j
q
G i
A i
N
A i
T i
i
ρ i G i
} J i
E i
ε i
�
�
�
�
�
�
also
J i = ε i E bi + (1 − ε i )G i
(13.2)
Therefore,
J i − ε i E bi
J i − ε i J i − J i + ε i E bi
q i = A i J i −
= A i
1 − ε i
1 − ε i
ε i (E bi − J i )
= A i
1 − ε i
So that energy from surface i
E bi − J i
⇒ q i =
(13.3)
(1 − ε i )/(ε i A i )
Then perform energy exchange between surface i and the rest of surfaces j:
net energy = energy out (radiosity) − energy in (irradiation)
q i = A i ( J i − G i )
where
N
N
A i G i =
F ji A j J j =
F ij A i J j
(13.4)
j=1
j=1
Therefore,
⎛
⎞
N
⎝
⎠
q i = A i J i −
F ij J j
j=1
258
Analytical Heat Transfer
FIGURE 13.1
Radiation heat transfer between N surfaces in an enclosure.