Reduction of radiative heat transfer in thermal insulations by use of dielectric coated fibers

0735-1933/89 $3.00 + .00 PrintedintheUnited States

INT. COMM. HEAT MASS TRANSFER Vol. 16, pp. 851-860, 1989 ©Pergamon Press pie

R E D U C T I O N OF R A D I A T I V E H E A T T R A N S F E R IN T H E R M A L I N S U L A T I O N S BY USE OF D I E L E C T R I C C O A T E D F I B E R S

Department

T. W. Tong and P. S. Swathi of M e c h a n i c a l and A e r o s p a c e E n g i n e e r i n g A r i z o n a State U n i v e r s i t y Tempe, AZ 85287 G. R. C u n n i n g t o n , Jr. Palo Alto R e s e a r c h L a b o r a t o r y Palo Alto, CA 94304

Lockheed

(Communicated by J.P. Hartnett and W.l. Minkowycz) ABSTRACT This paper reports an analysis on using c o a t e d silica fibers to reduce r a d i a t i v e heat t r a n s f e r t h r o u g h thermal insulations. C o n s i d e r a t i o n s were given to s i l i c a fibers of d i a m e t e r s 2, 5, and I0 ~m. They were c o a t e d w i t h either a 0.2 #m silicon c o a t i n g or a 0.2 ~m silicon inner c o a t i n g and a 0.I ~m s i l i c a outer coating. Calculations were p e r f o r m e d to d e t e r m i n e the ratio of r a d i a t i v e heat flux for c o a t e d fibers to that for u n c o a t e d fibers, The c a l c u l a t i o n s were made for b o t h constant fiber number d e n s i t y and c o n s t a n t bulk density. It was found that k e e p i n g the fiber number d e n s i t y c o n s t a n t r e s u l t e d in larger r e d u c t i o n s in r a d i a t i v e heat flow. For the test c o n d i t i o n s examined, r e d u c t i o n as high as 75 percent was shown to be possible.

Introduction An earlier

investigation

had on the r a d i a t i v e potential transfer been

for using in s i l i c a

extended

properties silicon

thermal

for m u l t i p l e

of s i l i c a

coatings

coatings

of the r a d i a t i v e

present

presents

851

fibers

[i].

to permit

properties

an analysis,

dielectric

to reduce

insulations

tai]orability paper

of the effect

coatings

indicated

radiative

The study

high

heat

[l] has

broader

of the fibers

w h i c h makes

[2].

use of the

The

852

T.W. Tong, P.S. Swathi and G.R. Cunnington, Jr.

findings through

in Refs. silica

I and 2,

on r e d u c i n g

insulations

for

Vol. 16, No. 6

radiative

temperatures

heat

ranging

transfer

from

1000

to

1600 K.

Because widely work

of

used

their

in many

considers

low b u l k thermal

insulations

or I0 ~m

in diameter.

coating.

To p r e v e n t

temperatures, also

made

Silicon oxidation

an outer

density,

silica

insulation

coating

of silica

parent

of 0.2 ~m thick of silicon made

fibers

have

applications.

been

The present

fibers

of 2, 5

is chosen

as the

at e l e v a t e d

of 0.I ~m thick

silica

is

considered. Analysis

Radiative

Properties

Figure The f i b e r coating

1 depicts is

assumed

thicknesses

The e x p r e s s i o n s

scattering

the to

fiber

geometry

be c i r c u l a r

are

uniform

and extinction

consideration.

and

infinitely

and the

incidence

for the r a d i a t i v e

(Osca)

under

properties,

(Oext)

i I

i

long. is

namely,

efficiencies,

the

and

I

COATINGS~

I FIBER---------

I

I

r

r

i i i INCIDENT WAVE

~

FIG l Geometry of fiber.

The

unpolarized.

the

Vol. 16, No. 6

RADIATIVE TRANSFER IN THERMAL INSULATIONS

back--scattered scattering These

fraction

albedo

radiative

incidence fiber,

(w)

(¢),

as the ratio

of incidence

of the coatings, and coatings

from all directions,

averaged

according

in Ref.

can be c o m p u t e d

the w a v e l e n g t h

of the fiber

are o b t a i n e d

can be found

is defined

properties

thicknesses

indexes

(bf)

2.

of Q s c a

to Qext"

the angle

(x),

the radius

and the complex

values

The single

once

are specified. for the

853

of of the

refractive

For

incidence

radiative

properties

to

r~/2 z=

21

(i)

z d¢ o0

where

z stands

scattered

for either

fraction

The a v e r a g e

0

sca or Qext" is given by

back-

2• IO sca bf de b-

:

f

(2)

6 sea

Radiative

Transfer

Heat

The analysis is o p t i c a l l y local

thick

radiative

approximated difference radiative

is c o n d u c t e d and

heat

the fibers

flux

between

are

process.

the b o u n d i n g conductivity

that

randomly

in an o p t i c a l l y

as a d i f f u s i o n

thermal

on the basis

surfaces

insulation

oriented.

thick

If the

the

medium

The

may be

temperature

is not

too

may be a p p r o x i m a t e d

large, as

a

[3,4]

3

4¢T m

(3)

[(I - ~ + 2~bf)oext] m where

T

m

is

temperatures, averaged

~ext

the

arithmetic

o is

extinction

=

the

mean of

bounding

Stefan-Boltzmann

coefficient

Oext d*N =

the

40extWf p~d

is

given

constant,

surface and the

by

(4)

854

T.W. Tong, P.S. Swathi and G.R. Cunnington, Jr.

where

d, • and p are

individual fibers

fibers,

the diameter,

respectively,

and Wf is the bulk

denominator

of the right

wavelength-averaged function

(ebx)

length

hand

and density

and N is the number

density

quantity

Vol. 16, No. 6

of the

side

density

insulation.

of Eq.

weighted

of the

(3)

against

of

The

is a the Planck's

at T m = I

~

ebk(Tm) dx

[(I

Making

use of Eqs.

between

uT:

~ + 2wbf)~ext] m

-

a coated

expression

(3) and

(4),

qr~coated

assuming

and an u n c o a t e d

for the r a d i a t i v e

• and N to be the same

insulation,

heat

flux

one can obtain

ratio

coated

[ x I (I - ~ + 2~bf)Qext d

constant,

the bulk

one obtains

the

density

of the

following

ratio:

qr,coated =

[RHS of Eq.

qr, u n c o a t e d Note

that

limits

for

the purpose

of the

integral

the

as

= [ x I (I - ~ + 2~bf)Oext d

For the case where

(5)

(I - ~ + 2~bf)qex t

(6)

uncoated insulation

is held

(Pd2)coated (6)](pdZ)uncoate d

of c o m p u t a t i o n

have been

the

replaced

(7)

lower

by

and upper

x I and

x 2,

respectively. Results Radiative

Properties for Qext'

Computations

the complex

-

refractive

and Friese

silicon.

The densities

g/cc,

a weighted

The w e i g h t e d silica

based

average

because

, and w have been -

reported

[6] for silica

respectively average

gf

index

Champtier

2.328

and D i s c u s s i o n

of silica [8].

by M a l i t s o n

the silicon

The density

is just

coating

[5]

and by Driscoll

and silicon

on the densities

density

carried

out using

and

[7]

for

are 2.2 g/cc

of the coated of silica

slightly

is thin,

higher

only

and

fiber

is

and silicon. than

0.2 pm as

that

of

Vol. 16, No. 6

mentioned

RADIATIVE TRANSFER IN THERMAL INSULATIONS

earlier.

to be 2, 5, and obtained

for

a silicon and

three

obtained,

the r a d i a t i v e

X 2 were

wavelength

chosen

range

at I000

wavelength 0.5 am

results fibers

range.

very

desirable

because

prevent

the fibers This,

oxidation.

substantially

the 2 ~m parent

fiber,

in the shorter

3.5,

there 6.5,

respectively. 1 for

x less

when

fiber.

coating,

are added,

fiber).

coatings

is in general

but

than 4 ~m for all

cases.

to

Qext

(3 to 8 pm

are added.

region

fiber

However,

is less

than

the

As far as bf is

an increase

scattering

to alter

At the shorter

region.

and 8 pm for the 2, 5, and

The

out to be

not added

wavelengths

wavelength

wavelength

The single

was

the

the coated

5 to 8 pm for the 5 pm parent

decreases

longer

coatings

From

~ is

and two coatings

turned

coating

longer

10 ~m parent

the d e c r e a s e

in the

has

of silica

that

one coatiug

2-4.

than 4 pm,

the parent

of the silicon When

Qext

than

outer

at the

wavelengths,

concerned,

with

than

were

7 to 8 ~m

by silica.

it is clear

in a way,

the silica

and 6 to 8 pm for the

increase

2-4,

properties

ratio

K.

characteristic shorter

over

rule with

in Figs.

in the

of low absorption

characteristics

it from

increases

a dip

At w a v e l e n g t h s

radiant

flux

to 1600

and bf are shewn

limits

integration

heat

to

This

trapezoidal

of i000

displays

in Figs.

small.

radiative

~'

different

between

range

is a typical

[9].

illustrated have

is r e l a t i v e l y

for

This

using

(7)

integration

The

for the radiative

Qext

to 1 b e c a u s e

difference

the

performed

1 degree

(6) and

of the b l a c k b o d y K.

(4)

the radiative

respectively.

at 1600

with

coating

at

Once

The

fiber

(3) and

properties

in Eqs.

chosen

were

inner

in Eqs.

ratios.

i0 pm,

silica

rule.

used

91 percent

for Oext'

insulations

close

radiative

were

results

a silicon

integrals

flux

1 and

for the t e m p e r a t u r e

wavelength

fiber;

trapezoidal

heat

as

(5) was

any coatings,

fibrous

the

Results

The results Without

The

diameters

purposes

with

they were

contains

in Eq.

fiber

silica

fiber

K and 95 percent

intervals.

obtained

very

coating.

by c o m p u t i n g

were

determine

energy

parent

and silica

of @ and a p p l y i n g

properties

silica

For c o m p a r i s o n

cases:

outer

evaluated

intervals

k I and

I0 pm.

coating;

a silica

were

The parent

855

at w a v e l e n g t h s

shorter

10 pm fibers,

albedo This

~ stays

very

is b e c a u s e

close

both

to

856

T.W. Tong, P.S. Swathi and G.R. Cunnington, Jr.

Vol. 16, No. 6

10

0.5Base Fbe, 2#m

---

:goofed Fiber '

---

F;ooled ;ibe, ' a,~r

"i,

~]i'er

0.4-

/:,\ /..-,:\ ,x I':' ,k./,'

IC~

2-

"A

/% /-,:,i,' "" (\I':.' ,7,,.

i! !,

"

/

r\

i

3

/;

:i,I,

0.3-

-0.6

0.2-

-OA

0.I

-I).2

b~

15

"2

0.0 2

0,8

4

6

5

7

g

I 2

I 3

I 4

I 5

I 6

I 7

I 8

I 9

0,0

10

x O•m) (a)

(b)

Radiative

FIG 2 p r o p e r t i e s for the 2 ~m s i l i c a and the c o a t e d fibers.

fiber

4 --

~ ; e ibur [:gm

--

C:~te¢ ~<,er I (bet

- - - C,:~ted Fiber :! [over

0.4-

0.8

0.3"

0.6

0.2"

-0.4

3-

,.<:.-..

I::3 •

':-'I',

-0.2

0

I 2

r 5

I 4

I 5

F 6

I ?

[ 8

0.0

[ 9

~ l l l J I I I 2 Z 4 5 6 7 8

(a)

Radiative

0.0 9

1

D

(b)

properties

and

the

FIG for

coated

3 the 5 #m s i l i c a

fibers.

fiber

Vol. 16, No. 6

RADIATIVE TRANSFER IN THERMAL INSULATIONS

857

0.5 --

~se Fiber ]0# Cooled Fiber I-boyer

1

Cooled ribel 2 Loyer

---

t

0.4-

- 0.8

0.3-

- 0.6

13

I,C::~ 0.2-

ol I 2

1

-0.2

0.0

I

l

I

3

4

,5

I 6

I 7

and

Radiative

The

results

number

for 63

the

less

the

and

except

that

in Figure

the

this

changes

in

number in

the

K.

insulation

is

66

smaller energy where

lower 6 shows

higher contained

I 8

I

9

10

fiber

results

61 are

mean

and

(7).

in

Fig.

5.

for

in

increase

region heat

and

For 63

flux

the

percent

the

percent.

The the

wavelengths Qext

occurs.

are

smaller

2 pm f i b e r .

ratio

for

at for

10 pm

because

reductions for

75

reduction

longer in

The

from

temperatures the

constant

applied.

percent. 64

for

(6)

corresponding

the

radiative

flux

are

is

applied,

the

Eqs.

ranges

The and

radiative

shown

heat

substantial

temperature the

are

coatings

reductions at

coating

density

in

insulation

1600

the

examining

defined

radiative

when

2 #m f i b e r

by

as

at

is

outer

the

ratio

achieved

radiant

silica

in

illustrated

flux

percent

are

blackbody

a

of

corresponding

reductions

I

7

spectrum.

nonabsorbing

best

is

5 pm f i b e r

fiber,

I

6

are

reduction

K to

I

,5

silica

constant

density

1000 the

be

for

reduction

I

4

FIG 4 p r o p e r t i e s for the I0 ~m and the c o a t e d fibers.

effect

heat

Significant

I

3

Transfer

can

radiative

I 2

(b)

combined

the

10

(a)

silicon

properties

I 9

x(~m)

Heat

The

[ 0

(.m)

Radiative

silica

-0.4

constant

is When

858

T.W. Tong, P.S. Swathi and G.R. Cunnington, Jr.

Vol. 16, No. 6

0.45

0.40

""""""..•" 21" ..*.'*'~"

Base Fiber l O/~m

0.35 s

•

• ,o

" Fiber 5Nm 0.30

•

,

,f

.,•../

~

m

'f/

Cooted Fiber 1-Loyer

---Coa(ed Fiber 2-Layer

f -"'" Base Fiber 2#m

0.25

0.20

1000

I

I

I

I

I

1I00

1200

1300

1400

1500

1600

To (K) Radiative

bulk

heat

density.

weight

of

This

the

reduction

in

that

observed

fact

that

maintain

FIG 5 for c o n s t a n t

situation

corresponds

insulation radiative for

there the

ratio

flux

heat

constant

are

same

fewer

bulk

properties

for

one

different,

the

radiative

consistently 60,

and

61

respectively.

the

be

transfer

fibers and flux

5,

and

to

is

in

the

tw o ratio

the

two is

reductions

that

the

not

coatings at

with at

than

due in

the

to

the

order

to

radiative

are

for

10 pm f i b e r s

The c o r r e s p o n d i n g

is

insulation

reduction

where

significant This

coatings

density.

case

Note

less

density.

number

the

fixed.

Although

The b e s t 2,

kept

number

density.

coating

higher. for

must

fiber

lO00 one 1600

significantly is K,

about

83,

coating, K are

46,

54,

Vol. 16, No. 6

RADIATIVE TRANSFER IN THERMAL INSULATIONS

025

I

I

I

I

I II

II

l

I

859

I

m . Cooted Fiber 1-Loyer ---Cooted Fiber 2-Loyer osss °~S

0.65

oS s# S s# SS

0.55

Bose Fiber 5#m~,.., ,*"

,,'

ssoss SS~' Base Fiber 2#m

, o.."- \

0,45-

-'°J

I

,./

ol /

..I__ ....

~.'..'~

Z'~'~'°''"

Bose Fiber lO#m~.__._

P

0.35

! 1000

"1

11O0

1200

I

I

I

1300

1400

1500

1600

To (K) Radiative

heat

and 60 percent. reductions fibers,

of 58,

flux

FIG 6 ratio for constant

The a d d i t i o n 57,

respectively,

of an outer

and 59 p e r c e n t

bulk

density.

coating

produced

for the 2, 5, and

at I000 K, and,

28,

I0 # m

45 and 52 p e r c e n t

at

1600 K. Conclusions It has been substantially applying

coated silicon

radiative

coatings

I0 #m fibers

were

by e i t h e r inner

demonstrated heat

that

transfer

to the fibers. considered. a 0.2 #m thick

coating

it is p o s s i b l e in s i l i c a

Insulations

The fibers silicon

coating

and a 0.I ~m s i l i c a

insulations

made

were

outer

to reduce

of 2, 5,

considered

and

to be

or a 0.2 ~m coating.

by

In

860

T.W. Tong, P.S. Swathi and G.R. Cunnington, Jr.

general,

smaller

t h e a d d i t i o n of a s i l i c a

reductions.

reduction density,

obtained

outer coating resulted

For the c o n d i t i o n s was

75 percent

and 63 percent

Vol. 16, No. 6

considered,

for constant

for constant

bulk

in

the

fiber

largest

number

density.

References i.

T. W. Tong, P. S. Swathi and G. R. C u n n i n g t o n , Thermal Insulation, ll, 7 (1987).

2.

P. S.

Swathi,

3.

T. W.

Tong,

Ph.D.

Q.

Thesis,

Arizona

S. Yang and C.

Jr.,

J.

State U n i v e r s i t y

L. Tien,

J.

Heat

(1989).

Transfer,

105,

76 ( 1 9 8 3 ) . 4.

K. Y. Wang, S. Kumar and C. Transfer, i, 289 ( 1 9 8 7 ) .

5.

I. H. Malitson,

J. Opt.

6.

R. J. C h a m p t i e r

and G. J.

7.

W. G. Driscoll, York (1987).

ed.,

8.

R. C. Weast,

J. Astle

M.

Soc.

T. W.

Tong and C.

Am.,

Friese,

Handbook

of C h e m i s t r y and Physics, 9.

L. Tien,

55,

J.

Thermophys.

1205

Heat

(1965).

Report

SAMSO-TR-202

(1974).

of Optics,

McGraw-Hill,

New

and W. H. Beyer, eds., CRC H a n d b o o k CRC Press, Baton Rouge (1986).

L. Tien,

J. Reat

Transfer,

56,

70

(1983).