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.
IVEN
• 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
he Stephan-Boltzmann constant (?) = 5.67× 10–8 W/(m2 K4)
All of the shape factors for the problem can be expressed in terms of F12 using
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
Where the radiosity (J1) and the irradiation (G1) can be calculated
Substituting [2] and [3] into this Equation
where
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