GATE ME 2023 Set 1 — Question 43
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Heat Transfer → Radiation → View Factors
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Question
A cylindrical rod of length and diameter is placed inside a cubic enclosure of side length . denotes the inner surface of the cube. The view-factor is
Correct answer
(D) 1 - ((π dh + π d²/2))/(6L²)
Solution
Let be the surface area of the cylindrical rod and be the inner surface area of the cubic enclosure.
From the summation rule for the enclosure (surface 2): , where is the required view factor .
Using the reciprocity theorem:
Since the rod is completely enclosed by the cube, all radiation leaving the rod must strike the inner surface of the cube, so .
Therefore, .
From the summation rule for the enclosure (surface 2): , where is the required view factor .
Using the reciprocity theorem:
Since the rod is completely enclosed by the cube, all radiation leaving the rod must strike the inner surface of the cube, so .
Therefore, .
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