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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