Project ForgeHeat Transfer
Convection & Radiation
GATE 2016
Hard
Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is Ro and that of the inner cylinder is Ri. The radiation view factor of the outer cylinder onto itself is
- A1 - √(Ri/Ro)
- B√(1 - Ri/Ro)
- C1 - (Ri/Ro)^(1/3)
- 1 - Ri/Ro
Explanation
By reciprocity and summation for two long concentric cylinders: A_i F_io=A_o F_oi=A_i (since the inner cylinder sees only the outer, F_io=1), so F_oi=Ri/Ro. Since the outer surface also sees itself, F_oo+F_oi=1, giving F_oo=1-Ri/Ro.
Source: GATE ME 2016 Set-2 (2016)
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