Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
View factor of a large cylinder of 10 cm radius and 60 cm length from a coaxial smaller cylinder of 5 cm radius and the same length is 0.34. View factor of the larger cylinder of itself (concave inner surface) is 0.25. The view factor of the larger cylinder with respect to either annular end is
Options:
(A) 0.17
(B) 0.29
(C) 0.33
(D) 0.42
Official Answer Key:
B
Step-by-Step Solution & Explanation
By the summation rule, the view factor from the large (outer) cylinder surface to all surfaces enclosing it (itself + inner small cylinder + two annular end discs) must sum to 1: F(large→large) + F(large→small cylinder) + 2×F(large→one end) = 1. By reciprocity, F(large→small) relates to the given F(small→large)=0.34 via areas: F(large→small) = F(small→large)×A_small/A_large = 0.34×(2π×0.05×0.6)/(2π×0.10×0.6) = 0.34×0.5 = 0.17. So 0.25 + 0.17 + 2×F(end) = 1 → F(end) = (1−0.42)/2 = 0.58/2 = 0.29 → option (B).
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