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ew actor

Dr. Prabal Talukdar

Associate Professor

De artment of Mechanical En ineerin

IIT Delhi

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View/Confi uration Factor

.

Radiation exchange between two or more

geometries and orientations, as well as on.

To compute radiation exchange between

any wo sur aces, we mus rs n ro ucethe concept of a view factor.

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Definition The view factor F is defined as the fraction of the

radiation leaving a surface i that is intercepted by j.

dAjcosj

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Derivation Rate at which radiation leaves dAi and is intercepted

dqiJ=Ii cosi dAi dJ-i

Ii = intensity of radiation leaving surface idJ-i = soild angle subtended by dAJ when viewed from dAi

= cosJ dAJ/R2

dqiJ= Ii(cosi cosj/R2 )dAidAJ

Assuming surface i emits and reflects diffusely

d =J cos cos /R2 dA dA

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Derivation contd

and is intercepted by j may then be obtained byintegrating over the two surfaces. That is

ji2

ji

iji dAdAR

coscos

Jq

=

where it is assumed that the radiosity Ji is

uniform over the surface Ai.

i j

Fij = radiation that leaves Ai and is intercepted by Aj/total

radiation leaving Ai

= qij / Ai

Ji

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Final Expression

ji2ji

i

ij dAdAR

coscos

AF =

Similarly, the view factor Fji

defined as the fraction of the radiation

that leaves A and interce ted b A can be ex ressed as

ji

A A

2ji

j

ji dAdARA

F

i j

=

Assn: diffuse emitters and reflectors and have uniform radiosity

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View Factor Relations Reci rocit Relation:

AiFij = AjFji

Summation Rule:

N

1j

ij

=

ii Value of Fii for a convex or flat surface?

ii

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View Factor Relations (contd) Radiation exchange in an enclosure of N surfaces: N2

view factors required

N11211 FFF

N22221

Summation rule can be applied to get N equations which

NN2N1N

Application of Reciprocity relation for N(N-1)/2 timesgives N(N-1)/2 view factors

So we need essentially N2-N-N(N-1)/2

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Example ,

32-3-3(3-1)/2=3

F12 = 1=

F21= A1/A2

2

- 1 2

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View Factor Relation

=

=n

1k

ik)j(i FF

=

++++== ini3ii2ii1iin

1k

iki)j(ii FAFAFAFAFAFA

=

=

n

1k

kik)i(jj

nini33i22i11)i(jj

FAFA

j

==

n

n

1k

kik

)i(j

FA

F

=1kkA

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Problem

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View factor for coaxial parallel

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View factor for perpendicular

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The Crossed-Strings Method

Surfaces. .