0.165 735.20 610.59 611.13 3511.5 79.97 6836 0.666 5172 20.63 1.85 15.98 11.58 13.78 14.25 15.240 0.165 700.45 637.38 637.96 3508.8 83.52 6634 0.666 8040 31.12 1.71 17.27 11.58 28.55 28.78

-0.036 2.083 409.38 301.33 301.46 3539.5 39.51 11107 0.665 0 0.00 1.10 0.89 1 1.58 4.43 5.72

2.510 2.108 491.74 352.15 352.33 3534.4 46.13 9993 0.665 4462 26.01 1.10 3.65 11.58 5.46 6.54

5.105 2.070 555.24 409.15 409.39 3529.2 53.56 9019 0.666 4456 23.45 1.13 6.40 11.58 6.38 7.33 7.650 2.096 613.07 466.83 467.14 3524.1 61.09 8236 0.666 4540 21.82 1 .36 9.40 11.58 7.91 8.69

10.190 2.121 668.61 524.94 525.34 3518.9 68.71 7594 0.666 4650 20.61 1 .58 11.88 11.58 9.49 10.15 12.700 2.096 718.25 582.97 583.46 3513.9 76.34 7060 0.666 4989 20.55 1.78 14.63 1 1.58 11.81 12.35 15.215 2.070 701.67 636.94 637.53 3508.8 83.46 6637 0.666 7899 30.59 1.71 17.25 11.58 27.80 28.04

0.000 -2.070 445.58 301.33 301.46 3539.5 39.52 11107 0.665 3637 23.55 1.10 2.03 11.58 5.87 6.89

7.620 -2.146 635.00 466.14 466.46 3524.1 61.00 8244 0.666 3930 18.91 1 .45 9.37 11.58 7.20 8.06

15.240 -2.096 710.20 637.38 637.96 3508.8 83.52 6634 0.666 6954 26.92 1.75 17.27 11.58 24.93 25.19

7.620 3.620 619.13 466.14 466.46 3524.1 61 .00 8244 0.666 4339 20.87 1.38 9.37 11.58 7.66 8.47

7.620 -3.620 671.44 466.14 466.46 3524.1 61.00 8244 0.666 3232 15.55 1.59 9.37 11.58 6.46 7.40

40
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 12:00:30

TA TB M PA PA-PB V f Qt Wqt

< K kg/h kPa kPa % U % 287.17 542.00 18.49 3543.3 84.9 60.82 6405 .

1.16

Hot-side Temperatures:

X Y Tw

cm cm K 1.270 -0.762 415.88

2.515 -0.762 447.41

5.080 -0.381 493.28

7.620 -0.381 537.32

10.185 -0.381 576.53

12.700 -0.381 610.99

13.970 -0.381 619.32

7.595 -3.048 461 . 44

Insulated-Side Temperatures and Calculated Data:

X Y Tw Tf Taw P V RE cm cm K K K kPa m/s

-0.020 0.191 349.81 294 . 78 295.05 3532.5 55.83 16238

1.288 0.191 409.26 312.69 312.99 3528.2 59.23 15608

2.586 0.140 446.34 332.20 332.53 3524.0 62.93 14981 3.810 0.165 467.88 351.18 351.56 3520.0 66.55 14425 5.042 0.191 486.65 370.68 371.10 3516.0 70.26 13903

6.350 0.203 507.88 391.72 392.18 3511.7 74.28 13388

7.620 0.191 528.95 412.34 412.85 3507.6 78.23 12925 8.903 0.152 548.01 433.24 433.81 3503.4 82.24 12493

10.160 0.216 566.41 453.77 454.40 3499.3 86.19 12101 11.430 0.191 587.19 474.64 475.32 3495.2 90.21 11731 12.637 0.140 602.33 494.60 495.34 3491.3 94.07 11402

13.912 0.165 610.91 515.33 516.14 3487.1 98.08 11082

15.240 0.165 581.69 534.43 535.30 3482.8 101.80 10806

-0.036 2.083 387.54 294 . 78 295.05 3532.5 55.83 16238

2.510 2.108 437.24 331.03 331.36 3524.2 62.71 15016

5.105 2.070 480.89 371.69 372.11 3515.8 70.46 13878

7.650 2.096 522.43 412.83 413.34 3507.5 78.32 12915

10.190 2.121 561.95 454.27 454.89 3499.2 86.28 12092

12.700 2.096 597.73 495.64 496.39 3491.1 94.27 11385

15.215 2.070 582.98 534.12 534.99 3482.9 101.74 10810

0.000 -2.070 422.40 294.78 295.05 3532.4 55.83 16238

7.620 -2.146 540.05 412.34 412.85 3507.6 78.23 12925 15.240 -2.096 590.91 534.43 535.30 3482.8 101.80 10806

7.620 3.620 529.05 412.34 412.85 3507.6 78.23 12925 7.620 -3.620 577.12 412.34 412.85 3507.6 78.23 12925

Uncertainties

PR h NU Wtw Wtf Ui~e Wh Wnu W/(m2 K) K >£ v0

°/£ /

t

0 .665 0 0 . 00 1 .10 0 ,.73 11 .58 4. 87 6.,06

0 .665 6359 40. 16 1 .10 1 ,.88 11 .58 5. 41 6..50 0 .665 5633 34. 16 1 .10 2..66 11 .58 5. 36 6..46

0 .665 5641 32. 94 1 .10 3,.55 11 .58 5. 63 6..68

0 .665 5782 32. 55 1 .10 4..52 11 .58 6. 09 7..08

0 .666 5853 31

73 1 .10 5,.61 11 .58 6.,70 7..61

0 .666 5870 30. 72 1 .10 6,.70 11 .58 7. 38 8..21

0 .666 5980 30. 26 1 .10 7,.55 11 .58 8.,06 8..83

0 .666 6118 29. 99 1 .17 8..46 11 .58 8. 85 9..56

0 .666 6177 29. 35 1 .26 9,.44 11 .58 9. 61 10..26

0 .666 6471 29. 88 1 .32 10..40 11 .58 10. 76 11.35

0 .666 6967 31

27 1 .35 11.41 11 .58 13.,00 13..49

0 .666 11141 48. 76 1 .23 12..34 11 .58 27.,54 27,.77

0 .665 0 0 . 00 1 .10 0 .73 11 .58 4.,47 5..74

0 .665 6045 36. 74 1 .10 2,.63 11 .58 5.,44 6..52

0 .665 6146 34. 53 1 .10 4..57 11 .58 6.,29 7..25

0 .666 6247 32. 67 1 .10 6,.72 11 .58 7. 69 8..50

0 .666 6403 31. 36 1 .15 8,.49 11 .58 9.,17 9..85

0 .666 6827 31

48 1 .30 10..45 11 .58 11

31 11.87

0 .666 10863 47. 56 1 .24 12,.32 11 .58 26. 62 26..87

0 .665 4234 27. 80 1 .10 1

.49 11 .58 5. 84 6,.86

0 .666 5357 28. 04 1 .10 6,.70 11 .58 6. 98 7..86

0 .666 9293 40. 67 1 .27 12,.34 11 .58 23. 26 23..54

0 .666 5865 30. 70 1 .10 6,.70 11 .58 7. 37 8..21

0 .666 4149 21. 71 1 .22 6,.70 11 .58 6. 12 7..10

41
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 12:06:58

TA TB M PA PA-PB Vf at Wqt

K K kg/h kPa kPa % U %

284.41 453.07 28.60 3538.9 159.6 60.87 6552.0 1.21

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 377.21

2.515 -0.762 398.27

5.080 -0.381 428.65

7.620 -0.381 459.11

10.185 -0.381 484.92

12.700 -0.381 507.40

13.970 -0.381 512.92

7.595 -3.048 408.72

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Utw Wtf Wre Wh Wnu

cm cm K K < kPa m/s W/(mJ •<) K K % % 7. -0.020 0.191 328.86 288.84 289.45 3517.0 85.03 25463 0.664 0 0.00 1.10 0.61 11.58 5.30 6.41 1.288 0.191 371.55 300.65 301.31 3509.4 88.63 24797 0.665 8918 57.83 1.10 1.29 11.58 5.49 6.56

2.586 0.140 398.31 313.51 314.23 3501.8 92.55 24105 0.665 7801 49.18 1.10 1.79 11.58 5.35 6.45

3.810 0.165 411.29 326.03 326.81 3494.6 96.38 23475 0.665 7947 48.80 1.10 2.37 11.58 5.58 6.64

5.042 0.191 423.36 338.88 339.73 3487.4 100.32 22867 0.665 8173 48.90 1.10 3.01 11.58 5.97 6.98

6.350 0.203 437.55 352.75 353.67 3479.8 104.58 22252 0.665 8259 48.09 1.10 3.72 11.58 6.48 7.41 7.620 0.191 451.73 366.34 367.33 3472.4 108.78 21685 0.665 8261 46.88 1.10 4.44 11.58 7.05 7.92

8.903 0.152 463.91 380.12 381.19 3464.8 113.06 21145 0.666 8446 46.74 1.10 5.00 11.58 7.66 8.47

10.160 0.216 475.92 393.64 394.80 3457.5 117.27 20645 0.666 8644 46.71 1.10 5.60 11.58 8.35 9.10

11.430 0.191 490.30 407.39 408.63 3450.1 121.57 20165 0.666 8657 45.69 1.10 6.25 11.58 8.96 9.66

12.637 0.140 499.85 420.54 421.87 3443.0 125.70 19730 0.666 9082 46.90 1.10 6.89 11.58 9.99 10.63

13.912 0.165 505.64 434.19 435.61 3435.6 130.01 19301 0.666 9645 48.73 1.10 7.56 11.58 11.87 12.41 15.240 0.165 483.70 446.77 448.28 3427.8 134.02 18925 0.666 14930 73.97 1.10 8.17 11.58 24.19 24.46

-0.036 2.083 367.85 288.84 289.45 3517.1 85.03 25463 0.664 0 0.00 1.10 0.61 11.58 4.53 5.79

2.510 2.108 390.48 312.74 313.46 3502.2 92.32 24145 0.665 8500 53.68 1.10 1.76 11.58 5.45 6.54

5.105 2.070 418.14 339.55 340.40 3487.1 100.52 22836 0.665 8798 52.57 1.10 3.04 11.58 6.19 7.16

7.650 2.096 446.37 366.66 367.66 3472.2 108.88 21672 0.665 8858 50.24 1.10 4.45 11.58 7.37 8.20

10.190 2.121 472.98 393.97 395.13 3457.3 117.37 20634 0.666 9007 48.65 1.10 5.62 11.58 8.62 9.34

12.700 2.096 496.69 421.22 422.56 3442.6 125.91 19708 0.666 9548 49.25 1.10 6.92 11.58 10.45 11.06

15.215 2.070 484.52 446.57 448.08 3427.9 133.96 18931 0.666 14636 72.53 1.10 8.16 11.58 23.52 23.79

0.000 -2.070 398.88 288.84 289.45 3516.9 85.03 25463 0.664 5041 33.54 1.10 1.05 11.58 5.83 6.85

7.620 -2.146 460.17 366.34 367.33 3472.4 108.78 21685 0.665 7510 42.62 1.10 4.44 11.58 6.68 7.59

15.240 -2.096 490.89 446.77 448.28 3427.8 134.02 18925 0.666 12408 61 .47 1.10 8.17 11.58 20.44 20.76

7.620 3.620 452.83 366.34 367.33 3472.4 108.78 21685 0.665 8154 46.27 1.10 4.44 11.58 7.00 7.87

7.620 -3.620 495.00 366.34 367.33 3472.4 108.78 21685 0.665 5461 30.99 1.10 4.44 11.58 5.76 6.80

42
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 12:13:23

TA TB

K K 282.80 406.89

M PA kg/h kPa

38.32 3540.3

PA-PB Vf kPa %

261.1 60.88

Ot Wqt

U %

6443.0 1.28

Hot-side Temperatures:

X Y Tw cm cm K 1.270 -0.762 356.43

2.515 -0.762 372.11

5.080 -0.381 395.05

7.620 -0.381 418.44

10.185 -0.381 437.42

12.700 -0.381 453.84

13.970 -0.381 458.21

7.595 -3.048 382.67

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Utw wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(m2 K) K K 7. % % -0.020 0.191 317.27 285.41 286.48 3503.2 113.04 34390 0.664 0 0.00 1.10 0.56 11.58 5.83 6.86

1.288 0.191 351.25 294.04 295.19 3490.8 116.81 33721 0.665 10986 72.27 1.10 1.00 11.58 5.61 6.67

2.586 0.140 372.36 303.44 304.67 3478.6 120.89 33022 0.665 9527 61.41 1.10 1.35 11.58 5.40 6.49

3.810 0.165 381.51 312.58 313.90 3467.0 124.88 32366 0.665 9764 61.69 1.10 1.76 11.58 5.58 6.65

5.042 0.191 390.20 321.98 323.38 3455.4 128.99 31725 0.665 10057 62.30 1.10 2.22 11.58 5.91 6.92

6.350 0.203 401.06 332.10 333.60 3443.0 133.45 31066 0.665 10099 61.26 1.10 2.74 11.58 6.32 7.28

7.620 0.191 411.55 342.03 343.63 3431.0 137.85 30451 0.665 10093 60.02 1.10 3.26 11.58 6.80 7.70

8.903 0.152 420.40 352.09 353.79 3418.9 142.34 29856 0.665 10313 60.13 1.10 3.68 11.58 7.33 8.17

10.160 0.216 429.24 361.96 363 . 78 3407.0 146.78 29299 0.666 10532 60.27 1.10 4.12 11.58 7.93 8.71 11.430 0.191 440.41 372.00 373.92 3395.1 151.31 28757 0.666 10456 58.73 1.10 4.59 11.58 8.40 9.14

12.637 0.140 447.31 381.59 383.63 3383.7 155.68 28261 0.666 10937 60.38 1.10 5.06 11.58 9.29 9.96

13.912 0.165 451.63 391.56 393.72 3371.6 160.25 27767 0.666 11468 62.21 1.10 5.55 11.58 10.85 11.44

15.240 0.165 433.74 400.73 403.01 3359.1 164.56 27330 0.666 16917 90.32 1.10 6.00 11.58 20.94 21.25

-0.036 2.083 352.18 285.41 286.48 3503.3 113.04 34390 0.664 0 0.00 1.10 0.56 11.58 4.63 5.87

2.510 2.108 365.94 302.88 304.10 3479.3 120.64 33063 0.665 10411 67.19 1.10 1.33 11.58 5.51 6.59

5.105 2.070 386.06 322.46 323.86 3454.8 129.21 31692 0.665 10814 66.92 1.10 2.24 11.58 6.11 7.09

7.650 2.096 407.35 342.26 343.86 3430.7 137.96 30436 0.665 10799 64.19 1.10 3.27 11.58 7.08 7.95 10.190 2.121 427.51 362.20 364.02 3406.8 146.88 29286 0.666 10860 62.12 1.10 4.13 11.58 8.11 8.87

12.700 2.096 445.42 382.09 384.14 3383.1 155.90 28236 0.666 11356 62.63 1.10 5.09 11.58 9.60 10.26

15.215 2.070 434.83 400.58 402.86 3359.3 164.49 2733 7 0.666 16402 87.59 1.10 6.00 11.58 20.16 20.48

0.000 -2.070 385.95 285.41 286.48 3503.0 113.05 34390 0.664 5454 36.56 1.10 0.85 11.58 5.85 6.87

7.620 -2.146 418.73 342.03 343.63 3431.0 137.85 30451 0.665 9128 54.28 1.10 3.26 11.58 6.45 7.39

15.240 -2.096 439.16 400.73 403.01 3359.1 164.56 27330 0.666 14381 76.78 1.10 6.00 11.58 18. 14 18.49

7.620 3.620 413.64 342.03 343.63 3431.0 137.85 30451 0.665 9791 58.22 1.10 3.26 11.58 6.69 7.60

7.620 -3.620 452.55 342.03 343.63 3431.0 137.85 30451 0.665 6294 37.43 1.10 3.26 11.58 5.53 6.60

43
Table 3 (continued)

Tube Specimen

Date: 9 March 1990

Time: 12:24:05

TA TB

K K 288.28 589.06

M PA kg/h kPa

15.56 3569.7

PA-PB Vf kPa %

67.0 60.86

Qt Wqt

W % 6369.0 1.15

Hot-side Temperatures:

X Y Tw cm cm K

1..270 -0 .762 435..29

2..515 -0 .762 473..38

5..080 -0 .381 527,.92

7,.620 -0 .381 579,.27

10,.185 -0 .381 626,.12

12,.700 -0 .381 666..97

13,,970 -0 .381 676..82

7..595 -3 .048 518,.73

Insulated-Side Temperatures and Calculated Data: Uncertainties

X Y Tw Tf Taw P V RE PR h NU Wtw wtf Wre Wh Wnu

cm cm K K K kPa m/s W/(mJ K) K K % % %

-0.020 0.191 359.17 297.46 297.65 3561.4 47.04 13589 0.665 0 0.00 1.10 0.80 11.58 4.77 5.98

1.288 0.191 428.28 318.63 318.84 3558.0 50.38 12974 0.665 5563 34.69 1.10 2.20 11.58 5.40 6.49

2.586 0.140 471.89 341.68 341.93 3554.6 54.01 12373 0.665 4906 29.18 1.10 3.13 11.58 5.37 6.46

3.810 0.165 498.25 364.12 364.40 3551.4 57.55 11849 0.665 4876 27.78 1.10 4.18 11.58 5.65 6.70

5.042 0.191 520.67 387.17 387.48 3548.2 61.20 11362 0.665 4988 27.26 1.10 5.34 11.58 6.13 7.11 6.350 0.203 546.02 412.03 412.39 3544.8 65.13 10888 0.666 5039 26.39 1.10 6.62 11.58 6.76 7.66

7.620 0.191 570.54 436.40 436.80 3541.5 69.00 10466 0.666 5067 25.51 1.19 7.91 11.58 7.48 8.31 8.903 0.152 593.50 461.12 461.57 3538.1 72.93 10076 0.666 5147 24.95 1.28 8.92 11.58 8.18 8.94

10.160 0.216 615.46 485.38 485.88 3534.8 76.79 9725 0.666 5260 24.60 1.37 9.99 11.58 8.98 9.68

11.430 0.191 640.09 510.05 510.60 3531.5 80.72 9397 0.666 5307 23.99 1 .47 11.15 11.58 9.76 10.40 12.637 0.140 658.12 533.65 534.24 3528.4 84.49 9107 0.666 5557 24.35 1 .54 12.28 11.58 10.94 11.52 13.912 0.165 668.29 558.15 558.81 3525.0 88.42 8827 0.666 5997 25.46 1.58 13.48 11.58 13.25 13.73 15.240 0.165 636.92 580.73 581.45 3521.6 92.05 8587 0.666 9264 38.27 1.46 14.57 11.58 27.21 27.45

-0.036 2.083 395.78 297.46 297.65 3561.5 47.04 13589 0.665 0 0.00 1.10 0.80 11.58 4.46 5.73

2.510 2.108 462.07 340.31 340.55 3554.8 53.79 12407 0.665 5237 31.24 1.10 3.09 11.58 5.44 6.53

5.105 2.070 514.60 388.36 388.68 3548.1 61.38 11338 0.666 5280 28.79 1.10 5.40 11.58 6.32 7.28

7.650 2.096 563.48 436.98 437.38 3541.4 69.09 10456 0.666 5375 27.03 1.16 7.93 11.58 7.79 8.58

10.190 2.121 609.86 485.96 486.46 3534.8 76.88 9717 0.666 5524 25.82 1.35 10.02 11.58 9.34 10.01 12.700 2.096 652.68 534.88 535.48 3528.2 84.69 9092 0.666 5870 25.68 1.52 12.34 11.58 11.51 12.06

15.215 2.070 637.94 580.37 581 .08 3521.6 91.99 8591 0.666 9117 37.68 1.46 14.55 11.58 26.54 26.78

0.000 -2.070 429.40 297.46 297.65 3561.4 47.04 13589 0.665 4070 26.57 1.10 1.73 11.58 5.86 6.88

7.620 -2.146 583.15 436.40 436.80 3541.5 69.00 10466 0.666 4631 23.31 1.24 7.91 11.58 7.08 7.95 15.240 -2.096 646.52 580.73 581.45 3521.6 92.05 8587 0.666 7897 32.62 1 .49 14.57 11.58 23.46 23.73

7.620 3.620 570.09 436.40 436.80 3541.5 69.00 10466 0.666 5085 25.60 1.19 7.91 11.58 7.50 8.32

7.620 -3.620 618.70 436.40 436.80 3541.5 69.00 10466 0.666 3726 18.76 1 .38 7.91 11.58 6.30 7.26

44
Table 4. Uncertainties in data analysis parameters

and calculated quantities

Uncertainty

Parameter

Major Source of

Uncertainty

Magnitude of

Uncertainty

Estimated or

Calculated

Tube Inner Diameter,

Wdh

Measurement 2% Estimated

Length of Heated

Zone , Wp

Measurement 1 mm Estimated

Location of Temperature

Probe, W]^ oc

Measurement 1 mm Estimated

Tube-to-Tube Flow

Uniformity, Wfu

Manifold Uniformity 5% Estimated

Pressure Loss

Coefficient,

Flow Geometry 0.2 Estimated

Fluid Temperature, Wt f Flow Uniformity 0.5-17.3 K Calculated

Total Heat Flow, Wq t Inlet and outlet

Temperature

1. 1-2.4% Calculated

Fluid Velocity, Wv Flow Uniformity 5. 5-6.0% Calculated

Friction Factor, Wf Entrance and Exit

Losses

12-14% for

Re>3000

37% at Re=2200

Calculated

Heat Transfer

Coefficient,

Flow Uniformity 6-13% for

0 . 2<x/L<0 .

Calculated

Reynolds Number, Wre Viscosity Function,

Flow Uniformity

12% Calculated

Nusselt Number, Wnu Flow Uniformity 6-13% for Calculated

0 . 2<x/L<0 .

45
480 VAC

75 A

Single Phase

Helium

Gas Supply

13.8 MPa (2000 psl)

1100 rn3 (39 000 set)

Pressure

Regulator

Valve 3

Radiant Heat

Heat Exchanger

Specimen

THTHTHTHTJ

Specimen Furnace

Section

Figure 1

.

Helium flow loop.

Vent

i

Flow

Meter

J

Flow

Control

Valve 4

Water

Bath

46
Figure 2. Specimen furnace, showing location of inlet gas temperature

and upstream pressure (A)

and outlet gas temperature and

downstream pressure (B)

47
3.8 mm

2.0 mm O.D

1 .0 mm I.D. (20 req'd)

3.2 mm

Figure 3. Tube specimen.

48
Quartz Sleeve

NQTE;

All dimensions in mm.

Figure 4. Technique for mounting thermocouples on tube specimen,

49
0.010

0.008

0.006

0.004

0.002

0.000

Figure 5. Friction factor (f) as a function of Reynolds number (Re)

for experiment 1, no heating.

50
T./T,

Figure 6. Percent difference between predicted and measured pressure drop

(Pq-Pi) as a function of wall-to-gas temperature ratio (Tw/Tf)

for heat transfer experiments.

51
T./T,

Figure 7. Percent difference between predicted and measured pressure drop

(Pq-Pj_) as a function of wali-to-gas temperature ratio (Tw/Tf)

for heat transfer experiments, using method of Rohsenow and

Choi to account for variable property effects.
Figure 8. Wall (Tw ) and gas (Tf) temperatures as a function of x/L;

experiment 5, 12.8 kg/h helium flow, and y/W = 0.

53
Figure 9. Wall temperature (Tw ) as a function of y/W at several x/L

locations; experiment 5, 12.8 kg/h helium flow.

54
X/

CM

£

n

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

coefficient (h) as a function of x/L; experiment 5, 12.8 kg/h

helium flow and y/W = 0.

55
Z5

z

Figure 11. Reynolds number (Re) and Nusselt number (Nu) as a function of

x/L; experiment 5, 12.8 kg/h helium flow and y/W = 0.

56
Figure 12. Modified Nusselt number (Num ) as a function of Reynolds number

(Re); all heated experiments with 0.2 < x/L <0.8 and y/W = 0.

57

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NISTIR 3941

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBLICATION DATE

June 1990

ID SUBTITLE

lT TRANSFER IN A COMPACT TUBULAR HEAT EXCHANGER WITH HELIUM GAS AT 3.5 MPa

« (S)

lglas A. Olson & Michael P. Glover

C MING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

) ARTMENT OF COMMERCE

3 XL INSTITUTE OF STANDARDS AND TECHNOLOGY

H tSBURG, MD 20899

f (RING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

f:ional Aeronautics and Space Administration

igley Research Center

mpton, Virginia 23665

7. CONTRACT/GRANT NUMBER

L7400C

8. TYPE OF REPORT AND PERIOD COVERED

•I MENTARY NOTES

n iCT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

* fURE SURVEY, MENTION IT HERE.)

We have constructed a compact heat exchanger consisting of

circular tubes in parallel brazed to a grooved base plate. This

tube specimen heat exchanger was tested in an apparatus which

radiatively heated the specimen on one side at a heat flux of

up to 54 W/cm^, and cooled the specimen with helium gas at 3.5 MPa

and Reynolds numbers of 3000 to 35 000. The measured friction

factor of the tube specimen was lower than that of a circular tube

with fully developed turbulent flow, although our uncertainty was

high due to entrance and exit losses. The measured Nusselt number,

when modified to account for differences in fluid properties

between the wall and the cooling fluid, agreed with past

correlations for fully developed turbulent flow in circular tubes.

' )RDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITAUZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

;>paratus; compact heat exchanger; circular tube; convection heat transfer;

liction factor; high temperature; National Aerospace Plane; radiative furnace;

urbulent flow; variable property effects.

BIUTY

JNUMITED

OR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS).

5RDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

VASHINGTON, DC 20402. 3RDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

68

IS. PRICE

NIC FORM

RNMENT PRINTING OFFICE: 1990-776-118/25134
.