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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. .