GATE 2021 ME (ME1) – Question 54
A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is denoted by 1 and the inner surface of the cube is denoted by 2. The view factor $F_{22}$ for radiation heat transfer is _____ (rounded off to two decimal places).
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Correct answer: 0.76 to 0.78
Explanation
The convex sphere cannot see itself, so F₁₁=0 and F₁₂=1. Reciprocity gives $F_{21}=A_1/A_2=4\pi(10)^2/[6(30)^2]=0.232711$.
The cube enclosure sum is F₂₁+F₂₂=1, so **F₂₂=0.77** after rounding.