Derive an equation for the net rate of radiant heat transfer from surface 1 in the system shown in the accompanying sketch. Assume that each surface is at a uniform temperature and that the geometrical shape factor F1–2 is 0.1.
GIVEN
? The system shown above
FIND
? An expression for the net rate of radiant heat transfer from surface 1 (q1)
ASSUMPTIONS
? Steady state
? A1 and A2 are gray, A0 is black
? Each surface is at a uniform temperature
? The shape factor F12 = 0.1
PROPERTIES AND CONSTANTS
All of the shape factors for the problem can be expressed in terms of F12 using Equation (11.46) and the fact that all shape factors from a given surface must sum to unity. Also
The net rate of heat transfer from surface 1 is given by Equation (11.67)
Where the radiosity (J1) and the irradiation (G1) can be calculated using Equations (11.69) and (11.66)
Substituting [4] into [1]
Substituting [2] and [3] into this Equation
where
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