PB 161623

92o. 122

A SURVEY OF THE LITERATURE ON

HEAT TRANSFER FROM SOLID

SURFACES TO CRYOGENIC FLUIDS

BY

R.J.RICHARDS, W.G. STEWARD, R.B.JACOBS

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical ^V^ete

October 1961

A SURVEY OF THE LITERATURE ON

HEAT TRANSFER FROM SOLID SURFACES

TO CRYOGENIC FLUIDS

by - R. J. Richards, W. G. Steward, R. B. Jacobs

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific dat§ that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

DISTRIBUTED BY

UNITED STATES DEPARTMENT OF COMMERCE

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WASHINGTON 25, D. C.

Price $1.25

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A SURVEY OF THE LITERATURE ON

HEAT TRANSFER FROM SOLID SURFACES

TO CRYOGENIC FLUIDS

by

R. J. Richards, W. G, Steward, R. B„ Jacobs

Cryogenic Engineering Laboratory

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A bibliography of 156 references on heat transfer from solid

surfaces to fluids and related phenonaena is presented. Heat

transfer data obtained from experimental work on cryogenic fluids are presented in graphical form. The theoretical and

empirical formulations appearing in the references are presented.

In those cases where sufficient information is available to make

numerical computations, the fornnulations are presented graphically to permit comparison with the results of the experimental

work.

Ill CONTENTS

Page

Abstract , H

1. Introduction 1

2. Nomenclature . 2

3. Graphical Presentations 4

Figures

1. Calculated Heat Transfer Rate for Liquid Helium 6

2. Experimental Heat Transfer Rate for Liquid

Helium 7

. 3. Calculated Heat Transfer Rate for Liquid Hydrogen 8

4. Experimental Heat Transfer Rate for Liquid

Hydrogen 9

5. Calculated Heat Transfer Rate for Liquid Oxygen 10

6. Experimental Heat Transfer Rate for Liquid

Oxygen 1

1

7. Calculated Heat Transfer Rate for Liquid Nitrogen 12

8. Experimental Heat Transfer Rate for Liquid

Nitrogen 13

4. Summary of Available Theoretical and Empirical

Formulations 5

4. 1 Natural Convection-Non-Boiling Liquid ... 14

4.2 Natural Convection-Nucleate Boiling .... 16

4. 3 Natural Convection-Maximum Heat FliaxNucleate Boiling 20

IV

Page

4. 4 Natural Convection-Minimum Heat FluxFilna Boiling 21

4. 5 Natural Convection- Film Boiling 22

4. 6 Natural Convection to Single Phase Gas ... 23

4. 7 Forced Convection-Non-Boiling 23

4,8 Forced Convection-Nucleate Boiling 24

4. 9 Forced Convection-Maximum Heat FluxNucleate Boiling 26

4,10 Forced Convection- Film Boiling 27

5, Conclusions 27

6, Topics of Study Found in the Heat Transfer Literature . 28

7, Bibliography 31

1 1. INTRODUCTION

Heat transfer problems confront investiga^tors in nearly every

branch of engineering. For cryogenic applications, it is necessary

to have some knowledge of the whole field of heat transfer and specifically those aspects that are obviously applicable to low

temperature systems.

The purpose of this note is to: (1) present a connpilation of the

recent (from 1940 to May I960) experimental work dealing with

heat transfer from solid surfaces to cryogenic fluids, (2) present

a compilation of theoretical and empirical formulations for heat

transfer to fluids in general, (3) compare and discuss (1) and (2),

and determine areas which need further study. (Information on

more recent work will appear in Advances in Cryogenic Engineering, Volume 6=1=)

Cryogenic heat transfer problems involve conduction, radiation,

and convection with and without phase change. A large part of the

available heat transfer literature is not directly concerned with cryogenic fluids but may be used with cryogenic systems. Therefore

references which do not deal with cryogenic fluids, but may be applicable, are included here.

A document which summarizes all of the heat transfer information that may be of value to the solution of cryogenic problems would

include most of the useful heat transfer literature. In order to define a manageable task the present survey is confined to information

applicable to situations in which a cryogenic fluid is involved in the

heat transfer mechanism.

The experimental data are presented in graphical form, for liquid

helium, liquid hydrogen, liquid oxygen and liquid nitrogen, the data

for each liquid being plotted on one sheet.

For those cases where meaningful computations eind comparisons

can be made the theoretical and empirical formulations are also presented in the form of graphs which are readily comparable with the

experimental graphs. Some discussion of these comparisons and

some limitations of the equations used are given in section 4.

* "Recent Advances in Cryogenic Engineering", Vol. 6, Plenum

Press, Inc., New York, N. Y., 1961.

2

The references are listed alphabetically by author in the Bibliography (section 7), In section 6, the references are grouped

according to those topics which (in our judgement) classify the material presented therein.

It is emphasized that this survey does not present the details of

the work contained in the references, and the reader who is interested in these details (e. g. , experimental techniques and theoretical

derivations) must go to the original publication.

2. NOMENCLATURE

2 A - Area of heating surface, cm .

2 , a - Thermal diffusivity, cm ,/sec.

c - Specific heat, joules/ gram °K.

C - Constant.

d - Tube diameter, cm.

, 2

g

- Acceleration due to gravity, cm. /sec .

2

G - Mass velocity, granns/cm . sec.

3 2 2

Or - Grashof number. Or = L, gp (3AT/|a .

2

h - Film coefficient of heat transfer, watts/ cm. °K.

J - Mechanical equivalent of heat, ergs/joule.

k - Thermal conductivity, watts/ cm. ° K.

L - Length of heating surface, cm.

Nu - Nusselt number, Nu = hL/k or Nu = hd/k.

2

p

- Pressure, dynes/cm .

2

p

- Atmospheric pressure, dynes/ cm .

3

^p - Pressure difference corresponding to the temper2

ature difference ^T, dynes/ cm . Pr - Prandtl number, Pr = c u/k.

P

Q - Heat transfer rate, watts,

r - Radius, cm.

•r - Bubble velocity, cm./sec.

Re - Reynolds number. Re = pud/[j. or Re = puL/fjL.

T - Temperature, °K.

AT - Temperature difference, °KAT = T - T^, for nonw BLi

boiling liquid or surface boiling of subcooled liquids,

AT = T - T for boiling saturated liquids- w s AT = T - T for heat transfer to vapor, w V

u - Velocity, cm. /'sec.

X - Mass fraction of vapor (quality).

P

- Coefficient of thermal expansion, (°K)

X. - Latent heat of vaporization, joules/gram.

p. - Absolute viscosity, poise.

2

V - Kinematic viscosity, cm./sec.

3

p

- Density, grams/ cm .

(T - Surface tension, dynes/ cm.

Subscripts

av - average

b - bubble

BL - bulk liquid

g

- gas

i ~ inside

L, - liquid

max - maximum

o - outside

out - outlet of heater

p

- pressure

s - saturation

V - vapor

w - wall

3. GRAPHICAL PRESENTATIONS

The following graphs present the experimental data found in the

literature and the curves calculated by raeans of the theoretical and

empirical formulations taken from the literature. The calculated

graphs are transparent overlays so that they can be easily compared

with the experimental data. Due to limited data on the properties of

cryogenic fluids some of the calculated curves do not cover the range

of the experimental data. Also some of the formulations neglect

factors such as diameter and conditions of the heating surface; the

experimental data show that these factors do affect the heat transfer.

5

3, 1 Experimental Data

The experimental data found during this survey and dealing with

helium, hydrogen, oxygen, and nitrogen are plotted in figures 2,

4, 6, and 8 respectively; the coordinates are heat flux versus temperature difference between the heating surface and the bulk of the

fluid. The data, notations, etc, are reproduced as found in the literature. For example, only those nucleate boiling heat fluxes

which the original author indicated as maxima are so identified on

the graphs. Pertinent information such as system pressure, heater geometry and orientation, etc, are given on the figures. Both

forced and natural convection data are included,

3, 2 Theoretical and Empirical Formulations

The results obtained by applying the various theoretical and empirical formulations to helium, hydrogen, oxygen, and nitrogen are

shown in figures 1, 3, 5, and 7 respectively. The formulations are

discussed in section 4, Computations were performed for most of

the formulation; however, for reasons given in section 4 it was either not possible or not desirable to perform computations with

some of the formulations.

3, 3 Comparison of Data with Formulations

Figures 1 through 8 are plotted so that the various theoretical

and empirical formulations can be easily compared with corresponding experinnental curves. In cases where geometrical factors,

pressure, or other parameters are required in order to make a

coihputation, the values chosen for these parameters are noted

next to the computed curves. These curves should be compared

only with the experimental curves having nearly the sanne values

for these factors. The computed results are compared with the

experimental data in section 4,

4. SUMMARY OF AVAILABLE THEORETICAL

AND EMPIRICAL FORMULATIONS

This summary is not intended to replace original publications.

The reader who is interested in detailed derivations, assumptions,

experimental and analytical techniques, etc., must refer to the

original papers.

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OGEN. g

predicted

ux

predicted).

only)

\

\\

\Vv ^^ \ ""^^S s

\ V 1 w s

tr E q= c ch \i c? s s S

t g o 1 1

'' s s

|:

UIDN cleate ling

he

.

(one

ionbo V \> \^

\^

^ < >>,,

:

FOR

LIQ

boiling

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nu

um

film

bo

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boiling

onvection, ^:';;5 sN

1

CI S '^• , 1-<

a:

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1 Ure o " ^ 'E 3 -o ~ CO)

Kg ^

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s

N

S

S

s

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CALCULATED

HEAT

TRANSf

(46

D

-

Equation

of

FORSTER

a

GREIF

^

(47

o

-

Equation

of

FORSTER

a

ZUBER

A

-

Equation

of

Mc

NELLY*'*'

Equation

of

ROHSENOW

a

G

0000

Equation

of

ZUBER

a

TRIBU

Equation

of

ZUBER

a

TRIBU

oEquation

of

BROML^Vl

fflEquation

of

CHANG""/^''^

'^^

(84 1

-

Equation

of

LEVY

-

Forced

con

e

-

Equation

of

COLBURN'"'

AEquation

of

DITTUS

a

BOELTE

(See

Mc

Adorns*^")

0) hf s i \ s

o w

S s. s. M \ s S>

c I s \

s

v^.

d) e

F \ Ns 5 o ^.

O o ^

C

=3 5

a.

o

o o Q d i

iij o

z

UJ

cc

UJ

u.

u.a hUJ

IT UJ o n a: - (- 3

< <9

a:UJ U. a

,U4D/UD'* '(xnnd iV3H) v/o

E o ai 3 r 7 b c '- o

<0

CJ c fc3 V

OH £E

mio) 8T3Co

fcXD co Z o p rii ^ to O o >

enc co C C\J 3 d ro _o

"in

X

O Eo

XT in

b

Q Oi _l fOlCO

=1

Q P —

X

b

O o

a.o T

D

X

T3 -^ LL OJ o 1 lOICD

lOlO) ri

_ o X

UJ ED

O. ^

rO|QD X ! <" o — O D 3R

OEE

(M

rOICO

QJ3 Q

CJ'o

in

ro ir —leg F -y n o

UJ ,^ tn -^

a> cu - Lu

CO

D> o > >

0) 3 (U JD ?» i

o» CD o ^ *- <

crH< >

rr

C c 3? 1 <

"5

S'

<r

Ooco

<L» D

\n3 2coo

III o T UJ <n ir. X 1-UJ

CL00 - o : C6 o

rr

XJ UJ _l N<

0-00 <

1- 8 z

UJ

UJ <J

Q

r ,J z

UJo cro

u_—I

UJ

05

UJ

fr (n " : LU UJ 5

UJ

Q.X

UJ

(O >.' <n </) _i (.J ^ - < <1 (/) rr :5 X ^> I X ^ I 03

J^ ' 1 ' ' 1 ' @ < m 9 « (§) a

,ujo/suD« (xniJ 1V3H) V/0

14

It is beyond the scope of this survey to analyze in detail the formulations for correctness, completeness, or importance. Neither

has there been any attempt to appraise the experiments with which

the formulations have been compared.

Differences in heating surface shape, orientation, composition,

roughness, cleanliness, duration of test, liquid subcooling, quality, agitation, etc. may cause large differences in test results

which are not taken into account by the formulations. Therefore

the results of the various experiments cannot, in general, be expected to agree quantitatively with each other or with the

formulations

.

The formulations are numbered consecutively with Roman

numerals.

4. 1 Natural Convection Non-Boiling Liquid

The first two formulations (I and II) of this group were used for

calculations on figures 1 and 3. Formulations III, IV, V, VI, and

VII were not used because comparable experimental data were not

found.

a. McAdams(89)''S for laminar flow past vertical planes and

cylinders, (Pr • Gr) = 10^ to 10^.

Q/A= 0.590^^

L

1/4

3 2 „_. . 1

Results calculated from this formulation are plotted on figure 1 for helium at pressures of 45 and 390 mm. Hg and on figure 3 for

hydrogen at 760 mm. Hg. These results may be compared with the

non-boiling helium experiments of Karagounis(75), figure 2; and

with the hydrogen experiments of Weil (143), figure 4. The helium

calculations agree with the experiments only at 45 mm. Hg pressure.

At 390 mm. Hg the calculated Q/A is approximately 1/16 of the experimental. Values of (Pr • Gr) for the He experiments were of

the order of 10 .

* Numbers in parentheses refer to the references in section 7.

15

The hydrogen calculations, figure 3, fall within the range of

the non-boiling experiments of Weil and Lacaze^ ', figure 4; however, only the 760 mm. Hg pressure was available for connparison.

Due to the very small heater used the products (Pr • Gr) for these

experiments were of the order of 10.

b. Touloukian et al. , for laminar flow past vertical

cylindrical surfaces, (Pr • Gr) = 2 x 10° to 4 x 10^^.

3 2 ^^^ Q/A. 0.726

^

L P g (3 AT \ , c^\

II

The remarks in section 4. 1. 1 also apply to this formulation.

The Q/A calculated by II is higher than that calculated by I by a

r . ^ 1 oW 0.726\

factorof

1.23^=-^-^J

c. Chang , for upward facing horizontal plane heating

surfaces. Chang's simplified equation is

1/3 Nu = 0. 146 (Pr Gr) . Ill . j_/ This formulation, derived from considerations of wave motion,

compares well with the empirical equation in McAdams'"") (IV)

for the turbulent range. The coefficient 0. 146 is an average of a quantity which varies slightly from one fluid to another. No

natural convection experimental data for horizontal heaters were

found for cryogenic liquids; therefore, calculations were not

performed with this formulation.

d. McAdams , for upward facing horizontal plane heating

surfaces, (Pr • Gr) 2 x 10' to 3 x 10 , the turbulent range.

1/3 Nu = 0. 14 (Pr • Gr) . IV

No natural convection experimental data for horizontal heaters were

found for cryogenic liquids; therefore, no calculations were performed with this formulation.

e. McAdams , for upward facing horizontal plane heating

surfaces, (Pr • Gr) 10"* to 2 x 10', the laminar range.

1/4 Nu = 0.54 (Pr • Gr) . V

16

No natural convection experinnental data for horizontal heaters

were found for cryogenic liquids; therefore, no calculations were

performed with this formulation.

f. McAdams , for turbulent flow past vej^tical planes

and cylinders (Pr • Gr) - 10 to 10 ,

Nu = 0. 13 (Pr . Gr)^^. VI

As experimental natural convection data for cryogenic liquids with

turbulent values of (Pr • Gr) are not available, calculations were

not performed with this fornaulation.

g, Touloukian , for turbulent flow Rast verticaL

cylindrical surfaces, (Pr • Gr) =4x10 to 9 x 10

1 29 1/3 Nu = 0.0674 (Pr • Gr)/ . VII

-1—

/

As experimental natural convection data for cryogenic liquids with

turbulent values of Pr • Gr, are not available, calculations were

not performed with this fornnulation.

4. 2 Natural Convection-Nucleate Boiling

The first three formulations of this group (VIII, IX, and X) were

used for the heat transfer calculations presented in figures 1, 3, 5,

and 7. Calculations were not performed with formulations XI, XII,

XIII, and XIV for the reasons given in the following paragraphs.

a. Forster t;^ . andAn-Grieir<46)

, ^ r 1/4 ^5/8 . 1/3, 2

^ A c p T c T ^Ta / \ , X Ap ,„„

A/A iT/ir>\-3/ L L'^L s\ / L s L \ P [\^^ ] vIII Q/A =1.2 10) — -n j 5 \ \^ J \^J

V

The values of Q/A for heliunn calculated according to this formu-

(7 b)

lation (figure 1) are larger than the experimental data of Karagounis

(figure 2) by a factor of four to ten.

Hydrogen and nitrogen properties data needed for this formulation are not available over the full range of the experimental

pressures. Because of this limitation and large differences between

17

experimental data only an approximate comparison between the formulations and the experimental results is possible.

The hydrogen and nitrogen calculations (figures 3 and 7) are

bracketed by the roughly-corresponding experimental data (figures

4 and 8). The oxygen calculations (figure 5) agree with the experimental average (figure 6) at AT - 1°K; however at 7°K the

calculated Q/A is two to ten tinnes larger than the experimental

values.

(47)

b. Forster and Zuber

frv ^ ^^ ^ A

^''^^ f^ t \ ^^ ^ 0.62 0,35

(T - T )k Xp Ap ^p^ p(T^-T)c^ Pt ^'"'^t n CyA. 1.5(10)-^ ^ ' ,%,^ 1-^

J-J J—

I

-Li

s' L^L L

IX

where T is the superheat temperature. In order to compare this

formulation with available cryogenic data it is necessary to assume

{T OS- T ) = AT = (T - T ). w BL

The calculations for helium performed with this formulation

(figure 1) agree with the experinnental data of Karagounis (figure

2) at 384-390 mm. Hg; however, at 40-45 nam. Hg the calculated

Q/A is approximately ten, tinnes larger than the experinnental.

The statements concerning the hydrogen and nitrogen calculations of the preceding section (4. 2. 1) also apply here.

(94)

c. McNelly^ '.

0. 33

n-?9c-o 0-^9^ 0.69/pd\0.31, ^L - 1\ * „

Nu = 0. 225 Pr^ Re^ ^-~ ] — ), Xa L ^ \^ J \P^ J

2.22 k p p 1.06 3.22

or Q/A = 0.0082 (|-

j

JiiL / _il " \ ^t. Xb

J-j The experiments indicate that the increase in Q/A due to a given

pressure increase is considerably greater than that wliich is calculated by this formulation. For example, the calculated helium Q/A

18

(figure 1) is roughly six times as great as the experimental results

of Karagounis (figure 2) at 45 mm. Hg pressure, and one sixth as great at 390 mm. Hg.

The hydrogen Q/A calculations give results that are significantly smaller than the experimental results (see figures 3 and 4),

whereas the oxygen calculations were higher than the experiments

by a factor of 15 to 100.

d. Chang , for horizontal plane surfaces.

Nu = 0. 146 il+Pr(C^Br -1

1-1 I l—\ 1

2/3 ^1/3 XI

where

^lPl 1 Br = Q/A — ;— is the "boiling number": <b is the contact angle

V 2

(in degrees) of liquid with solid surface; C and n are experimentally determined constants which depend upon the fluid. All the

physical properties are to be evaluated at the arithmetic mean

film temperature.

The experimental constants have not been determined for cryogenic fluids.

r^., (53)

e. Giimour

.0.6 p(rg, 0.425 T^r^^-0-3

(4^^ (-^^ =0.00ir^\ , XII

cG vk ; V /

V ^L -

1

-2

where G = -: is the mass velocity (in gm. sec. cm. ) of liq- A p

} ^ b

V

uid which replaces the boil off vapor. V is the vaporization rate

(gm. /sec. ). The factor g in the third group of this formulation

was not present in reference 53 but was needed with the units of

the present survey.

The formulation was not compared with experimental cryogenic

data because the vapor (boil off) rate in the experiments is not

known.

19

, ^,. ^., (105)

f. Nishakawa

^ and t, , "coefficients of foaming ability", are given in Table II of

reference 105 for several non- cryogenic liquids. M is a constant

which depends on the condition of the heating surface and is independent of the physical properties of the liquid. M has the

dimension 1/length. N (reference 105 uses the symbol P) is a constant dependent upon properties of distilled water and has dimensions energy/time. The experimental constants have not been

determined for cryogenic fluids.

g. Piret and Isbin , for boiling inside vertical tubes.

0.8 0.6 0.33

h du p cu. tTs, ^ . 0. 0086 I'-i^i-il^ f4^^ ' "

. 0. 0086 (—^ii-^ i-^H^] ( -^] ' XIV

where u is the mean liquid-vapor velocity, m

The authors correlate the data for six non-cryogenic fluids

with a mean deviation of only 4 percent.

As the experimental investigations with cryogenic fluids do not

give the velocity of circulation, it is not possible to compare this

formulation with cryogenic experiments.

h. Rohsenow

f^ ^ \ ^ 0-33 1.7

f^ = C —==— I— \ -i^-^ , XV

where C is a coefficient which depends on the nature of both the

fluid and the heating surface; it has not been determined for cryogenic fluids.

20

4. 3 Natural Convection-Maximum Heat Flux-Nucleate Boiling

No computations were made with the first formulation (XVI)

because the required experimental data for cryogenic fluids are

not available. The other formulations (XVII and XVIII) were

used and are plotted on figures 1, 3, 5, and 7.

(41)

a. Ellion

Q ^ k :~ P^^^b^max ! TciJL I * TT - T 'i ^vt

A (r ) I H^ 11 k '

1 max b max '- j l j .. _,

The values for the exponents in this equation are taken from experimental data on water and carbon tetrachloride. No computations

were ma.de with this equation because there are no experimental

data on bubble radius and bubble velocity for cryogenic liquids.

b. Zuber and Tribus

P .nl/4 Q ^ . <J-g' "^L - W\ \ A

max

=24^Pv

^

1 '- p —J\/ -I v Refer to discussion in section c.

-*- + ^ . XVII

Pl

f 128)

c. Rohsenow and Griffith

p p 0.6 ^ =0. i55(fD^)p \( ^ "

'' ^» xvm

max ^ v

where (fD, ) is the bubble velocity and is approximately the same

for several fluids. The value used here for (fD ), taken fronn experimental data on water, ethanal, benzene, etc., was 7.8 cm, /sec,

The results calculated from these formulations (XVII and XVIII)

are plotted on figures 1, 3, 5, and 7. They compare reasonably

well with some of the experimental data which are identified (in the

original publications) as maximum nucleate boiling heat fluxes. The

experiments with liquid helium may have been carried to these

raaxima; however, this was not stated. The equation of Rohsenow

and Griffith (XVIII) predicts a maximum heat flux close to the

21

experimental helium curves. The equation of Zuber and Tribus

(XVII) predicts a maximum heat flux for helium which is about 2

to 5 times higher than the experimental curves. For liquid hydrogen both equations predict a maximum heat flux which is close to

the experimental data.

Both equations predict larger maximum heat fluxes with oxygen and nitrogen (2 to 3 times higher with oxygen and 2 to 4 times

higher with nitrogen) than have been observed.

/ 139)

d, Sydoriak and Roberts

A -A 1/2 Q channel f 2gL - in{l+xR\| ^.^.

A A ^L [2R + 1 \ xR yj

where A is the area of the heated wall of a vertical cylindrical

channel whose horizontal cross section area is A , , and

^ / \

/

channel where R = (p^ - p )/p . L, V v Computations were not made using equation XIX because values

of quality were not given by other experimenters. However in reference 139, the equation is compared with experimental results;

the agreement is good.

4. 4 Natural Convection-Minimum Heat Flux-Film Boiling

1 ^ •, (153)

a. Zuber and Tribus

o-g p^ p -.1/4 L - V I XX

Ia ) r 2aK 2\ mm.

V V

Results calculated by this equation are plotted on figures 1, 3, 5,

and 7. None of the experimental cryogenic papers state that minimum film-boiling heat fluxes were measured. The equation

predicts a heat flux which is smaller (by a factor of 1/1000) than

the experimental curves for helium. However, it predicts minimum

heat fluxes for film boiling which compare very closely with some

of the experimental data for liquid hydrogen and liquid nitrogen. No

experimental data in the film boiling range were found for liquid

oxygen.

22

4. 5 Natural Convection- Film Boiling

Computations were made with two of the following formulations

{XXI and XXII) and the results were plotted on figures 1, 3, and 7; formulation XXIII was not used because its use requires experimental constants which are not known for cryogenic fluids.

(13)

a. Bromley , for horizontal cylindrical

3/4 Q/A (neglecting radiation) = 0. 62k

surfaces and viscous flow.

P„/Pt P„xg^nl/4 v(^ L - ^v)^

^o^

AT^^^ XXI

The results of calculations with this equation are plotted on figures

1, 3, and 7. The values used for d in the computations were the

same as those used in the experimental investigations. As there

are no experimental data with liquid oxygen, no calculations were

made for figure 5.

The calculations for helium predict a smaller diameter effect

than the actual experimental data show; the calculated curves are

higher than the experimental by factors of about 1, 2 to 1.7 for the

5.5(10) mm. diameter wire and by factors of 3 to 5 for the

51(10) mm. diameter wire. The hydrogen calculations predict

heat fluxes that are smaller than the experimental results by a factor of 2/3 to 1/2, and the nitrogen calculations predict heat

fluxes that are smaller than the experimental results by a factor

of 3/4 to 1/4.

b, Chang^^^^

1/3

Q/A (neglecting radiation) = k ^^^L - ^v^ ^^v AT XXII

^ L 2 J

Stt u k at

V V

This formulation predicts heat fluxes for helium that are considerably smaller than the experimental results. For hydrogen the

calculated results are approximately 100 times larger than the

experimental values, while for nitrogen the calculated results are

about 10 times larger than the corresponding experimental values.

(13)

"

c. Bromley , for vertical cylindrical surfaces

with viscous flow, neglects radiation.

3/4 rPv(PL - Pv)^^ i ^'^ 3/4 Q/A = Ck^^^ ^-\ ^— ^^ ^^1"

The constant, needed for each fluid, is not known for the cryogenic fluids.

4. 6 Natural Convection to Single Phase Gas

No experimental data for natural convection to a single phase

gas at cryogenic temperatures were found. Various formulations

are available for various heater geometries. Refer to McAdams

for examples.

4. 7 Forced Convection-Non-Boiling

Forced convection non-boiling experimental data were found for

liquid hydrogen and liquid nitrogen only.

(25)

a. Colburn , for turbulent flow in pipes.

Q/A = cG^T' ^ ^.2/3 dGN-'-^' 0.0007+0,065, i

. XXIV

.^^^ /' L v h^ J J Refer to discussion in section b.

b. Dittus and Boelter, see McAdams , for turbulent flow in pipes.

, ,^.0.8 0.4

Q/A = 0.023dT^(

^^ : ^^ XXV

In order to avoid plotting a curve for each of the many flow rates,

pressures, etc. , given in the experimental references, average

values of the parameters (based upon the information in references)

were used in the computations with these formulations. In some

cases the properties of the liquids are not available at the high pressures used in the experimental work. The results calculated for

hydrogen predict heat transfers at least 10 times larger than the

experimental data.

24

The results calculated for nitrogen are smaller (by a factor of

2/3 to 1/4) than the experimental curve.

4. 8 Forced Convection-Nucleate Boiling

Only the first formulation (XXVI) of this group was used for the

heat transfer calculations plotted on figure 7. Calculations were

not performed with the other four formulations for the reasons

given in the following paragraphs.

a. Levy

• 2 3

Q/A = L^L^L 1 - X ( T - T ) , XXVI

where b, is obtained from a curve of 1/b^ versus p \ in reference 84. L L V

None of the experimental papers gives the average quality which

is needed in this formulation. In order to compare this formulation

with the experimental data of Dean and Thompson (figure 8) it

was assumed that the quality was zero at the point where their data

indicate that nucleate boiling begins. The result of this one calculation plotted on figure 7 connpares very closely with the

experimental point.

(34)

b. Dengler and Addoms

h 3. 5 T^ = F-^f- XXVII

h 0. 5 L (X),,

where F = 0. 67

d 0.1

(AT-AT.)(^ — )

I w

(F is used only when it exceeds unity), 4ft is the slope of the vapor6 -• sat

pressure versus temperature curve, AT. is the temperature difference

(T - T.„, ) for the initiation of nucleate boiling in tubes,

w BL

0.9 p 0.5 u 0. 1 o {—] f -^V ^nd

(X),, VI -V KpJ VV

25

h is the heat transfer film coefficient for liquid alone as obtained

from the Dittus and Boelter equation (XXV). This formulation is to

be used only for a range of 7—r— from 0. 25 to 70.

(x)

tt As experimental data for cryogenic fluids, in which the average

quality of the boiling mixture is known, are not available, no computations were perforined with this information.

Co Mumm , for boiling inside of horizontal tubes

for values of quality fronn to 0. 40.

Q

A(T - T ) k^

w s L, [" '

• ""-U - iA

1.64-.^ • 0.464nGd ,0.808 Q I ei

L ^"J

XXVIII

d is the "equivalent inside diameter" of the heater tube. The

numerical coefficients and exponents were determined by experiments on water inside an electrically heated horizontal tube. No

computations for cryogenic fluids were made with this formulation

because of the absence of the required experimental data.

d. Stroebe, Baker, Badger , for boiling

h =

inside long vertical tubes.

7. 8(10) V'^

c \i\ 2

P

XXIX

cr (AT^)

0. 13

The coefficients and exponents were obtained by tests with water.

The authors of reference 138 point out that the equation is entirely

empirical and the geometry of the test section (a 2 in. O. D. by 20

ft. long tube) was constant during all the tests.

No factor was obtained which could account for the effects of

geometrical changes and the equation should be used with discretion for conditions appreciably divergent from those covered in

the work.

Since dimensionless groups are not used, the same units should

be used as those in reference (138), namely:

26

S = surface tension, dynes/cm.

3

V = specific volume, ft. /lb.

^T = T - T^^ film temperature differelice, °F

w BL

2

h = heat transfer coefficient, BTU/hr. ft. °F

/ 2 3Q\

e. Sydoriak and Roberts

1/2 A, , ^x g Linfl+x R r, •

, ^ channel

.

out / ^

'^ out out-" \ „.,^,^ Q/A = ^^Pl{^ ( Ze 1 ;| ^^^

^ out ^ X R ^

-^ out

\^here A is the area of the heated wall of a vertical cylindrical channel whose horizontal cross section area is A where

R = (Pt - P )/p ^rid where Z = the hydrostatic head of liquid,

. L V ' V . e equivaTent to the pressure drop across the heater. The p and x V

are taken at the exit end of the heater. The mass fraction of vapor

(quality) and the pressure drop across the heater on the forced flow

experiments of authors other than reference 139 were not given.

Comparison of the predictions of this equation with the experimental

work done by Sydoriak and Roberts for nitrogen varies with the quality at the exit of the heater; at low qualities the ratio of their

experimental heat flux to their calculated heat flux is 0. 48 and at

high qualities this ratio is 0.95.

With hydrogen the measured results average about 0. 7 of the

calculated results. No trend of this figure with quality was apparent; however, the quality was quite high in most of the runs.

4. 9 Forced Convection-Maximum Heat Flux-Nucleate Boiling

(52) , a. Gambill and Greene , for maximum

heat flux to fluids in vortex flow.

Q/A = [359, 700 u + (7. 10)(10^)][1. 29 - 0. 049(L/d)], XXXI

where u is the "superficial axial velocity",

ax

The correlation was made from data taken on water. There

were no data found for cryogenic fluids in vortex flow.

27

4. 10 Forced Convection-Film Boiling

(98)

a. Motte and Bronnley derive correlating equations for

three assumed cases of convection film boiling in which the heat

transferred into the liquid by (1) thermal conduction, (2) "eddy

conduction", and (3) eddy conduction with the time of contact that

is small compared to the ratio of the scale of turbulence to the

intensity of turbulence. These equations are used as a basis for

correlation only and are not to be considered as exact equations.

The correlations were not made with cryogenic fluids. The equation in case 2 best fits the data taken with several fluids such as

hexane, carbon tetrachloride, and alcohol. This equation is:

, W -7.29 fVv"' ^^^ fl^.u"l.x u"L~--°-°5

XXXII

, p \» h ' dAT s p^i ATk p \\ u^ / V v V V ^ L, '

u* = incident velocity of liquid on tube

u" =: velocity of liquid in conduit where level of turbulence

is determined.

1 + 0. 4(AT)c 2

P i

5. CONCLUSIONS

a. The existing experimental data on heat transfer between

solid surfaces and cryogenic liquids (heliura, hydrogen, nitrogen,

and oxygen) vary appreciably between experimenters, even when

heater geometries and orientations, pressures, etc. are comparable. The variations are both in the magnitude of the heat flux

and in the shape of the heat-flux-versus-temperature-difference

curves, and are possibly due to uncontrolled parameters such as surface roughness and contamination.

b. Existing theoretical and empirical formulations are in qualitative agreement with some of the experimental data. More

carefully controlled experiments are needed, and formulations which

account for parameters such as surface condition should be developed.

28

c. No experimental data were found for: natural convection

without boiling for oxygen and nitrogen; forced convection without

boiling for helium, hydrogen, and oxygen; forced convection with

nucleate boiling for helium; and forced convection with film boiling for helium.

6. TOPICS OF STUDY FOUND IN THE

HEAT TRANSFER LITERATURE

Following is an alphabetical list of the topics covered in the

papers of this survey. These topics deal with some phase of

heat transfer; although some of the papers are not concerned with

cryogenics directly, they may be applicable to low temperature

systems. Reference numbers are listed under each topic.

Acceleration of the Heating Surface (effect of)

52, 56, 77, 78, 79, 95, 153

Binary (two component) Fluids

11, 72, 74

Bubble Dynamics

6, 7, 22, 35, 38, 41, 43, 45, 47, 56, 57, 58, 68, 71, 87, 89,

108, 110, 111, 152, 155

Composition of Heating Surface (effect of)

29, 44, 69, 70, 76, 87, 115

Contamination of Heating Surface (effect of)

3, 4, 20, 24, 63, 69, 90, 115

Correlations (theoretical and empirical)

II, 12, 13, 14, 15, 18, 19, 20, 25, 28, 31, 34, 37, 41, 42, 43,

44, 46, 47, 48, 49, 52, 53, 54, 55, 60, 64, 66, 67, 69, 71, 72,

73, 74, 81, 84, 86, 87, 90, 93, 94, 97, 98, 100, 105, 108, 109,

III, 112, 119, 123, 124, 128, 133, 136, 138, 140, 151, 152, 153

Cryogenic Fluids

5, 13, 14, 24, 26, 49, 59, 61, 62, 63, 64, 66, 75, 94, 97, 99,

112, 116, 130, 139, 142, 143

Descriptive Material (Photographic Studies, Etc.)

2, 34, 41, 44, 57, 58, 72, 89, 97, 120, 145, 146, 147, 148

29

Film Boiling Experiments

4, 13, 14, 15, 41, 49, 50, 57, 59, 66, 71, 89, 90, 97, 98, 99,

108, 121

Film Boiling Theory

3, 6, 13, 14, 15, 18, 19, 41, 66, 67, 71, 89, 97, 98, 121, 151

152, 153

Forced Convection Heat Transfer to Single Phase Gas

61

Forced Convection Heat Transfer to Single Phase Liquid

32, 41, 42, 71, 72, 79, 89, 119, 126, 132, 133, 150

Forced Convection Boiling Heat Transfer

3, 5, 16, 21, 25, 31, 34, 37, 41, 42, 46, 53, 57, 59, 70, 72,

74, 81, 89, 93, 97, 100, 112, 116, 123, 124, 126, 130, 137,

139, 141

Geometry of the Heating Surface (effect of)

49, 58, 69, 70, 71, 77, 78, 79, 90, 98, 124, 146, 147

Maximum Nucleate Boiling Heat Flux (Burnout)

3, 4, 12, 17, 20, 21, 38, 41, 42, 52, 57, 58, 70, 71, 72, 73,

76, 82, 89, 108, 128, 131, 137, 153

Natural Convection Heat Transfer to Single Phase Liquid

10, 18, 40, 41, 75, 89, 136, 140, 142, 143, 144

Natural Convection Heat Transfer to Boiling Liquid (pool boiling)

4, 12, 13, 14, 18, 19, 24, 28, 29, 41, 43, 44, 62, 63, 64, 69,

75, 87, 89, 90, 99, 108, 109, 116, 123, 124, 151, 152

Nucleate Boiling Experiments

4, 20, 24, 27, 29, 34, 41, 42, 43, 52, 59, 62, 63, 64, 69, 71,

74, 75, 83, 89, 90, 97, 99, 100, 103, 104, 105, 108, 111, 116,

119, 123, 124, 127, 137, 139, 151, 152

Nucleate Boiling Theory

6, 11, 12, 18, 22, 46, 51, 53, 63, 71, 74, 83, 89, 94, 97, 100,

103, 104, 105, 111, 119, 123, 124, 126, 127, 128, 139, 151, 152

30

Orientation of Heating Surface

24, 29, 40, 66, 70, 89, 102, 138

Pressure Effects on Boiling Heat Transfer

4, 20, 21, 24, 26, 31, 34, 37, 41, 42, 44, 55, 63, 64, 70, 71,

76, 87, 89, 90, 97, 100, 103, 112, 115, 124, 125, 126, 129,

130, 146

Quality (mass fraction of vapor) Effect on Boiling Heat Transfer

16, 24, 34, 93, 100

Roughness of the Heating Surface

16, 27, 29, 52, 69, 70, 146, 147, 153

Subcooling Effect on Boiling Heat Transfer

3, 6, 18, 19, 21, 28, 29, 37, 41, 42, 46, 57, 58, 70, 75, 84,

89, 98, 109, 124, 125, 138, 146, 147, 153

Surveys of Previous Work

6, 20, 23, 39, 52, 72, 89

Transient Boiling (effects of rapid changes)

6, 87

Transition Boiling Experiments (changing from nucleate to film)

40, 108, 146, 153

Transition Boiling Theory

153

Turbulence or Agitation Effects on Boiling

16, 113, 122, 146

Vibration Effect on Boiling

10

Vortex Flow with Boiling

51, 63, 81, 133

Wetting Agent Effect

4, 40, 115, 146

31

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V>. S. UEPAilTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C, and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover.

WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer Structure. Plastics. Dental Research.

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Properties. Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. 0{>- erations Research. Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog Systems.

Applications Engineering.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Solid State Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Molecular Kinetics. Mass Spectrometry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research.

Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter-^ave Research.

Microwave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research.

Navigation Systems.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.






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