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Blackbod Radiation Exchan eRate at which radiation leaves surface i and intercepted by j

ijii ji F)JA(q =

EFA=

For a black surface J i = E bi

Similarly, bj ji ji j EFAq =

Net radiative exchange between the two surfaces:

)TT(FAEFAEFAqqq 4 j4

iijibj ji jbiijii j jiij ===

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Chart

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Radiation Exchange between Diffuse, Gray

is the net rate at which radiation leaves surface i and

can be expressed for a gray bodyq i = Ai(J i G i)J i = E i+ iG i

J i = iEbi+(1- i)G ii = i i i i

G i = (J i - iEbi)/(1-i)= - - -

ibi JE =iii A / )1(

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Radiation Exchange between

To use the last equation, surface radiosity J i must known. Todetermine this quantity, it is necessary to consider exchangebetween surfaces of the enclosure

Total rate at which radiation reaches surface i from all surfaces,

=

=N

1 j

j j jiii JAFGAN

,

Cancelling the area A i and substituting in=1 j

jiijii

q i = i i i

=N

jijiii )JFJ(AqSummation rule

=1 j

== =N

1 j jiji

N

1 jijii )JFJF(Aq

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Radiation Exchange between

NN

Preferable

== 1 j

ij j

1 j

iijii

ibii

JEq

=

when temperature is known

iii

=N

jiibi JJJE=

1 j ijiiii )FA(A / )1(

=

=

1 j1

iji

jii

)FA(q

Preferable when q i is known

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Set of Al ebraic Equation1NN1ii1111 CJaJaJa =++++

iNiNiii11i CJaJaJa

=++++

NNNNiNi11N CJaJaJa =++++

[ ][ ] [ ]CJA =In Matrix form,

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Problem

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Problem (contd)

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Problem (contd)

2222 A / )1(q

=

For the hypothetical surface, J 3 = E b3

So, only unknowns are J 2 and J 1

A3

A1

=

=

1 j1

iji

ji

iii

ibi

)FA(A / )1(JE

1232

321

212

12

222

22b

)FA()FA(A / )1( +=

24

24

22b

33b3

m / W7348TE

m

==

===F21= ?

F23 = ?

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Problem (contd)=

Y/L = 10/1 = 10= =

F12 = 0.39

F21 = (A1 /A2)F12= 1x1 15 x .= 0.26

F13 = ?

F13 = 1-F 12= 1 0.39= 0.61

31 1 3 13=(10/(2(10.1)0.61

= 0.305= F 32=F 32

F23 = ?

F23 = (A3 /A2)F32 = 0.41

1

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Problem (contd)7536J67.1J26.0 =

JJJJJE1

311

2111b +

=

510002J39.0J10 21

131121111

=+

J 2 = 12528 W/m 2

kW7.77A / )1(

JEq222

22b2 =

=