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Masters Theses Student Theses and Dissertations

1971

A study of a nitrogen heat pipe A study of a nitrogen heat pipe

Jay Dudheker

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A STUDY OF A NITROGEN HEAT PIPE

by

JAY DUDHEKER, 1932-

A THESIS

submitted to the faculty of the

UNIVERSITY OF MISSOURI-ROLLA

in partial fulfillment of the requirements for the

Degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

Rolla, Missouri

1971

1.9426.0

ii

ABSTRACT

An experimental heat pipe, 33.25 inches long and 0.75

inches in diameter, with modacrylic fiber wick and liquid

nitrogen as its working fluid was constructed to study the

operating characteristics of a cryogenic heat pipe. The

effective thermal conductivity and the axial temperature

distribution were determined for various levels of power

input. The effect of inclination angle on the above

parameters was also measured.

iii

ACKNOWLEDGEMENTS

The author wishes to express his sincere appreciation

to his advisor, Dr. B.F. Armaly, for his guidance, counsel,

and constant encouragement throughout the project and pre­

paration of this thesis.

The constructive criticism of Dr. H.J. Sauer and

Dr. J.B. Prater is appreciated.

Sincere thanks and appreciation go to my wife Georgia

for her patience and understanding throughout the past year.

TABLE OF CONTENTS

ABSTRACT • . • • •

ACKNOWLEDGEMENTS .

LIST OF FIGURES

LIST OF TABLES

NOMENCLATURE •

I. INTRODUCTION

II. REVIEW OF LITERATURE

iv

Page

ii

iii

v

vii

• • viii

1

5

III. DESCRIPTION OF THE EXPERIMENTAL APPARATUS • 15

IV. EXPERIMENTAL PROCEDURE AND DATA REDUCTION • 24

v. RESULTS AND DISCUSSION

VI. CONCLUSIONS AND RECOMMENDATIONS •

BIBLIOGRAPHY •

VITA ••

APPENDIX A.

APPENDIX B.

. . . . . . . . . . . . . . . .

EXPERIMENTAL DATA AND RESULTS

THERMOPHYSICAL PROPERTIES OF NITROGEN • • • . • • • • • . .

34

43

45

47

48

53

Figure

1.

2.

3.

4.

5.

6.

7.

8.

9 .

10.

11.

12.

13.

14.

15.

LIST OF FIGURES

Heat Pipe • • • • • . . . . . . . Radial Temperatures at Evaporator and Condenser Sections . • • • . • •

Cryogenic Tank . . . . . . . . . Heat Pipe with Vacuum Jacket

Calibration Curve for Nitrogen Storage Tank. . . . ·· . . . . . . . . . . . . .

Thermocouple Locations

Experim~ntal Set-Up of Nitrogen Heat Pipe Assembly . • • • • • • • • •

Experimental Results for the Case of Horizontal Level . . • . • • . • .

Steady State Temperature Distribution, Horizontal Level • • • . • • • • • • • •

Experimental Results for 1 Degree Inclination Angle with Evaporator Above Condenser • . . • . . • • • •

Experimental Results for 1.75 Degree Inclination Angle with Evaporator Above Condenser • • . . . • • • . • .

Experimental Results for 5.25 Degree Inclination Angle with Condenser Above Evaporator • • . . • • • • . • . . .

Steady State Temperature Distribution for 5.25 Degree Inclination Angle with Condenser Above Evaporator . . •

Effective Thermal Conductivity for the Heat Pipe at Different Angles of Inclination • • • • • • • •

Effective Thermal Conductivity of Saturated Wick in Evaporator and Conden­ser Sections Based on Chi's Analysis

v

Page

3

10

16

17

20

21

23

27

28

30

31

32

33

35

38

Figure

16.

B-1

B-2

B-3

B-4

B-5

B-6

B-7

B-8

B-9

B-10

LIST OF FIGURES (continued)

Comparison of the Total Experimental Temperature Difference • . • . • • •

Vapor Pressure of Nitrogen • • • • • • •

Density of Saturated Liquid Nitrogen

Density of Gaseous Nitrogen (Saturated Vapor) • . • . • . . • • . . • .

Dynamic Viscosity of Liquid Nitrogen •

Dynamic Viscosity of Gaseous Nitrogen at Atmospheric Pressure • . . • • • • •

Heat of Vaporization of Nitrogen •

Surface Tension of Saturated Liquid Nitrogen . • • • . . •.•••..

Specific Heat of Saturated Liquid Nitrogen . . . . • • • • •..

Thermal Conductivity of Saturated Liquid Nitrogen . . . . . . . . . . . . . . . .

Thermal Conductivity of Gaseous Nitro-gen at Atmospheric Pressure • • . . . • • .

vi

Page

41

54

55

56

57

58

59

60

61

62

63

Table

A-1

A-2

A-3

A-4

A-5

LIST OF TABLES

Experimental Results, Heat Pipe Operating in the Horizontal Position

Experimental Results, Heat Pipe Operating at 1 Degree Angle, Evaporator Above Condenser • • • • • • • • . • .

Experimental Results, Heat Pipe

. . .

Operating at 1.75 Degree Angle, Evaporator Above Condenser • • • • • • • • • • • • •

Experimental Results, Heat Pipe Operating at 5.75 Degree Angle, Condenser Above Eva para tor . . . . . . . . . . . . . . . . .

Deduced Experimental Results • • . • • • • •

vii

Page

49

so

so

51

52

Symbol

a

A

b

c p

e

g

K ss

L

NOMENCLATURE

Quantity

Sonic velocity

Vapor passage cross-sectional area

Property of wick, due to tortuous path taken by fluid through pores

Specific heat at constant pressure

Wick porosity

Acceleration due to gravity

Constant factor of propotion­ality

Latent heat of vaporization

Thermal conductivity of liquid saturated wick

Thermal conductivity of stainless steel tube

Effective thermal conductivity of heat pipe

Total length of heat pipe

Length of adiabatic section

Length of evaporator section

Length of condenser section

viii

Units

ft/sec

dimensionless

dimensionless

ft/sec 2

lbm-ft/lbf-sec2

Btu/lbm

Btu/hr-ft-0 R

ft

ft

ft

ft

Symbol

• m

Q

t

T . Cl.

T co

T . el.

T v

!J.P c

!J.P g

NOMENCLATURE (continued)

Quantity

Mass of liquid

Mass flow rate

Heat transfer rate

Capillary wick pore radius

Outside radius of containing stainless steel tube

Inside radius of containing stainless steel tube

Radius of vapor space

Thickness of wick

Temperature at the inner wall of the containing tube at the condenser

Temperature at the outer wall of the containing tube at the condenser

Temperature at the inner wall of the containing tube at the evaporator

Temperature at the outer wall of the containing tube at the evaporator

Vapor temperature

Capillary pumping pressure drop

Pressure drop due to gravity forces

ix

Units

lbm •

lbm/hr

Btu/hr

ft

ft

ft

ft

ft

_oR

lbf/ft2

lbf/ft2

Symbol

b.P v

9

lll

NOMENCLATURE (continued)

Quantity

Pressure drop in vapor phase

Pressure drop in liquid phase

Contact angle

Viscosity of liquid

Viscosity of vapor

Density of liquid

Density of vapor

Surface tension of liquid

Inclination angle of heat pipe

X

Units

lbf/ft2

lbf/ft2

degrees

lbm/ft-hr

lbm/ft-hr

lbm/ft3

lbm/ft3

lbf/ft

degrees

1

I. INTRODUCTION

The heat pipe is a self-contained structure made

out of a thin-wall sealed tube lined on the inside with

a wick which is saturated by a working fluid. The main

attractive feature is its capacity to transfer heat

better than the best metallic conductors, such as silver

or copper. For instance, thermal power of 11,000 watts

[1]* was transferred by a one inch heat pipe over a

distance of 27 inches with practically no temperature

drop. By way of comparison a copper rod of the same

length and nine feet in diameter weighing about 40 tons

would be required to produce the same results. The opera­

tion of a heat pipe is accomplished by continuously evapor-

ating and condensing the working fluid, and transferring

heat by mass flow from evaporator to condenser utilizing

the latent heat of vaporization.

Since its invention by Gauler in the year 1942,

and a subsequent follow up by Grover [2] at Los Almos

Scientific Laboratory, more and more educational institu-

tions and industries from various fields have become

interested in its development and applications. It has

received considerable attention in space technology due to

its light weight and its ability to perform satisfactorily

under zero gravity. Other industries are also making use

*Numbers in brackets indicate references listed in Bibliography

2

of this principle to service their needs and requirements.

For example, the railroad [3] industry are experimenting

with large capacity heat pipes (i.e., 10 to 20ft. long),

with water as working fluid, for use in transit to main­

tain some commodities, such as tar, at high temperatures.

Most of the research and development has been restricted

to heat pipes operating at relatively high temperatures,

above normal ambient temperature. The design techniques

and operating characteristics of these heat pipes have

been well defined by a considerable number of investiga­

tors. Review of the technical literature has indicated,

however, that only two experimental studies have been per­

formed on heat pipes operating in the cryogenic temperature

range with nitrogen [4,5] (139.3°R) as the working fluid

and only two theoretical analyses [6,7] on the design of

cryogenic heat pipes has been published.

The heat pipe, shown in Figure 1, is a sealed slender

long thin-wall tube which is lined on the inside with a

saturated wick. Heat added from a source to a section of

the tube, called the evaporator, causes the working fluid

to evaporate. This action causes a pressure gradient to

exist between the hot and the cold end of the tube which

forces the vapor to flow through a central passage towards

the cooler section of the tube known as the condenser.

As the vapor enters the condenser, condensation takes place

and energy equivalent to the latent heat of vaporization

is released. Due to surface tension forces present in the

CONDENSER SECTION

(HEAT SINK)

ADIABATIC SECTION

FIGURE 1. Heat Pipe

EVAPORATOR SECTION

(HEAT SOURCE)

w

4

wicking material, the condensate returns along the wick

from the condenser to the evaporator section, and the

above fluid cycle is repeated.

The purpose of this study is to investigate

experimentally the operating characteristics of a cryo­

genic heat pipe operating with nitrogen as a working fluid

in order to evaluate existing analytical models and experi­

mental results.

5

II. REVIEW OF LITERATURE

Since the initial work of Grover several heat pipe

analyses have appeared in the literature. Cotter [8] was

the first to develop the equations governing the dynamics

of heat transfer in a heat pipe. The formulation was

based on a balance of pressure drops due to the various

significant mechanisms promoting the energy transfer, and

is given as

( 1)

In order that the heat pipe operate satisfactorily,

the capillary pumping head developed in the wick due to

surface tension forces, ~Pc' must remain larger or equal

to the sum of all other pressure drops, for example the

pressure drop due to viscous forces in the liquid, ~P 1 ,

the vapor pressure drop, ~Pv' and the pressure drop due

to gravity forces ~P • g Maximum heat transfer capability

of the heat pipe is achieved when the capillary pumping

head is equal to the sum of all other pressure drops.

Mathematical expressions relating the pressure drop

to other system properties have been obtained by several

investigators. For example, the capillary pumping head

which can develop in a wick structure is given by

(2)

6

Experimental evidence indicates [9] that the effective

capillary wick pore radius in equation(2) can be taken as

half the width of the opening between two parallel threads

plus half the thread or wire thickness, and the value of

contact angle e, which the liquid meniscus makes with the

capillary channel formed by parallel threads of the fiberp

can be assumed zero. An expression for the liquid pressure

drop in the wick was derived by Cotter using Hagen Poise-·

uille law, and assuming laminar flow through the porous

media. The final expression is given by

= b~l Q(Le+Lc)

2n(r~-r~)p 1er~hfg {3)

where (L +L ) is the total length of the heat pipe. The e c

expression for the pressure drop in the vapor phase was

obtained also by Cotter. The vapor flow was treated as

a laminar, incompressible flow in a circular duct with

constant injection along the evaporator section and suction

along the condenser section. This expression is given by

4~VQ(Le+Lc) =

npvr!hfg (4)

In most cases this pressure drop is negligible relative

to other pressure drops encountered in the heat pipe. The

gravitational pressure drop can be simply calculated from

~p = + P' ~ L cos ~ g 1 gc

(5)

7

This gravitational effect could enhance or reduce the

heat transfer capability of a heat pipe. If the condenser

is at a level above the boiler, the gravity effect in-

creases the heat transfer while in the reverse case it

decreases the heat transfer. When the heat pipe is in a

horizontal position the gravity effects are nil.

Haskin modified Cotter's results, equations (3) and

(4), for application to a heat pipe with an adiabatic

transfer section between the evaporator and condenser. His

results indicate that the above equations are still appli-

cable to this new geometry if the length parameters (Le+Lc)

appearing in the above expressions is changed to(L +La),

where La is the length of the adiabatic section and L is

the total length of the heat pipe.

To determine the maximum capability of the heat pipe,

the equality in equation (1) is used. By substituting the

various expressions for the pressure drops, for the case of

a heat pipe with an adiabatic transfer section, a relation

for the maximum heat transfer capability of the heat pipe

can be obtained in terms of wick, vapor and liquid proper-

ties and geometric parameters.

2crcose rc

+ P1 }- L cos {I ( 6) c

8

Haskin sol_ved the above equation, neglecting the gravita-

tiona! term, and deduced the following relationships for

optimum capillary pore radius, optimum wick thickness

ratio, and maximum heat transport as

r =[ b].llpvr! r/2 (7) c 2 2 811 p1e(r -r ) v w v

where

= (8)

and

Rearranging and using the optimum value described in

equation (8), the optimum value for heat transport can

also be expressed by

= 2'TTr~hf9crcos9 3 (L+La)

(10)

(9)

Joy [7] included the gravitational term in equation

(6), and derived the relationship for optimum capillary

pore radius and maximum heat transport. His final results

are given by

9

b~ 1 (L+L )gLcos~ 2 [( a ) +

21Thf e(r2-r2 )g g w v c

(11)

and

2crr0-r~p 1 ....2. gc Lcosfl

0max = (12) b~l (L+La) 4r 2~ (L+L )

+ c v a

21Thfge(r~-r!>P 1 4 1Tpvhfgrv

The total temperature drop across the length of the

heat pipe, between evaporator and condenser, is equal to

the sum of the individual radial temperature drops in the

evaporator and the condenser. This drop in temperature

has been treated by Chi [6] and the results are given by

(Figure 2) •

Teo-Teo= (Teo-Tei)+(Tei-Tv)+(Tv-Tci)+(Tci-Tco> (lJ)

The radial temperature drop due to conduction through the

stainless steel container is given by

Q r T - T = ln(ro) eo ei 21TK L ss e w

(14)

and Q

r T ci - Teo =

2iTKSSLC ln(r o)

w (15)

Tv TCI

Teo

B-B

STAINLESS STEEL TUBING

B CONDENSER

SECTION

WICK

VAPOR

ADIABATIC SECTION

A EVAPORATOR

SECTION

Tv TEl

TEO

FIGURE 2. Radial Temperatures at Evaporator and Condenser Sections

A-A

..... 0

11

for the evaporator and condenser, respectively. The

radial temperature drop across the saturated wick thick­

ness is given by

T I - T = e~ v

Q 27Tr L K we m

t

t exp

for the evaporator section, and

Tv - T . = Cl.

Q 27Tr L K w c m

m cP exp(- 47Tr L tK

w c m

{16)

for the condenser section. The mass flow rate appearing in

these expressions can be calculated using the following

expression.

xn = o hfg

( 18)

The possible use of the theoretical equations for predicting

heat pipe operating conditions depends heavily on how well

the properties of the saturated wick are known,such as ther-

mal conductivity, porosity, permeability and pore radius.

This kind of information, however, is not available and

more research is needed to specify more accurately these

properties.

Several limiting conditions on the operating character-

istics of a heat pipe have been reported in the literature.

12

These limitations prevent the heat pipe from achieving

its. optimum operating conditions. For example, the vapor

in the core could reach sonic velocity resulting in a choked

flow condition in the heat pipe. The heat flux attained

under such a choked condition represents the maximum pos­

sible heat flux which could be smaller in magnitude than

the optimum value predicted from equations (10) and (12).

This limiting criteria [10] is specified by

{19)

For cryogenic heat pipes, this limitation can be ignored

due to the low magnitude of the optimum heat fluxes.

Another significant limiting condition could be caused

by the entrainment of liquid in the vapor. Vapor and

liquid in the heat pipe normally travel in opposite direc­

tions and frictional forces under this limiting condition

could cause the liquid to leave the wick structure and

become entrained in the vapor. This effect, under severe

conditions, could prevent the liquid from returning to the

condenser under the action of capillary forces and cause

the heat pipe to fail. Experimental studies conducted by

Kemme [11] have indicated that this limitation could be

controlled by selecting a fine pore wicking material. If

it is necessary to use coarse pore materials as a wick, the

inner surface which contacts the vapor should be covered

13

with finer wicking material. The magnitude of the heat

flux under which this limiting condition is reached could

be calculated by

~P crhf Q = v g A Z

(20)

where Z is a dimension associated with wick surface and

nearly equal to wick thread diameter.

Heat transferred by the heat pipe can also be

limited by condenser and evaporator parameters. A high

energy flux at the evaporator section could cause a

phenomenon similar to film boiling where a film of vapor

can become trapped between the wick and the tube. This

film in effect increases the resistance to radial heat

flow and thus results in a corresponding increase in

evaporator temperature which leads to heat pipe failure.

In addition the working fluid must be free of all impurities

for proper heat pipe operation. Impurities which are more

volatile than the working fluid would collect in the con-

denser section and those which are less volatile would

collect in the evaporator section. These impurities in

effect reduce the effective areas of the condenser and the

evaporator resulting in a reduced heat transfer capability

of the heat pipe. At any instance during the heat pipe

operation, the capillary forces must exceed all other active

and opposing forces. When such a criterion fails to exist,

14

for example due to an increase in gravity forces, the

heat pipe fails. This limitation is known as wick limi­

tation.

The above review indicates the lack of sufficie-nt

experimental investigations of heat pipes operating in

the cryogenic temperature range. The prediction of heat

pipe operating conditions depends on how well the wick

properties are known. This type of information presently

does not exist, and thus experimental work is needed to

further study the heat pipe operating characteristics in

this low temperature range.

15

III. DESCRIPTION OF THE EXPERIMENTAL APPARATUS

The experimental apparatus consisted of a cryogenic

tank, which provided an environment at liquid nitrogen

temperature (139.3°R); a heat pipe, on which measurements

were made; a vacuum jacket, which provided thermal pro­

tection to the heat pipe; and a precalibrated tank

acting as a nitrogen gas reservoir.

The cryogenic tank, shown in Figure 3, consists of a

double jacketed rectangular container 3.5 x 0.58 x 1.5 feet

in dimensions. It was fabricated out of 16 gauge stain­

less steel sheet metal and strengthened along its length

by several beams, 0.25 x l inches, to prevent buckling

when vacuum is applied to the surrounding jacket. The

jacket was maintained under a vacuum, approximately 12

microns, during the experiment in order to reduce the

evaporation rate of the liquid nitrogen contained within

the cryogenic tank.

The experimental heat pipe, shown in Figure 4, was

33.25 inches long and made of 22 gauge stainless steel,

type 304, tubing and has an outside diameter of 0.75 inches.

In order to form a closed tube, two stainless steel flanges

were silver soldered at the two ends. A 0.125 inches stain­

less steel tube was welded to one of the end caps to serve

as a fill and evacuating line. The heat pipe was divided

1-

UJ

:::£ u <

t J --

J. <t

(.!:)

:E

::::> ::::> u <

t >

z 0 ....... I-<

t __J ::::> (/)

z -

: •• ~ : .. ·• •• ·-•• 6' : ".: • : • ' : · ... " .. t.: : .. " .:· . ~ .... ·: : . .

I 1 I : 1 : I I 1 . . '•

. I 11

11 II I

• .. .,

I 11

11

11

1

.. . .. I Ill IIIII

. . . .. ~ I

I 1 1 'II

• ' . I I

.. U

J

I Ill II II

.. (.!:)

' . 0

. 0

::

I II II II

.. I-

.. -

I '1'1

11

11

z

.. . . . 0 -

I 11

11 I Ill

. ::::>

. c;

. .......

I II II 1 Ill

. __J

.. . .. I 1

11 1

1 I I

.. .. 1

I I I . . .

I Ill IIIII .. ' ' .

I I I J

• . ' . .

; .. '~~· .. "' •' ,: •' .:··.,a:.:::·:~.: !•-' .,. ... ". ~ :.• .. •:•"• ' ......... '

~ ... .

"" ' .

~ )

:a: ::::> CL

O::::>

:E

1-U

::::>

<(a..

>

16

. M

FILL LINE

HEAT PIPE

PRESSURE GAUGE

TO VACUUM LINf

INSTRUMENT FEED THROUGH

THERMOCOUPLE LEADS

CONDENSER SECTION

ADIABATIC SECTION

' FIGURE 4. Heat Pipe with Vacuum Jacket

EVAPORATOR SECTION

VACUUM JACKET

~ ~

18

into evaporator, condenser and adiabatic sections. The

evaporator section was 10 inches long. Energy was added

to this section through a nichrome wire resistance heater,

15 feet long which was wrapped uniformly around the

peripheral surface area of the evaporator. Scotch tape

and general electric adhesive, No. 7031, were used to

electrically insulate and at the same time provide good

thermal contact between the heater wire and the heat pipe

surface. The condenser section was 10 inches long at the

other end of the tube, and served as a heat sink while the

middle section between the evaporator and the condenser

served as the adiabatic section.

In order to isolate the evaporator and the adiabatic

section of the heat pipe from direct contact with the

cryogenic environment, they were enclosed inside the

vacuum jacket as shown in Figure 4. A cap was silver

soldered to the heat pipe on the line separating the con­

denser from the adiabatic section to provide a seal when

connected to the vacuum jacket. A tube was welded verti­

cally to the jacket and was used as an evacuating line and

a housing for the instrument wires. The open end of this

connecting tube was then closed by an instrument feed­

through flange and a connection was made to the vacuum

pump line.

A stainless steel cylindrical bottle, 0.318 cubic

feet in capacity, was used as a storage tank for nitrogen

19

gas. This bottle was equipped with a pressure gauge

which was calibrated as a function of mass contained within

the bottle. For any given pressure and room temperature,

the mass of nitrogen within the bottle could be read

directly from Figure 5. This bottle was connected to the

heat pipe through the feed line and was used to charge

and determine the amount of nitrogen charged into the heat

pipe. The feed line was also equipped with a pressure

gauge to measure the pressure within the heat pipe during

operating conditions.

The axial temperature distribution along the external

surface of the heat pipe was measured by thermocouples

and a potentiometer. The thermocouples were copper­

constantan, 5 mils in diameter. Six thermocouples were

distributed as shown in Figure 6 (one on the evaporator

section, four on the adiabatic section, and one on the

condenser section) • Each thermocouple was tempered by

rapping the thermocouple leads around the tube for a length

of six inches to insure accurate temperature measurements.

Electrical energy was supplied to the evaporator section

through the heater from a 110 volt - 60 cycle AC outlet.

A powerstat was used to vary the energy input and an AC

wattmeter was used to measure the energy added to the heat

pipe.

The wick was made out of modacrylic fiber cloth which

is a synthetic fiber woven from 18/1 cc. yarn. The fiber

-.. ~

~ '-'

1'1'"\ c::> r-i

X (/) (/) <( ~

z UJ C) 0 0::: .,_ -z

20

160r---------------------------------

40

30

20

10

PRESSURE (PSI)

FIGURE 5. Calibration Curve for Nitrogen Storage Tank

CONTAINING TUBE

CONDENSER SECTION

ADIABATIC SECTION

EVAPORATOR SECTION

I~ 8,25" •I

1... 11'' ~

1~ 14 .5'' ... 1

1... 18" -----------~~ 1~ 22.5'L--------+i

~ 25.5''"----------+t

FIGURE 6. Thermocouple Locations N ~

22

had 64 ends and 43 picks of yarn per square inch and was

a plain weave. The weight of the fiber was 3.6 ounces

per square yard and its thickness was 0.015 inches.

This material was selected because of its fast wicking

properties and its high capillary pumping head. The

capillary pumping head was measured for four types of

wicking materials, 100 mesh stainless steel screen and

rnodacrylic acrilon, and polyester fibers by dipping them

in distilled water and observing the speed and the maximum

height of wicking achieved by capillary pumping. The

modacrylic fiber was superior to the other three materials.

Three layers of this material were wrapped and inserted

into the heat pipe to serve as a wick. The wick was tightly

held by a helical spring inside the heat pipe tube.

The heat pipe with its protective vacuum jacket was

suspended inside the cryogenic tank through a rotating

device in such a way that the entire assembly could be

rotated and locked in position in either direction (Figure

7) . This assembly was used to investigate the operating

characteristics of the heat pipe at different angles of

inclination. For evacuating the cryogenic tank, the heat

pipe, and the vacuum jacket, each was connected to the

vacuum pump through appropriate swagekck fittings and

valves as shown in Figure 7.

PRESSURE GAUGE IIPREs-··

VACUUM GAUGE

0

POTENTIOMETER

c

0 0

TO ELECTRICAL

SUPPLY

POWER~TAT

SURE GAUGE LIQUID NITROGEN LEVEL

II- -~--=- ~ ~:- -p - = - --- ----- -- -

N2 SUPPLY n ... L-nun vnvuun runr \...LN2 CONTAINER '1"\1'\""r'T'I r-

FIGURE 7. Experimental Set~Up of Nitrogen Heat Pipe Assembly

t.J w

24

IV. EXPERIMENTAL PROCEDURE AND DATA REDUCTION

The successful operation of the heat pipe relies

heavily on purity of the working fluid and the non­

presence of any foreign destructive material in the wick

structure. To insure this state, the heat pipe and all

the connecting tubings were evacuated at room temperature

to approximately 5 microns and then flushed by nitrogen

gas. This,procedure was repeated at least six times to

dilute and remove any non-condensable foreign gas from

the heat pipe. A leak check was performed to insure the

isolation of the heat pipe from the surrounding environ­

ment. The heat pipe structure was then adjusted to a

horizontal level by a liquid level indicator situated

temporarily on the condenser section. The degree of

accuracy to fix the entire heat pipe in horizontal

position by this method could not be ascertained.

As a final step in the preparation of the heat pipe,

the whole assembly·, consisting of the cryogenic tank, pro­

tective jacket and the heat pipe tube, was evacuated for a

period of 48 hours. The cryogenic tank was partially

filled, to cover the whole heat pipe, with liquid nitrogen

and acted as a heat sink. Every three hours, throughout

the experiment, liquid nitrogen was added to the cryogenic

tank to maintain the liquid nitrogen level above the heat

pipe approximately constant.

25

To determine experimentally the amount of energy

loss by conduction through the containing tube wall and

instrument wires and by radiation to the protecting

jacket, energy was added to the evaporator section while

the heat pipe was evacuated. It was observed that for

the temperature drop range, between the evaporator and

condenser, covered during the experimental run, this

energy loss varied between 0.025 and 0.045 watts which is

insignificant relative to the energy transferred by the

heat pipe during the experiment.

To operate the heat pipe, nitrogen gas was injected

to the heat pipe through the fill line from the calibrated

plenum bottle. At this time electrical energy was not

being added to the evaporator section. Due to the fact

that the heat pipe's condenser section was at nitrogen

temperature (139°R), the gas added was immediately conden­

sed. This condensate then was carried by the capillary

action of the wick towards the evaporator section. The

axial temperatures along the heat pipe were monitored

throughout the condensation process. As the condensate

travelled through the wick towards the warmer end, the

temperature at each cross section dropped rapidly. The

entire heat pipe was at nitrogen temperature (139°R) within

ten minutes from the start of the filling process. This

indicated that the wick was operating well and being

26

saturated with liquid nitrogen. The magnitude of the mass

that was charged into the heat pipe was 0.1 pounds and

corresponds to a pressure drop from 100 psi to 36 psi in

the calibrated plenum bottle (Figure 5) • This amount was

chosen as sufficient to saturate the wick based on the

calculation from

(21)

This amount of mass was kept constant throughout the

experiment.

The experimental results consisted of the axial tern-

perature distribution for various power level input to

the evaporator section and for different angles of inclina-

tions. The operating pressure for every case was also

measured. For the horizontal level the power input was

varied from 5 to 110 watts and the steady state operating

pressure and temperature distribution for each of these

runs are reported in Table A-I and Figures 8 and 9. The

angle of inclination of the heat pipe while the condenser

was below the evaporator was fixed at 1.0 and 1.75 degrees

and while the condenser was above the evaporator at 5.25

degrees, to study the effects of inclination angles on the

heat pipe operating characteristics. In each case the

steady state operating pressure and the axial temperature

distribution were recorded for various power level input

to the evaporator section. The results of these runs are

I 901- I

,-...

7+ I

0::

I 0 .......,

1-<l I UJ u

I z UJ 0:: 50 UJ

I u. u. -t:l I UJ 0:: :::J I 1- 30 <( 0::

I UJ Q.. 0 6T total ~ UJ b. 6T condenser 1-

10J 0 !J.T evaporator

I -- 6 T copper rod

10 30 50 70 :JU J.J.V 1\)

~

POWER INPUT (WATTS) FIGURE 8. Experimental Resultsfor the Case of Horizontal Level

-Lt: 0 -

UJ Lt: :J t­< Lt: UJ a.. ~ UJ t-UJ u < u.. Lt: :J (/)

240 . EVAPORATOR'

230. SECTION ADIABATIC SECTION

50 WATTS

30 WATTS

20 WATTS 10 WATTS

DISTANCE FROM EVAPORATOR END (INCHES)

CONDENSER SECTION

FIGURE 9. Steady State Temperature Distribution, Horizontal Level

"' 00

presented in Tables.II,III, IV and Figures 10, 11, 12

and 13.

29

In each experimental run the effective thermal con­

ductivity of the heat pipe, based on a solid rod area of

0.75 inches in diameter equivalent to the diameter of

the heat pipe and a length of 17.25 inches equivalent to

the distance between thermocouples number 1 and 6, was

calculated using the Fourier conduction law.

(22)

where ~x and ~T are the spacing and the temperature differ­

ence between thermocouples 1 and 6 respectively, and q is

the heat flux through the heat pipe. This effective thermal

conductivity was then compared with that of copper [12] at

the same average temperature.

-. 0:::

0 -I-<J

UJ u z UJ 0::: UJ u. u. -Q

UJ 0::: :J I-<( 0::: UJ ~ ~ UJ I-

40 I

I 30 I

I 20 I

I I 0 ~T total

10 6. ~T evaporator

I 0 ~T condenser

-- ~ T copper rod

15 20 25 30 POWER INPUT (WATTS)

FIGURE 10. Experimental Results for 1° Degree Inclination Angle with Evaporator Above Condenser

w 0

,..... 0::

0 -1-<I

LLl u z LLl 0:: LLl LL LL -Q

LLl 0:: ::> 1-<( 0:: LLl c.. ~ LLl 1-

50~--------------------------------~

40

30

201 l/ 0 fiT total

-- fiT copper rod

10 5 10 . 15 20 25 30 35

POWER INPUT (WATTS)

FIGURE 11. Experimental Results for 1.75° Degrees Inclination Angle With Evaporator Above Condenser

w ~

-. ~

0

"""' 1-<J

LU u z LU ~ LU u.. u.. ..... Q

LU ~ ::l 1-<C ~ LU a.. ~ LU 1-

100....----------------------~

80

60

40

I

20 I-/ I

I

I I I

I I

I I

I

t.T condenser

0 t.T total

-- t.T copper rod -_L

4 60--· 80 100 120

POWER INPUT (WATTS) FIGURE 12. Experimental Results for 5.25° Degree Inclination Angle With

Condenser Above Evaporator

w ~

-0:: 0 .........

UJ 0:: :::J .... < 0:: UJ 0.. ~ UJ .... UJ u < u.. 0::: :::J en

. 230 ..

EVAPORATOR 210 ~sECTION

190

170

160

150

5

ADIABATIC SECTION

10 15 20

DISTANCE FROM EVAPORATOR END (INCHES)

CONDENSER SECTION

25

FIGURE 13. Steady State Temperature Distribution for 5.25 Degrees Inclination Angle with Condenser Above Evaporator

w w

34

V. RESULTS AND DISCUSSION

The results of experimental measurements for the

nitrogen heat pipe, summarized in Appendix A, indicate

that it is possible to achieve relatively high effective

thermal conductivity in the operating temperature range.

For example, for horizontal operating conditions at low

heat fluxes (20 watts) , the effective thermal conductivity

of the heat pipe was eight times that of copper at the

same average temperature (Figure 14). The effective

thermal conductivity decreased with an increase in heat

flux, and with an increase in the angle of inclination with

evaporator above the condenser section.

For the case of horizontal operating condition the

axial temperature drop between evaporator and condenser

and the radial temperature drop in each of these sections

is presented in Figure B. The axial temperature distri­

bution along the surface of the heat pipe for different

heat fluxes is presented in Figure 9. It is evident from

these figures that the temperature drop across the length

of the adiabatic section is relatively small. It is also

apparent from the plot of the radial temperature drop in

condenser and evaporator sections, that the thermal resis­

tance across the condenser is smaller than that across the

evaporator for small heat fluxes and this trend reverses

a: 0

I 1-u.. I

0:: :c

......... :::J 1-~

>-1--> -1-u :::J Cl z 0 u _J

<C ::E: 0:::: LIJ ::J: 1-

LIJ > -1-<..J LIJ LL LL LIJ

35

7000 r----.=1-----,---::::----:--------0 condenser raised s.zso

5000

Lmoo

3000

2000

600

500

400

300

0 horizontal operation

0 evaporator raised 1°

~evaporator raised 1.7so - copper rod

80 AVERAeE TEMPERATURE ( 0 R)

FIGURE 14. Effective Thermal Conductivity for the Heat Pipe at Different Angles of Inclination

36

for heat fluxes higher than 95 watts. This behavior can

be physically explained from the fact that the boiling

phenomenon, nucleate boiling, taking place in the evaporator

at low heat fluxes has a relatively higher heat transfer

coefficient than the condensation phenomenon taking place in

the condenser. At higher heat fluxes, however, when the

radial temperature drop in the evaporator is high, the

boiling phenomenon could change from nucleate to film

boiling resulting in a rapid decrease of the heat transfer

coefficient. Under these conditions bubbles and vapor

film becomes trapped between the wick and the inner surface

of the tube and prevent the liquid from coming in contact

with the warm surface. The exact temperature difference

at which the boiling phenomenon changes from nucleate to

film in the present geometry cannot be specified due to the

presence of the wick and the lack of experimental results

on this type of a problem. Also at this stage the increase

in the temperature difference between evaporator and con­

denser i~ mainly due to the temperature rise of the evapora­

tor section while the temperature in the condenser section

approaches an asymptotic value.

As discussed in' section IV, Chi developed a mathe­

matical model for predicting the total temperature drop,

between evaporator and condenser, as a function of heat

flux. This model assumes that the total temperature drop

is due mainly to radial temperature drop across the

37

evaporator and condenser sections, meaning isothermal

adiabatic section. This model was used to predict the

radial temperature drop obtained experimentally across

the evaporator and the condenser. Equations (15) and

(17) were used for the condenser section. The thickness

appearing in equation (17) was taken as 0.045 inches equiva-

lent to the thickness of the wick. It was found that in

order to use this model and predict accurately the experi­

mental temperature drop, the thermal conductivity must be

taken as a variable as shown in Figure 15. It was inter­

esting to note that the required value was higher than the

thermal conductivity of liquid nitrogen (0.0795 Btu/hr0 R

Ft) which implies that the radial heat transfer mechanism

was at least in part due to direct condensation on the

tube wall, instead of conduction through the liquid nitro­

gen layer. The upper half of the tube in the condenser

section could be exposed to direct condensation. The

gravity forces could have forced the liquid film to drop

to the lower half forming a pool, while leaving the upper

half partially exposed. This feature could explain the

reason for the high thermal conductivity obtained from the

above analysis.

To predict the radial temperature drop in the evapor­

ator section, equations (14) and (16} were used. The

thickness appearing in equation (16} was taken as 0.045

inches, equivalent to the thickness of the wick. It was

.,._ LL

I 0::::

0 I

0::: :J:: .......... => .,._ J:O

> 1-..... > ..... 1-u :::> Q z 0 u _. < ~ 0::: LIJ :::J: 1-

10 evaporator 0.81- 0 6 condenser

I I

0.7

0.6

0.5

0.4

0.3

0.2

0.1

.0

POWER INPUT (WATTS)

FIGURE 15. Effective Thermal Conductivity of Saturated Wick in Evaporator and Condenser Sections Based on Chi's

Analysis

w aa

39

found that in order to predict accurately the experimental

results the thermal conductivity must be varied as a func­

tion of heat flux as shown in Figure 15. This variation

of thermal conductivity confirms what was discussed earlier

regarding the changes in the boiling phenomenon which

takes place in the evaporator section. At high heat

fluxes the thermal conductivity decreases due to the vapor

bubbles trapped in and below the wick. As can be seen from

Figure 15, at high heat fluxes the thermal conductivity re­

quired to predict the experimental results,while using

this model, in the evaporator section becomes lower than

the values at the condenser section due to this type of

boiling mechanism.

The effect of inclination angle, with reference to a

horizontal level, on t~e operating characteristics of the

heat pipe was experimentally measured for the case of 1

and 1.75 degrees with evaporator above the condenser and

5.25 degrees with evaporator below condenser. The results

are shown in Figure 10, 11, 12 and 13, respectively. It is

evident that when the evaporator is above the condenser,

gravity forces limits the capability of the heat pipe and

reduces its effective thermal conductivity. These cases

represent an example of a wick limiting heat pipe where

the capillary forces are not sufficient to overcome both

the gravity and viscous forces. The reverse is true for

the case of evaporator below the condenser where the

40

gravity forces add to the capillary forces. The effective

thermal conductivity for different angles of inclinations

is shown in Figure 14. It reaches a high value of approxi­

mately 20 times that of copper at low heat fluxes for the

case of 5.25 degrees, evaporator below condenser, and low

value of 1.25 that of copper for the case of 1.75 degrees

with evaporator above condenser.

The experimental results are compared with the results

of Haskin in Figure 16. The present total temperature dif­

ference is smaller than that of Haskin's at the same heat

flux input. In comparing the two experimental results for

the horizontal case a difference of approximately 55 degrees

exist for the same heat flux with the net result of higher

effective thermal conductivity for the present experimental

heat pipe. This difference could be due to differences in

design, type of wick material used and the different loca­

tions of the thermocouples. No attempt has been made to

optimize such a heat pipe in either study. A small error

in the horizontal level of the heat pipe could contribute

to some of these differences. The general trend of the

results, however, agree favorably.

The maximum heat transfer capability of this nitrogen

heat pipe w~s predicted from equation (9), using the proper­

ties of liquid and gaseous nitrogen, Appendix B [12,13],

which was approximately 500 watts. The maximum heat trans­

ferred during the experiment was only one fifth of the

,...... 0:::

0 .........

!;:} UJ

f5 0::: UJ u.. u.. ..... Q

UJ 0:::

~ UJ 0...

ffi 1-

•

Haskin 6T evaporator high by 1°

() Has~in 6T evaporator low by 1° ~ Haskin 6T horizontal operation

• present exp. evaporator high by 1° 41 present exp. horizontal operation

~ present exp. condenser high by 5.25°

I'OtVER INPUT (WATTS)

FIGURE 16. Comparison of the Total Experimental Temperature Difference

~ 1-'

42

predicted value. The radial thermal resistance at the

evaporator and condenser sections, which is not taken into

consideration in deriving equation (9) are probably the

cause of this difference.

43

VI. CONCLUSIONS AND RECOMMENDATIONS

The experimental heat pipe designed with the moda­

crylic fiber wick proved to operate satisfactorily in the

cryogenic temperature range. The adiabatic section for

the case of horizontal operating conditions was operating

approximately isothermal for heat fluxes below 20 watts

and with approximately 8 degrees drop for a heat flux of

100 watts. The effective thermal conductivity was approxi­

mately 8 times that of copper for the horizontal case, and

increases to 20 times that of copper for the case of 5.25

inclination angle with evaporator below condenser. The

major resistance for heat flow at high heat fluxes appears

to be the radial thermal resistance at the evaporator sec­

tion where bubbles and vapor film could become trapped in

and under the wick structure.

As the angle of inclination increases with evaporator

above condenser the effective thermal conductivity de­

creases and the maximum heat flux capability of the heat

pipe decreases. The reverse of the above is true for the

case of evaporator below condenser. In comparing the

present results with that of Haskin's, it appears that the

present effective thermal conductivity is higher for the

same heat flux loads. This difference is probably due to

differences in design, wick material and locations of

44

thermocouples. A small error in the angle of inclination

could contribute to some of this difference between the

two experimental results.

To improve the experimental set up and increase the

heat pipe maximum heat flux capability the present heat

pipe design should be modified to include highly conduc­

tive paths such as metal fingers in the evaporator section.

These paths would decrease the radial thermal resistance

in this section. Also, a copper sleeve should be installed

over the evaporator section to make it isothermal. An

additional pressure gauge should be installed at the

evaporator end to detect pressure difference between

evaporator and condenser.

Research is needed in the area of measuring effective

thermal resistance for conditions similar to the ones

existing in the evaporator and condenser sections, caused

by boiling and condensation on the interior area of a

cylindrical surface covered by a wick. This type of infor­

mation is essential, and not presently available, for

analytically predicting the operating characteristics of

the heat pipe.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

45

BIBLIOGRAPHY

Eastman, G.Y., "The Heat Pipe", Scientific American, May 1968, p. 38-46.

Grover, G.M., Cotter, T.P. and Erickson, G.F., "Structures of Very High Thermal Conductance", Journal Applied Physics, Vol. 35, 1964.

Coyle, E.C. and Gyer, W.T. "The Development of Large Capacity Heat Pipe", ACF Industries, Inc., St. Charles, (work under progress - report unpublished), Personal Communication, December 1969.

Haskin, W.L. "Cryogenic Heat Pipe", Air Force Flight Dynamics Laboratory, Technical Report AFFDL-TR~ 66-228, June 1967.

Philip, E.C. and Aleck, s.w., "Development of Cryogenic Heat Pipes", ASME Paper No. 70-WA-ENER-1, Dec. 1970.

Chi, s.w. and Cygnavowicz, T.A. "Theoretical Analysis of Cryogenic Heat Pipes", ASME Paper No. 70 HT/SPT-6, June 1970.

Joy, Patrick, "Optimum Cryogenic Heat-Pipe Design", ASME Paper No. 70 HT/SPT-7, June 1970.

Cotter, T.P., "Theory of Heat Pipes", Los Alamos Scientific Laboratory, LA-3246-MS, March 1965.

Katzoff, s., "Notes on Heat Pipes and Vapor Chambers and Their Application to Thermal Control of Spacecraft", SC-M-66-623, October 1966.

Dzakowic, G.S., Tang, Y.S. and Arcella, F.G., "Experi­mental Study of Vapor Velocity Limit in a Sodium Heat Pipe", ASME Paper No. 69-HT-21, August 1969.

Kemme, J.E. "High Performance Heat Pipes", Los Alamos Scientific Laboratory, Thermionic Conversion Specialist Conference, Palo Alto, Calif., October 1967.

46

12. Scott, R.B., "Cryogenic Engineering", D. Van Nostrand Company, Inc., Princeton, New Jersey, 1966, p. 277-286.

13. Johnson, V.J. "A Compendium of the Properties of Materials at Low Temperature (Phase I) - Part I -Properties of Fluids", United States Air Force, Wright Patterson Air Force Base, Ohio, Oct. 1960.

47

VITA

Jay Dudheker was born on November 21, 1932, in

Patna, India, where he attended elementary and secondary

schools. He graduated from Oswal Jain High School in

June, 1949.

He entered the Seattle University in Spring of 1961

and received the Bachelor of Science degree in Mechanical

Engineering in May, 1965. The following fall he entered

the UMR Graduate Engineering Center of St. Louis.

On August 4, 1968, he married Georgia Leventogianni

of Patras, Greece. During the course of his research work,

he and his wife have been blessed with the birth of one

child, Maryann, on September 1, 1970.

APPENDIX A

EXPERIMENTAL DATA

AND RESULTS

48

Run Power Number Watts

1 10

2 20

3 25

4 30

5 40

6 50

7 60

8 70

9 80

10 90

11 100

12 110

TABLE A-I EXPERIMENTAL RESULTS

HEAT PIPE OPERATING IN HORIZONTAL POSITION

Evaporator Adiabatic Section Condenser

T 0 R 1 T 0 R 2 T OR

3 T 0 R 4 T 0 R 5 T 0 R 6

143.50 141.50 141.50 141.50 141.50 139.30

152 148.20 147.67 147.67 147.67 139.30

157.34 152 151.50 151.50 151 139.60

160.40 154.67 154.10 154.10 153.10 140

166.80 159.20 159.20 158.10 157.10 140

172.95 163.50 162.40 162.40 159.40 140

182.5Q 170 168 167 164.50 140

200.20 173.40 171.50 170.50 167.50 140.20

211.91 177.30 174.40 173.40 170.50 .140.20

221 180.10 177.30 176.40 174.40 140.30

223.95 183 180.91 178.20 176.40 140.40

242 186.70 183 181.51 179.10 140.40

-

Operating Pressure

PSIA

16.70

27.70

31.70

37.20

47.70

58.70

74.70

90.70

104.70

118.70

137.70

147.70

.. \D

TABLE A-II EXPERIMENTAL RESULTS

HEAT PIPE OPERATING AT 1 DEGREE ANGLE, EVAPORATOR ABOVE CONDENSER

Run Power Evaporator Adiabatic Section ~ondenser Operating Number Watts T 0 R T 0 R T 0 R T 0 R T 0 R T 0 R

Pressure 1 2 3 4 5 6 PSIA

13 5 142 141 141 141 141 139.30 14.70 14 10 146.30 144 144 144 144 140 16.70 15 20 179.20 149.67 148.74 148.74 147.6~ 140 26.70

TABLE A-III EXPERIMENTAL RESULTS

HEAT PIPE OPERATING AT 1.75 DEGREE ANGLE, EVAPORATOR ABOVE CONDENSER

. Run Power Evaporatoi Adiabatic Section Condenser Operating

Pressure Number Watts T 0 R IT. 0 R T 0 R T 0 R T 0 R T 0 R PSIA 1 2 3 4 5 6

16 5 155.20 141.50 1~1.50 141.50 Ull.50 139.30 14.70

17 10 187.62 144 143 143 143 140 14.70 ----- -~---~ --·-

' I

I I

I

U1 0

Run Number

18

19

20

21

22

23

24

25

TABLE A-IV EXPERIMENTAL RESULTS

HEAT PIPE OPERATING AT 5.75- DEGREE ANGLE, CONDENSER ABOVE EVAPORATOR

Power Evaporator Adiabatic Section ~ondenser Operating Watts T 0 R T 0 R T 0 R T 0 R T 0 R T 0 R

Pressure PSIA 1 . 2 3 4 5 6

5 140.50 140.50 140.50 140.50 140.50 . 139.30 14.70

10 142 141 141 141 141 139.30 14.70

20 145.34 142 142 142 142 139.30 14.70

30 151 143 143 143 143 139.30 20.70

50 163.40 153.10 153.10 153.10 153.10 140.50 34.70

70 174.40 159.40 159.40 158.34 157.80 141 46.70

90 204 163.54 162.20 161.40 161.40 140.90 59.70

120 228.34 170.50 169 167 .. 50 167.50 141.50 69.30 ---- -

'

U1 .....

52

TABLE A-V DEDUCED EXPERIMENTAL RESULTS

Run Vapor 6T(Total) 0 R 6T (Cond.) 0 R 6T (Evap.) 0 R Number Temperature T1 - T6 T - T T - T

OR v 6 1 v

1 141.31 4.20 2.01 2.19

2 149.83 12.70 10.53 2.18

3 152.20 17.74 12.60 5.14

4 155.20 20.40 15.20 5.20

5 159.80 26.80 19.80 7.00

6 164.25 32.95 24.25 8. 70·

7 169.75 42.50 29.75 12.75

8 174.40 60.00 34.20 25.80

9 178.00 71.71 37.80 33.91

10 181.30 80.70 41.00 39.70

11 185.20 93.55 44.80 48.75

12 187.00 101.60 46.60 55.00

13 139.30 2.70 0.0 2.70

14 141.31 6.30 1.31 4.99

15 149.50 39.20 9.50 29.70

16 139.30 15.90 0.0 15.90

17 139.30 47.62 0.70 48.32

18 139.30 1.20 0.0 1.20

19 139.30 2.70 o.o 2.70

20 139.30 6.04 0.0 6.07

21 145.20 11.70 5.90 5.80

22 154.00 22.90 13.50 9.40

23 159.50 33.40 18.50 14.90

24 164.75 63.10 23.85 39.25

25 168.00 86.84 26.50 60.34

APPENDIX B

THERMOPHYSICAL PROPERTIES

OF

NITROGEN

53

c U\

....-!

c:: C

'J ....-!

c:: C

'· ....-!

c oc

,-... <t: -cr.. a.

-· UJ

o:-::J U

:· u: u

: o:-a.

54

s:: <U O

l 0 J.t ~

..... z ~

0 <U J.t ::s U

l U

l <U J.t tl.t

J.t 0 ~

"' :> . ...... I IXl

fi1 :::> t.!) H

I'Ll

55

50

-~'of'. .... u.

40 .......... ~ c:Q ....I -> .... -cr.

35 :z: L1.l Q

30

?.5

1. 1::>. 17S TEMPERATURE {0 R)

FIGURE B-2. Density of Saturated Liquid Nitrogen

55

215

-r-r-. 1-u..

' ::E: c:tl _J --> 1--en :z: u.: ~

56

20.~----------------------------------------~

10.

1.0

.lf)

FIGURE B-3. Density of Gaseous Nitrogen (Saturated Vapor)

57

0.6~------------------------------------~

0.5 LC'.

Co ....-\

X

-.. n .1~ ('.J 1-u..

.......... u ~ u:. I u.. ~ 0.3 .....1 -->-1--(/)

0 u UJ f1.? -> u ..... ~-

< :z >-~ 0.1

120 1~0 ?00 TEMPERATURE ( 0 R)

FIGURE B-4. Dynamic Viscosity of Liquid Nitrogen

.......... c r-1

X -('.; 1-LL

........ u UJ U)

I LL JXI ...J -->· l-.... en 0 u en -> u -~ <( z >-Cl

L~

1

I 1~n

I I I 34()

I I ?.?n !nn )f)() 3~'1 42n 60

TEMPERATURE (0 R)

FIGURE B-5. Dynamic Viscosity of Gaseous Nitrogen at Atmospheric Pressure

U1 co

59

100~----------------------------------,

BO

-~ Jll 60 ..J ........

~ ..... JXl -z: c -..... LH1 <( 1'-l -0:: 0 0... < > LL. ~n 0

..... < LU :X:

120 140 lf'O 1~0 ?.?.n

FIGURE B-6. Heat of Vaporization of Nitrogen

L.r. c: r-f

X -..... u.. ........ u.. Q:l _J -z: 0 -en z LLl ..... UJ u <( u.. 0::: ::::> cr.

68

64

no

56

52

l.JR

llll

1 ... 0 TEMPERATURE (0 R)

FIGURE B-7. Surface Tension of Saturated Liquid Nitrogen

60

-c::: 0

I X: ~ ..J ........ ~ I-~ -I-<( w :r: u -u.. -u UJ a.. (Jj

n.65

O.f'0

n.ss

n.sn

16'1

TEMPERATURE (0 R)

FIGURE B-8. Specific Heat of Saturated Liquid Nitrogen

61

......... u.

0 I

1--u. I

0::: :r: ....... => 1--al _..

>-1---· > -1--u => 0 z 0 u _J <( ~ c.::: U.J :t: 1--

0.09

1),08

0.07

0.~6

(),05

0 I Q!J

0.03

100

CRITICAL TEMPERATURE (227.4)

FIGURE B-9. Thermal Conductivity of Saturated Liquid Nitrogen

62

.::so r-1

X

-. 0::: o, t-u. I

0::: :I:

........ ::::> t-.xi -> t--> -. t-u ::;) Q z 0 u ..J <( ~ 0::: w :I: t-

gn

RO

70

IRn ?.on ??.n ;.z~n ~~n ?.RO 300 320 TEMPERATURE (0 R)

FIGURE B-10. Thermal Conductivity of Gaseous Nitrogen at Atmospheric Pressure

a\ w