GATE ME 2014 Set 2 — Question 52
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Heat Transfer → Radiation → Radiation Exchange
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Question
A hemispherical furnace of radius has the inner surface (emissivity, ) of its roof maintained at , while its floor () is kept at . Stefan-Boltzmann constant is . The net radiative heat transfer (in kW) from the roof to the floor is _______
Correct answer
24 to 25.2
Solution
1.Identify surfaces and properties:
Surface 1 (Roof): Hemisphere, , , .Surface 2 (Floor): Circular base, , , .
2.Determine view factors:
All radiation from the floor (2) hits the roof (1), so .By reciprocity: .
3.Calculate net heat transfer ():
Since , the first term in the denominator is zero.
.The value falls within the range of 24.0 to 25.2.
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