Project ForgeHeat Transfer
Convection & Radiation
GATE 2023
Hard
A cylindrical rod of length h and diameter d is placed inside a cubic enclosure of side length L. S denotes the inner surface of the cube. The view-factor F_S-S is
- A0
- B1
- C(πdh + πd²/2)/(6L²)
- 1 − (πdh + πd²/2)/(6L²)
Explanation
Since S and the rod form a complete two-surface enclosure, F_S-S+F_S-rod=1. Since the rod is convex, F_rod-S=1, so by reciprocity A_S·F_S-rod=A_rod·F_rod-S=A_rod, giving F_S-rod=A_rod/A_S=(πdh+πd²/2)/(6L²). Therefore F_S-S=1−(πdh+πd²/2)/(6L²).
Source: GATE ME 2023 Official Paper (2023)
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