GATE ME 2026 Set 1 — Question 54
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Heat Transfer → Radiation → Radiation Network & Shields
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Question
Two rectangular surfaces both having area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of and emissivity of , while the other is insulated and in radiant balance with a large surrounding room at . If the fraction of radiation leaving the hot surface which reaches the cold surface is , then the equivalent overall resistance for the radiation heat loss from the hot surface is _______ (rounded off to 2 decimal places).
Correct answer
2.5 to 2.6
Solution
1.Identify the surfaces:
Surface 1: Hot surface ().Surface 2: Insulated/Reradiating surface ().
Surface 3: Surroundings ().
2.Determine view factors:
Given . Since , .From summation rule: .
By symmetry, .
3.Calculate resistances in the radiation network:
- Surface resistance of surface 1: .
- Space resistance between 1 and 2: .
- Space resistance between 1 and 3: .
- Space resistance between 2 and 3: .
Surface 2 is reradiating, so the network from node to (surroundings) consists of two parallel paths:
- Path A: Direct with resistance .
- Path B: with resistance .
5.Total resistance:
.Rounding to 2 decimal places, the equivalent overall resistance is .Continue learning with Success Tracker
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