Heat Conductivity of Gases and Liquids Vargaftik Filippov, Tarzimanov, Yurchak

8/18/2019 Heat Conductivity of Gases and Liquids Vargaftik Filippov, Tarzimanov, Yurchak

1/202

,

CO

Oi

CO

Q

JTD-MT-2^1-133-71

FOREIGN

TECHNOLOGY

DIVISION

HEAT

CONDUCTIVITY

OP OASES

AND

LIQUIDS

by

N . B .

Vargaftlk,

L .

P.

Plllppov,

A .

A.

Tarzlmanov,

and

R.

P .

Yurchak

D

u j

E

B

s

m

c

Approved

for

public

release;

Distribution

unlimited.

i

Reproduced y

NATIONAL TECHNICAL

INFORMATION SERVICE

Springfi«M. *. 21151

W l


2/202

.

THIS DOCUMENT

IS BEST

QUALITY

AVAILABLE

THE

COPY

FURNISHED

TO DTIC CONTAINED

A

SIGNIFICANT NUMBER OF

PAGES

WHICH

DO

NOT

REPRODUCE LEGI LYo


3/202

mm»»

FTP'MT-2^-133-71

EDITED

MACHINE RANSLATION

THERMAL

CONDUCTIVITY

OP GASES

AND

LIQUIDS

By: N . B . Vargaftlk, L .

P .

Pilippov,

A .

A . Tarzlmanov,

and R . P . Yurchak

English

pages:

84

Source:

eploprovodnost' Gazov

. 1

Zhldkostey,

Moscow, 1970, pp. 1^-155.

This

document Is

a SYSTRAN machine aided

translation,

post-edited for

technical

accuracy

b y:

ohn

R.

Sechovlcz.

UR/0000-70-000-000

Approved

for public

release;

distribution unlimited.

TMII

RANSLATION

S

A

MNMTIOH

OP

TNf

OHM».

NAL

PORIMN

TIKT

WTNOUT AN Y

ANAtYTICAL

M

lO iTOKIAL OMMINT. STATIMfNT S

O B

THIOMIS

AOVOCAT IOOR IMPLIf0

AMI

TNOS I O P TNI SOURC I

ANOOO

NO T

NIC SUMLY

RIPLICT TNI POSIT ION

00 PINION P

NI

ONI ION I CNNOLOOV .

PMPARIO

IYI

TRANSLATION I V I SMN

POR I ION I CNNOLOOY

DIVISION

•P.APR.

ONIO.

FTP-MT- H-m~7i

PHI

12

Nov.

If 71


4/202

EMM**

Translator's

note:

n

several

occasions,

symbols

found in

formulae

and calculations appear

to

have

been

rendered

incorrectly

in

the

original

document.

They will be shown

exactly

as they appear

in

the original.

ä


5/202

T A B L E P

O N T E N T S

U . S. Board n

Geographic

ames Transliteration ystem

^

Designations f he Trigonometric unctions

V

Foreword

i

Chapter . Questions

of

he Measurement

Procedure

of

Thermal

Conductivity

Natural Convection

Temperature

um p

T he

ole

f he

rocess

f

Heat

Transfer

y

adiation

....

Concerning ew Methods

for

Measuring

he

eat

Conductivity

f Gases

and iquids 0

Chapter I.

Analysis

f he

xperimental

Data.

Recommended

Values

f Thermal Conductivity

5

Helium 5

Neon 1

Argon

8

Krypton

5

Xenon

9

Hydrogen 2

Nitrogen

8

Oxygen

4

Air 9

Carbon Dioxide

6

Ammonia 04

V a p o r s

o f . Hydrocarbons

o f

t h e

Methane Series

a t

Atmospheric

Pressure

10

M e t h a n e

2 2

f

Ethane

2 6

Propane 31

Butane

34

P e n t a n e

36

Hexane 37

Heptane 40

^0-^- 24 -1 3 3 -71


6/202


7/202

U .

S .

BOARD

ON GEOGRAPHIC NAMES

TRANSLITERATION SYSTEM

B l o c k talic ransliteration Block t a l i c ransliteration

Ai

A

a A ,

a

9 P p

, r

B

6

B

6

B, b

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c

C e S,

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B

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v

T

T

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m

T,

t

r

r

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g

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y

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N

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hi

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e

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0

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10

»

J O

1 0

Yu, yu

n n

n

n

P,

a

n

fl

n

Ya, ya

W F e

*

̂£

Initially,

after

owels,

and

fter , b;

elsewhere,

len

written s n

Russian,

transliterate

s

8

r

.

T he se

f

diacritical marks

s

referred, but

uch marks

m ay

e mitted

hen xpediency dictates.

PTD-MT-24-133-71

ü


8/202

n

'OUXHÜiQ RE H E .

O R t t E S P O N D I H G USSIAN H O

M G L I S H

DESICMATIONS

? " K L

HIOOIIOMEIKIC

UNCTIOMS

Russian

s i n

e o s

t g

ctg

SSO

cosec

• h

e h

t h

e t h

« e h

csch

a r e

s i n

a r c

e o s

a r c

t g

a r c

c t g

a r e

SS O

are

cosse

a r e

s h

a r e

o h

a r e

t h

a r e

c t h

a r e s c h

a r e

eseh

rot

If

English

sin

cos

tan

oot

B SC

esc

sinh

cosh

tanh

coth

sseh

eseh

oln- ̂

eos"

1

tan-1

oof

1

sse

esc

-1

-1

sinh

1

eosh-

1

tanh-

1

coth-

1

sseh-

1

eseh-

1

earl

log

FTD-' T-2'


9/202

This

eference

ook

epresents

ystem-

atized nd ritical urvey

f

he

asic

xper-

imental

ata or he

ost

widely

tudied

substances

n

iquid nd

aseous

tates (for

helium,

eon,

rgon, krypton, xenon, ydrogen,

nitrogen,

xygen,

ir,

arbon

ioxide,

mmonia,

ten ydrocarbons, arbon

etrachlorlde,

thyl

alcohol nd

water).

Tables

f

he

most

eliable

alues

f

he

thermal onductivity

of

all he

ited

ubstances

in wide

ange

f emperatures nd

pressures

have

been

ompiled.

There

re 0

ables,

61 llustrations,

and

56

ibliography

ntries.

T he ook

s ntended or wide

ircle

of engineers nd

cientific

workers

f various

branches

f

echnolopry,

nd

lso

or

tudents

and

graduate ssistants.

PrD-MT-24-133-71


10/202

f

MMMnHMHHBHMHaBMHBMHMnHHHHMRS^'

1

'

1

'' '

POREWORD

In

he

most lvarse ranches f modern cience nd echnology

data

n

heat

conductivity

of

many

ases

and

iquids

re

mployed.

In

connection

with

his here xists he eed or

he

ompilation

of

ables

f he

ecommended

eference

alues f he hermal

conductivity

ased n

areful

nalysis

of

he

xisting

experimental

results.

This

work hould e iewed

s

part f he

rogram

of he

State

ureau

of Standard

nd

Reference

Data

Q S S S D )

for he

ublica-

tion

f undamental

manuals

n

he roperties

of

ubstances,

hich

are

idely sed n

modern

echnology nd

re

ecessary or

he

successful

evelopment

f

ew

cientific-research

works.

Recently n

he

S A

n ommission f he

National

Bureau

of

Standards

he

am e

ork w as artially carried ut t he Thermo-

ohyslcal

roperties

esearch

enter Purdue

University.

A s

esult

there

as ublished

n

966-1968 book

n

wo

parts

[1],

/hlch

ives

the ecommended

alues

f he

hermal onductivity of 0

olid

substances

nd

2

ubstances n he

iquid

nd gaseous

tates.

In

his

ublication f he B S he

emperature ependence

f he

thermal onductivity

as

stablished nly or are ases (with 1

atm),

nd

or

iquids

he values

f he

hermal

onductivity

as

given nly

n

he

aturation

ine. T he ependence f he hermal

conductivity

n

he ressure

as

ot stablished. It

s

atural hat

such ata annot satisfy he emands of modern cience nd

echnology.

It

hould

e oted

hat

for

many

ubstances,

presented

n

he

ables

.

:rr-2'j-i33-7i i

.

.,


11/202

of

he

B S ,

here

xists

In he

iterature

xperimental

ata

n

he

thermal

onductivity

t

sufficiently

igh

pressures.

It

s

lso

ignificant

hat n umber

of ases he alues f

the hermal

onductivity

f

gases nd

iquids ecommended

n

1] re

based n veraged

urves

constructed ccording o he

ata

f arious

authors

without

he

necessary

nalysis

f he methods

f

measurement

employed

or

he

egree of ccuracy f he nitial xperimental

results. T he

ethods

f btaining

eferenced

ata y

eans

f

simple

veraging

f existing experimental alues, ithout onsideration

of

heir qualities as

ed

o he act

hat

n he

ables

f he

National

ureau

of

Standards

f

he

S A

1]

he

alues

of

he

thermal

onductivity

f water vapor t levated

emperatures

significantly

iffer

rom

hose

dopted n he nternational ables

In

9 64 2,

3]

nd

o beyond he imit

f

olerances

stablished n

these ables.

W e

uggest hat he

eferenced

ecommendations

must e

ompiled

by eans

of areful

election

f he ost

eliable nitial

ata

for

ignificant

umber

of ubstances.

For iquids nd ases.

In

hose

ases

here

t

Is

ossible.

It

s

ssential

o

epresent

he

dependence

f he hermal conductivity

n

he

emperature nd

pressure.

Such

ork n he ompilation f

ables f

ecommended

alues f

the

hermal onductivity

s ery

aborious.

It

can e

one

sufficiently

well

nly

y ersons

aving

experience n

xperimental

research

n

his

rea. A s

a

result,

a

eries

f

books

ust

e

published.

T he

resent

ook

s

he first

f

his

eries. It

Includes ata n

he

hermal onductivity f 5

ubstances

n he

liquid

nd

as

hases,

most

widely

tudied

n

n

xperimental

espect

in

wide ange

f

emperatures

and

ressures.

T he

uthors

hought t ecessary

hat

he

ompilation f

he

tables

e receeded

y

erious analysis

f

certain

principal

problems

f

he

methodical haracter nd y

discussion

f ew

methods,

which

re being

eveloped nd sed t

he

resent

ime

or

the

measurement

f

he hermal

onductivity

f

ases

nd

iquids.

PTD-MT-24-133-71

il

-

.


12/202

Therefore,

pecial

ttention was

iven

o he

ole

f

he

processes

f

eat

ransfer y adiation f medium proton eat

conductivity).

The mportance

f

his

roblem

has

ecently

een

clarified

n

onnection with he arrying

ut of

number

f

theoretical

nd

xperimental

nvestigations,

from which, n

particular, it

as

concluded

hat

hese rocesses can

oticeably

Influence

he esults of measurements f

hermal

onductivity

f

liquids

nd

ompressed ases

ven

t

ow

emperatures.

Work

n

the

ompilation

f

eference ables

and

specially

he

election

f

the ample

ubstances

make his roblem n rgent ne.

T he

corresponding material

xpounded

n

Chapter

as

een written

y

L.

P.

FllloDOV.

T he uthors also xamine he

roblem

f atural onvection,

since

ecently

here

ave

ppeared ew nteresting

esults

on

he

Investigation

f

natural

onvection

n

arrow learances.

O f reat

ignificance s he

rincipal of electing

material

for he

ompilation

f ables f

eference ata

n hermal onduc-

tivity.

A t

he resent

ime,

nfortunately,

here re

s

et

o

generally

ccepted riteria nd enets

which

might erve s he

basis

or

orresponding

nalysis.

T he asic material must

e

ompiled rom

he

esults

f ystematic

experimental nvestigations,

onducted

n

wide

ange f tates

by

well

orked ut methods.

T he ecessary

onditions

re horough

consideration

y he author

f ll

he

ossible ources f rror

of he xperiments and

proven stimate f

he

ccuracy.

Besides

this

material,

it

s

advisable

o se he

ata

f

uthors, hich

refer o

arrow

ange

f

states,

f

he

nvestigations

f

each

f

them

ncompass

arge

umber

of

ubstances. T he

esults

f

nonsystematlc

easurements,

onducted

n

arrow

ange

f

emper-

atures nd pressures, can

e

xamined

nly

n

he

ase

where

here

is

detailed

description

f

he

xperiment,

he

method

f

ntroduc-

tion

f

orrections

is

described, nd

o

rror stimates

hich

suggest

oubt

ave

een iven. O ne

hould

ot

use he

ata f

investigations carried ut

y

hose

uthors

hose

esults

differ

PTD-MT-2i»-133-7i

iii


13/202

anomalously without isible easons

r om

he

otality

f

he

mos t

reliable

data

v en If nly

n ne

substance, specially If he

experiment

wa s

escribed

with

nsufficient

detail.

he

formulated

criteria ave,

f

ourse,

a

general haracter;

during heir

practical

mployment

t oes

without

aying

hat he ompilers

will

a v e xperience

n

arrying

ut xperimental

esearch

n he

given ield, nd

horough

amiliarity

with

he

riginal orks

a nd

with

heir

riticism.

Even or e

omplicated s the

roblem f

valuating

he esults

used, nd of he

election

f

weights,

which

hould

e prescribed

for

hose

data

u r i n g

he

processing

f

he

material

or

a m p l e

liquids.

Here

t

s

specially

esirable

o

a v e

or e

r

ess

objective ethods f uch n

valuation.

O n e f

he

possible

methods

s described n w ork 43,

where

he

weights

f

data,

belonging

to

ndividual authors, ave been

escribed

y he omputation f

divergences

from

he

otality

f

he

o st

eliable

alues

,

stablished

during he averaging of he ata f ll he uthors.

S u c h method

allowed

s to

haracterize

he

esults f

a ch

uthor

y

a

oncrete

number .

A

imilar device

a s

sed

n

ombination 5],

here he

data of

all

he uthors a s broken

own nto

hree roups

depending

on

he

ivergence

r om

he

esults,

selected

s the

m o s t

reliable.

In everal

nstances

he stimates of he degree

f

reliability

by

he

or k ethod

4] er e

s ed

n

his

eference

ook

also,

primarily

he n he uthors* evaluations f he rror

w e r e

clearly

contradictory with he ariation of

he

orresponding

data

r om

the

veraged

values

f he whole. However , he

s e

f this

ethod

for

all

he

data

wa s

ot

thought dvisable,

ven

f nly because

there

rises

he

roblem

f

he

possible ifference n he

weighting

factors

or

arious

emperatures. In

onnection

with

his.

In

he

processing

f

he

data

or

a m p l e

iquids

-

oluene,

carbon

tetrachlorlde, nd also or benzoyl

nd

thyl

lcohol

he

os t

simple method

f

valuation

wa s mployed: the elected ata were

broken

own

Into

wo r o u p s epending n whether he

probable

rror

of he

xperiment

a s

within

%

r

whether

t

xceeded

this value.

In valuating he

o u n d a r y

imit f rror or his irst g r o u p

we

PTD-riT- -̂lSa-Tl x


14/202


15/202

For all ubstances

xamined

n

his ook he ependence f he

excess hermal

onductivity s unique

unction

f he

ensity n

those

egions

f

he

arameters

f

state.

In

which

eneralization

f

the xperimental ata

has

een arried

ut. A n

xception

s

water

vapor,

for

which n

ertain

nterval

f

densities

the

stratification

of

X

with

espect

o sotherms is bserved.

With

espect

o orrelations (1 )

nd

2) ables

ave

een ompiled

for

he moothed ata or

hose

ubstances epresented

n

he

ook

t

equal ntervals f

emperatures

nd

pressures.

N ot

iven

re

he

alues

of he hermal

onductivity

for egions close

o

ritical, lthough

recently

here

has een

arge

umber of orresponding nvestigations.

Here

here

as

etected

ery

trong

ependence

f

he

hermal

conductivity

n

he

emperature nd pressure, owever here re still

no ufficiently

eliable

ata

o

e

ecommended.

Therefore,

n

he

book

here

re o abulated

alues

f

or

he

egion

.9


16/202

r ^

I

The

otality

f e comme n de d ubstances

ncompasses

a

wide

range

f

alues of hermal onductivity r om .005 o

.5

W/(m.deg).

The

ook

ives

he

ange

of

emperatures,

n

which

ach

of

he

cited ubstances ca n

be

mployed

s

a

ample

ubstance,

/e

lso

estimated he

possible olerances

for

he alues

of he hermal

conductivity for

hese ubstances.

O n

he

basis

f

n

nalysis f

arge body f xperimental

ata

on

hermal onductivity

of

mixtures

a nd

olutions

f

arious ypes

It Is

possible

o

onclude

hat

he effect

f

mixtures n

he

thermal onductivity f

ases

nd

iquids

s

omparatively mall.

The

content

of mixtures

In enths

of raction of

percent,

s

a

ule,

does

ot

oticeably

hange

he

hermal

onductivity.

Requirements for

he

purity

of ubstances,

therefore,

are ot

overly

strict.

FT

D-MT-2H-133-71

xll


17/202

CHAPTERI

QUESTIONS

OP HE MEASUREMENT ROCEDURE

OP

HERMAL

ONDUCTIVITY

Natural Convection

The xclusion f he

effect

f

onnective eat ransfer

s

one

of

he

most

essential questions

n

he practice

f

measurements

of

he

hermal onductivity f iquids

a nd ases.

Fo r he escription of natural

onvection n

he o r m of

connection n lmenslonless

criteria

e sually se elationship

Nu~f(Or,Pr)-f(Ra)

3)

or

,=4i-/(/fc).

T"'

1

" 4)

where

T."

Ra'Gf'Pr

Raylelgh

umber;

X

1

effective

hermal onductivity,

which

ncludes molecular

hermal onductivity X nd

onvectlve eat

transmission;

e

he

oefficient f onvection.

PTD-:::

,

-2i«-i33-7i


18/202

In

1934 Kraussol^, [11] generalized

the

experimental

data

available

at

that

time

about

natural

convection

in a

limited

space,

using relationship

(4). As

the determining dimenpion

d

he

selected

the thickness of

the liquid layer 6

;

then Ra - '̂f

6

'

For

horizontal

and vertical layers, regardless of their configuration

Kraussold-,

obtained

a

single curve

(Fig.

1) . In

this

case

the beginning

of

convection (e >

1.00)

occurs when R a > 1000. During

measurement of

X

all

the

authors were

usually guided by this Kraussold curve for

the

selection

of

dimension

6

of

the

measuring

cell

and

the

difference,

of

temperatures in

the

investigated

layer

of

liquid.

In

certain

cases

corrections

were inserted

into

measured

values

of X,

by using

this curve. [Translator's

note:

unable to find exact spelling of

foreign names in

text. hen English spelling

is common,

I

will

use

it,

otherwise

I

will

transliterate

the

names.]

• ̂ f

Ü - v*

*

» • < , - « •

Fig. 1 .

The

relationship of

the

coefficient

of convection

to

Or

and Pr criteria according

to

data

of: I

- Kraussold

[11]; II -

Shlngarev fl^] for Saratov

gas

(1);

for C0

2

C2).

In the last 10

years a

number

of new experimental investigations

of

natural

convection has been

conducted,

mainly

in

liquids,

which

are located in the space between coaxial cylinders.

he

results

of

these

investigations

were

presented by

t h e 3rd International

Conference on Heat Exchange (1966) in three

reports:

ees,

Sherrif,

Grigul'

and Gauf [12].

Qrigul'-

and Ga uf studied

local

and average

coefficients of

heat em i s si on

during

natural convection

in

a

horizontal annular clearance.

They

applied optical methods of

investigation

of

convection,

determining

the

distribution

of

temper-

atures and heat

flows

with the aid of an

interferometer.

Generally

FTD-MT-24-133-71


19/202

the

reatest

quantity

f xperimental ata

s obtained

or

horizontal

a n n u l a r learances

nd

considerably

ess

or

ertical. In

om e

works,

or

x a m p l e

[13]*

he Kraussold u r v e as ee n

efined,

some ifferences a v e

been

evealed n he

alue

f or

horizontal

a nd

ertical

learances.

v

However ,

all hese

nvestigations,

s

he

esults

f earlier

experiments,

generalized

y

Kraussold

11],

ave

een

btained

n

comparatively

wide

learances:

6

7-300 m . A t he

a m e

ime,

when

f

iquids nd ases

s

etermined

at igh

pressures,

6

0.2-0.5

m , and he

length

f

m e a s u r i n g

ylinders

I

100

a m v

Therefore,

he

nvestigation

f

natural

onvection

t

u ch

omparatively

small

alues

of

nd

l* ^ a s

f nterest.

• '

v

."

;

R. V.

Shlngarev IM ]

ur ing

nvestigation f

he

hwmal

conductivity

f

O -

y

he ethod

f

heated ilament d «0.1 m ;

6

r

4 m ;

1*

00 m ) conduc ted xperiments at arious

t nd

extrapolated

he

e a s u r e d

alues of

'

to t • •

or

he purpose f

obtaining rue alues

f

. The nstallation wa s

ocated

n

vertical position. Measurements ndicated hat u r v e

= f

Ra),

constructed

r om xperimental

ata,

ies noticeably

ower han

he

K r a u s s o l d urve,

s

s vident

r om

Fig. 1.

From

xperiments

It

lso

ollowed

hat

the beginning

f

onvection

e

.00)

takes

place

t

Ra

500.

Th e u t h o r

ffered wo

quations

or

etermination

of

he oefficient

f

onvection

:

when

500


20/202

A . A .

Berkenhelm

tudied natural onvection

n

narrow

nnular

clearances

t

arious

alues

f

from

.5

o

m

nd

100

m .

A s

n

nternal

ylinder

here

erved

latinum

ilament

(d

0.1

m),

external

glass ube, he

iameter f

which

aried.

Experiments

were onducted with water and thyl lcohol with

ertical

nd orizontal

position f

he

measuring

ube. Results f experiments Fig. 2)

showed

hat

atural

onvection

with

ertical

nd

horizontal

position

of

he

measuring ube

s escribed

y

arious urves.

They

both

lie

elow

he

Kraussold urve. With

ertical

osition

of

ylinders

the

uthor

proposed equations:

for

egion

2JOO


21/202

•

Y u. L .

Rastorguyev

nd

.

Z. eller

15]

n

n

nstallation,

based

n

he

eated

ilament method

a

0.1

m ; .6? mm;

I

100

m ),

rranged ertically,

etermined

he alues

f

nd

on he

asis

f

experiments with arious

liquids

(Pig. 3).

for his uantity

n

egion

400

a 000 roposed

quation

• -0,402 (Pa)W».

(9)

T he

xamination

f

all

he

ew works,

n which

natural

onvection

w as tudied

n arrow

nnular

learances

on nstallations

y

he

heated

ilament

method,

llows

making

he

ollowing

onclusions:

1 .

curve.

Curves e

-

f

(Ra) are

located

lower

than

the

Kraussold

2 .

he

beginning of convection

(e >

1.00)

is

observed

at

number

Ra

>

2000,

i .e .,

greater

than

Kraussold (e

>

1.00

when

R a

> 1000).

he

Initial

sec t i on of

curves

e

f

(Ra) is

considerably

flater

than

for

the

Kraussold curve.

3 .

ith horizontal

pos i t i on

of the

clearance

the value

of

e

is

higher than

with

vertical, but lower than according to Kraussold

curve.

£

m

w

tmmA tti mf

j

^

a 4-«S'»"

«

0

0 '

/C *

W*

W*

trPr

Pig.

3.

Relationship

f o r nd

Pr 15]: I

-

ccording o

Kraussold-

Mlkheyev

equation; I ccording

o

data

of Berkenheim;

II

ccording

to

data of Rastorguyev nd

Heller

or

carbon

etrachlorlde

1),

exane 2),o

toluene 3) nd benzene (H).


22/202

It

hould

e

ndicated

hat eometric imensions

(6

nd

) n

[13-15]

re

ery

lose

o

he

imensions,

sually

tilized

n

he

heated ilament method

uring

measurement f

hermal

onductivity.

In his

ase

he

learances

re

sually laced

ertically.

O n

he

basis

f

esults f 13-15] or vertical learances t

s ossible

to

raw n

veraged

urve

or

f Ra).

T he

urve onstructed

by

s

p

o

a

30,000

s iven

n

ig. 4.

T he

eginning

of

convection

s

elected

t

a

2000.

Experimental

alues

of

e,

obtained

n

13-15],

are eflected

rom his curve

within

% .

T he

curve

an e

ecommended

for evaluation

f

natural

onvection

during

he

measurement

f

hermal

onductivity

f

iquids

and

gases y he ethod f

ertical

eated ilament.

1 .20

1 , 1 0

1.00

/

1

W 45

4, 0

* .S

gR a

i

10' tWs Ŵ*

2 1 0 *

JHfto-GrPr

Fig.

4 .

Generalized

relation-

ship

of

th« coefficient

of

convection to

Rayleigh

criter-

ion

(experiments

with

vertical

heated

filament).

Natural

convection

in a

narrow

annular clearance

(6-1

mm)

with

cylinder

diameter

d

10 mm and I

10 0

mm was studied by

Yu.

L .

lastorguyev

and

A. A .

Nemzer [16].

he cylinders were

placed

vertically.

On

the

basis

of experiments,

conducted

up

to

values

R a

5000,

the authors proposed equation

«-0.402

( / ? a )

0

. »

(10)

for region

1700

1.00)

is

when R a

> 1700.

This

equation can

be

used

for

vertical

coaxial

cylinders

at

R a

numbers

up

to 5000.


23/202

Temperature um p

T he ffect f

emperature

um p s ubstantial uring measurement

of

he

hermal onduotlvlty f ases.

During

xperimental

etermination f he

hermal

onductivities

of

gases

e

sually

measure

he

wall

emperature f

n nstrument.

B ut

t

s

known

hat etween olid

nd

as,

hich

re

located

at

istance

f mean ree

ath, there

xists emperature

um p 6t

This

henomenon as

xperimentally

tudied

y any nvestigators:

Smolukhovskly, nudsen,

lmiryazev,

azarev nd thers.

T he

question s described

n

detail n iterature, for

example, n

he

books

f

ennard

17]»

evlen

[18]

nd Clark

nd McChesney 19].

As

Is established,

h '̂

t

emperatüre.JuW p t or moderately

rarefied

ae

s roportional

o

he emperature radient

dt/dn

along

he ormal o he

wall urface fit*

dt/dn),

nd he

proportionality

actor

.

s

nversely

proportional

o

he

as

pressure

(Y A/P), Usually, y

measuring

he.thermal

onductivity

of ases at

low

pressures (when

f e

tm), uantity 6t

s

aken

into

ccount

y

onducting ests

at

arious

ressures;

Mum

~ /,,,-)-—-.

T he

consideration

f

his

correction s specially

ssential

for ases

with

omparatively

ow

molecular

weight nd t igh

temperatures.

A s

pplied

p

oaxial

ylinders

he

method

f

ccount

of

he

orrection

s ubstantiated n

20],

and

or

heated

ilament

In 21]. T he measured alues f hermal onductivity ot llowing

for

he orrection

re lways ower

han

rue alues f .

•:

*

.-

•

•

Thie,neglect

f

his

ffect

t

igh

emperatures can

ead o

•

substantial

rrors,

specially

for gases

with

omparatively

ow

i..5,

t

'.V

-

'.

"

. '.

'

:

- .,

•«..»


24/202

molecular

weight,

s,

for xample,

ook

place

n

he ase

f

-nitrogen. Figure

,

aken

rom 30],

hows

he

esults f measure-

ments

f he

hermal

onductivity

f itrogen, btained y arious

authors.

A t

levated emperatures

he

iscrepancies ere

very

noticeable

hey

eached

2 % .

Ueglect

f

he

emperature

Jump

specially

ppeared n

he esults f

experiments

f

Schäfer

and

Reuter 31], nasmuch, s heir

ata

efer o he

egion

f

high emperatures p

o

400

o

K .

tu

43

.̂

»U

O

• ? s o

m

isx

e

1

1

- <

I

I S O

ftß

S C O

—

•

\.

Q

1

V

*

»

J

L

of

A 1

|-

i

ob

•

> •

•

0

o

- J

1

•

:rp

'

S

.._

_

. . . j

*

•

1

1 _

,

e

iCO

e:j

«is

mo

i*c

Pig. 5. Experimental

ata

of

arious

authors

n

he

hermal

onductivity f

nitrogen: 1 rank 22]; 2

Natell,

Jennings

[23];

3

hotki

21»] ; » .

Geier,

chäfer

25];

5- lays,

l

ann

[26];

Weiss 27];

Stops

[28],;

8 ibland, arton 29].

After he

ntroduction

f

orrection

or emperature um p he

corrected

experimental

ata

ay

well

n ne

urve, s s

vident

from Pig.

6,

taken rom £30]. T he eviations of experimental

atja.,

obtained

y

arious

methods,

ie

within

% .

.'_


25/202

• . v ; fc

Pig.

6.

The

elationship

of

thermal

onductivity of

nitrogen

o emperature ccord-

ing o arious

ata,

orrected

taking

nto ccount

he

emper-

ature ump. Designations re

the

a m e s n Fig. .

.

A n

nalogous

ituation

ook

place

with

xperimental ata

n

the

hermal

onductivity

f rgon

[32], lthough

n ess

clearly

expressed

form.

nasmuch s

he

molecular

weight

f

argon s

higher

han

itrogen.

The

Role

of

he Process

f

Heat

Transfer

by Radiation

There

Is very reason o

believe

hat

eat

ransfer

aused y

the ohoton" echanism n

u m b e r f practically

mportant

ases

plays

a

ery ignificant

ole

n

he

process

f

nergy

ransfer,

especially

at

elatively

igh

emperatures. In

particular, here

are heoretical nd

xperimental

rguments

o

he

effect

that

he

process

of

he

adiation

ransfer

a y

oticeably

distort

the

sual,

molecular heat onductivity

of

iquids, beginning with

emperatures

of

he

rder

f

0

o

S.

A t

he

a m e

time,

he

nformation

which

e

have ow

vailable o

s

is

ery mall, a nd he roblem equires

thorough

tudy.


26/202

f.-.-

Tanlng

his into ccount,

he

authors

thought

t ossible to

thoroughly

analyze

the

rocess

f

adiant

ransfer. To

ignificant

degree he material

resented here is riginal.

1

T he

xistence

f processes f

adiation

nd

bsorption

of

radiant

nergy

leads

o

he

ppearance

of

upplementary mechanism

for heat

transfer.

This

radiation

echanism oexists

with

he

r.oleoular

heat

conductivity

nd n eneral

complicates

considerably

the otal rocess

of heat

transfer.

T he

implest s

he

rocess

in

media, hich

ay

e xamined

s

almost ransparent In

he

egion

of

requencies

close

o

he

maximum

f

lanck function.

It

takes

place, for example,

n

ases

f elatively low

ensity,

here eat

transfer

y radiation

eads

o heat xchange

etween he

oundary

surfaces

and

he

resulting

heat

flow

s

a

imple

otal f molecular

and

adiant

heat. What

s

ore omplex

s the

ransfer

f heat in

partially

ransparent media.

T;ie

ssential

ole f he

rocess

of

adiation

f edium w as

first

nderstood nd

iscussed,

pparently,

y

.

G .

Guton,

ho

as

occupied with he tudy f he hermal

onductivity

f

molten lass

B^].

Then

his

roblem

w as xamined n

pproximation

for lat ayer,

-ithout

consideration f he iffusion

ature f

he adiation) by

L .

?.

Filippov

35]

n

onnection

with

ebate

etween

.

B .

Vargaftik

[36,

37], on

he

one

and, and

eys and

andell

[38]

on

he

ther,

;n

he problem f

hermal

conductivity

of water

apor, n

he

course

of which

he merican

uthors

advanced

he

roposition

hat

the

hen xisting ifference n he esults could e ttributed

o

the

ole

f

heat transfer

y

adiation [38, 39]. T he

mathematical

formulation

f he roblem n he

eneral form as

ut

ogether y

Y u.

A .

ourinov

40]. Later,

recognition

as

iven

o

he

orks

of

Kelett

fkl] and Genzel

[42]. In he first f hese n

pproximate

examination

as

made for he ase

f

flat layer n

he

assumption

of

ndependence f

he oefficient

of bsorption

rom

he

frequency

ôr

more

detail, see

he onograph

of

.

?.

Pilipcov

T he

study

of heat onductivity of iquids" [33].

NO T EPRODUC IBLE

10

i


27/202

("gray

edium")

and without

consideration f

he

iffusion ature

f

the

adiation.

In

he

econd

work

he

distribution

f

ntensity

with

respect o

ngles

as aken

nto ccount nd

umber

f

mportant

particular

ases

ere

xamined-.for. transfer n lat

ayer transfer

by

adiation

n he

bsence

f molecular hermal

onductivity,

he

general

ase

f ransfer

n

medium

with trong

bsorption,

nd

he

general ase f

ransfer

n

gray"

edium). In

.

P.

Pilippov's

work

[̂ 3]

he eneral

roblem

or

lat

layer as

xamined

nd

an

nalysis as given

or wo imiting

cases:

strong nd weak bsorp-

tion. A eneralization of hese

esults

as

ade n he

ork

f

E .

A .

Sidorov

M].

T he ase f

ransfer

n lat layer of

"gray"

edium

as

xamined

f

ate

n

he

orks

f

oltz

^S-̂ S]

nd

Hohler 49],

T he

esults

f he development

f

work ^3] re

presented

elow.

T he nitial elationship or n nalysis ay

e

he quation f

transfer f

adiant

nergy,

written

n

he

ssumption

of he

existence

f

ocal

hermodynamic

quilibrium,

COJ» -̂«« -«/. 11)

This equation expresses

the

fact

that

the change

in the

intensity

of radiation I in a direction which

comprises

angle

u with

the

axis

x is

caused by the

natural radiation

of an

element

of the

volume

of

tne

medium

(the

first

term o f the

right

side) and

by

the

attenuation

of

intensity as a result

of absorption

(the

second

member

of

the

right side).

Equation

(11)

obeys

Kirchhofs

law,

expressing

the coefficient

of

volumetric radiation

of

the

medium

through the

intensity of the equilibrium

radiation

in a

vacuum

e,

the

coefficient

of

absorption

a

and

the

index

of

refraction n

(the

process

of

dispersion in this case

is

not taken

into

account).

Integration

of equation

(11)

for

a

flat

layer

o f width L with

the

temperature gradient,

perpendicular

to

the walls (axis s),

s ; i v e s the formulas for

the

intensity of radiation in a positive

(I

and negative

(I~)

direction

of

the axis:

U


28/202

t

I

cot d ,

/+-/M0)«

c , , ,

4 -

J

-rl

CO»»

. )

1

'

M*J

To

find

the

values

of

the

intensity on

the

boundaries

I

( 0 )

a n d I~(L) we use the

relationships

for

the

mirror

reflection:

'

+

(0 -H

* , /

O ) .

'-(*)-•. +

* , / ♦ ( * .

where

R a nd

^

re

he

oefficients

of

eflection.

For

he

+

differences in

intensities

I

a nd

w e

btain he xpression

/._/-

« p i l l -ä/̂ J^J U n ' O

-Ä.)/^*

+

t --4L

x(l-/^.)+-^

^

J

«« •*

•

r f i +

jr

where

ß

s

the factor f

he

ecurrence

f

eflections;

12

•

•


29/202

The

otal hermal flow s ade p

of

he

flow

f nergy

of

radiation

nd

he flow f molecular hermal onductivity:

Q

« ;j(/+_/-)co$

Mw/v-X^-,

12)

(here

u s he

lementary

solid

angle;

v

s

the

frequency). In

he

stationary tate

I.e.,

JU^jQcosOrf-rf»».

—ii^-.

13)

tf^

r fx

x

äx

J/

Expression (13)

s

a

omplex Integral-differential quation.

T(x)

HT )

n(T , v ) .

Th r ough he gency f

T(x)

o n

hese a m e

values

lso epends he

heat flow. It

s

significant

hat n eneral

both

erms n

expression

12) for

heat

flow

re nterdependent;

the

ntegral

radiation

er m

hrough

he agency

f

T(x)

depends

on , he econd

term or

he a m e reasons depends po n

he optical haracteristics.

The

radiation

nd molecular

contributions)

to

he

hermal

low

prove o e

onadditive,

dlspite he ssumption

bout

he additivity

of

ransfer

mechanisms.

determining

he function T(x)

-

he

distribution

of

emperature in

the layer.

It s clear

hat n he eneral

ase

he istribution

of

emperature t

fixed

emperatures of he

urfaces epends

simultaneously n

he

functions

13


30/202

To

nalytically nvestigate he

eneral

ase,

etermined y

formulas

(11)-(13), without

additional

ssumptions

s too omplex.

Therefore,

e

will

henceforth

imit

urselves

o he

following

special

assumptions:

1.

e will

xamine

ases

f

mall

ifferences

n emperature

o n boundaries, hich will

llow

s o imit

urselves o he

irst

two

terms

of

he

xpansion f he

unction

nto series.

2. e will s s u m e that t is

possible o isregard he ependence

of

he

coefficients

f bsorption

nd efraction

n he emperature.

3.

or

he

a ke

f

implicity

e

will

ssume

hat

i R ?

*

The

numerated

ssumptions

simplify

he

nvestigation,

but

hey

do

ot

deprive t

f sufficient

enerality nd o ot

impose ny

significant limit

n

he

applicability

f ts

esults

to ctual

systems.

Equation 13) n his case

can

e

ransformed

o

he

fo rm

L

£=jVd.

x),

Wdl

(14)

where

y

**'


31/202

Prom formula

(

i

»)-(8)

It is

clear

that

K

0

when

\~

*

0

and

the

distribution

of

temperatures

In

the

layer

approaches

a

linear

one.

n

correspondence

with

this

the

s o l ut i o n

for

the

temperature

can be found

In the form:

AT

7--ir

i

4r . j c

+

-|-9(xl

►

... .

20)

disregarding

he higher erms

f he

xpansion

o eries

with

respect o a nd

xamining hereby

only

the conditions, nder

which

ivergences

f

he

e m p e r a t u r e

ield

r om

inear

ne

re

sufficiently

mall

n

o m p a r i s o n

with T.

Physically, his

eans

the

xamination

f

he

processes

under

which

he

ecisive

factor

Is

he

molecular heat ransfer, while adiation plays he

ole

of

distortion

actor.

In he

pproximation f 20)

the

olution

f quation

(15)

ha s

the

or m

r-r.-iTir+ *(*)-( -^.)*(

0

) i .

2D

where

-

«-'-11

^

/?«-»*

-'>-) ]ds. 22)

A n

analysis

f

o r m u l a s (21),

(22) allows

u s

o

establish

that

he

emperature istribution

urve a s

a ending point

in

he

middle

f

he

layer

L/2)

nd

s

onvex n

he

wall

with

he esser

t e m p e r a t u r e

nd

s concave

n

he pposite

wall. It s also

possible

to

emonst ra te

a

umber

f

particular

peculiarities

f

he

emperature

distribution

n

hese

r

ther

oncrete

nstances

[33].

The

istribution of emperature, escribed

y

o r m u l a s

(21),

(22), llows

u s

o

lso btain

general

ormula

or he

otal eat

flow n

he

xamined

pproximat ion

15


32/202

L L

^

(1+«/?-*'•)»»

(23)

For ow-absorbing media

he

ormula ssumes he

orm

Q-_

xir

r̂ .

j T j

l+R *

d $

+

+

2̂«

•••

(24)

T he first

erm

of his ormula expresses

he

eat lo w ue

o

molecular

heat

onductivity, he

econd

describes

he

ffect

f

radiation

f

he walls, nd

he

hird - he

ought or hange

n

the eat

lo w s

result

f

he

processes f

adiation

nd

absorption

f adiant nergy y

he medium.

T he

aximum

value

f

this erm s qual

o

2i7=£

r ^ - r f » .

JdT

For

he

alue

f

he

elative

hange

n

heat flow

s

he

pper

limit

(for

n

bsolutely

lack

ody)

e

btain

he

xpression

0 3

k

dTi

(25)

A Q

In

practical

stimate

he

alue

^

or gases

hich

re

ow-

absorbing

media

he

ntegral

f

ormula

25)

can

e onveniently

replaced y xpression

J

..*-*A

(26)

where s he as ressure; s he imit

f

he

elati'onahip

f

the

degree

f

blackness f he lat ayer f gas o

he product.

. 'iJL,

with he

atter

ending

oward ero;

nd

s

he onstant f

the

tefan-Boltzmann

aw

or

hemispherical

adiation.

1 6


33/202

In

he

evaluation

of

26)

he

emperature

ependence

of can

h

be

isregarded

n

omparison

with

A s

esult

e

btain

£ ••i£t3t

t

27 )

Th is ormula

an

e

sed

or

valuating

he nfluence f

boundaries

f he nvestigated

effect. Thus, for carbon ioxide

gas

at

oom

emperature

nd pressure

of

ar

2.«lO"

l

I

,

f

• « ~

,

,

I.e.,

he

change n he

eat

low s esult of

adiation

f

he edium

ca n

n his case

ecome

oticeable t istance f

everal

centimeters. A t

a pressure f 000 ar

his

ffect

s ald

o

e

(at

istances

far emoved

rom

ritical oint)

lready

t

istance

of

everal

millimeters.

W e

will

lso

btain

imilar

order f

alues

for

water

apors.

T he

ole

of adiation

ncreases with

extraordinary

Intensity with he ncrease n

emperature.

In he

other imiting

case, for trongly-absorbing

media

formula

23)

assumes he orm

*-¥-TIH*T- « )

T he ffective

oefficient

f heat

onductivity

s

omposed

of w o erms which re ndependent one

rom

he

ther

he coefficient

of

molecular

eat conductivity nd he oefficient

f adiant

(radlatlonal) heat

onductivity.

n

which he

atter lso haracterizes

only

he

edium

s uch

nd oes

ot

epend n

he onditions

n

the

walls nd he onfiguration

of

he

ystem.

T he

oefficient

f

radiation

heat

onductivity s xpressed

y he formula

3

J

«if

-JT

(the

erivation

of

his

ormula s

also iven n ork

50], hich

w as specially eserved

or

he

problem

f

onditions f pplicability

of he

oncept f he

coefficient of

adiation heat

onductivity

in

onnection

with

ttempts t he

distribution f

ormulas

of

uch

type,

xisting

n

he

literature,

for cases

f

media

with

oor

absorption).

17


34/202

•

■

I

It

hould be oted hat

t

s

precisely the otal effective

heat

onductivity,

xpressed y ormula 28),

which u s t

be

igured

In

he Prandtl

nd

Nusselt criteria

or

hese ases, hen he

thickness

f

he

thermal

limiting

ayer

s

considerably

reater

*

than

he

pposite

alue of he effective

oefficient

f

bsorption

V)f

he

ed ium.

Let

s

urn

o

ormula 23),

which

escribes he eat

low

n

the

eneral

ase.

Effective

adiation

eat

conductivity

ay. be

represented s

'-Tj«'fr

( « .

D*.

(30)

where,

•'••''-4-±h^*}

In

he

eneral

ase

he

effective adiation

eat

onductivity

and ts ependence n

parameters

nd

,

being

unctional

of

o(v),

will

e

different

or arious

media.

Only

for

he

ypothetical

"ej ray" edium, for

which

const, an

e write

i«

VmS,*fiP*(*,l).

(32)

F o r m u l a

32) is he

basic

esult

of

he

o r k

f Poltz

46].

The

function

was

btained y

im

n

o m e w h a t

ifferent

but

similar

o r m :

*-i[.-£


35/202

T he

et

f curves—(»I,/?)

Is epicted

n

Pig.

.

rom

he orm

of his ependence

t

s ossible

o

ra w he

ollowing

ignificant

conclusions:

1. he

adiation

heat conductivity

f

he walls

with

evel

of blackness

f

1

)


36/202

SV

may

e

sed

for evaluation f

he pper imit of he possible nfluence

of

adiation

ransfer

n lat

ayer.

1

It s

orth

emphasizing

he

strong

nature f he

emperature

ependence f

his

riterion

(vr

J

)

nder

onditions

typical

or

hanges

n

eat

onductivity

f

boundary fluids ( X ̂ .1-0.3

W/(m-deg);

^

m).

A t oom

temperatures

he

ercentage

f heat

xchange y

adiation

hould

not

xceed

ew

ercent. However, at

igher

emperatures. In

narticular

t

emperatures

lose o he ritical points, he ole

of

adiation

an

e

onsiderably

ore

ubstantial, specially

because he onditions of

he

ransparency n his

rea

passing

from

he as to

he iquid

tate,

can e

specially nfavorable

(aL

̂1).

It

s

nown

hat n

mportant

ole can

e

played

y

radiation

or

high

emperatures melts (glasses, lags). It

can

be

Just

s

reat

n

solid

onm

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Heat Conductivity of Gases and Liquids Vargaftik Filippov, Tarzimanov, Yurchak

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