GATE ME 2022 Set 1 — Question 35
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Heat Transfer → Radiation → Stefan-Boltzmann & Wien's Laws
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Question
A flat plate made of cast iron is exposed to a solar flux of W/m at an ambient temperature of C. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low temperature absorptivity of . Use Stefan-Boltzmann constant W/m-K. Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ C (round off to the nearest integer).
Correct answer
210 to 225
Solution
Given:
Solar flux absorbed, W/m
Ambient temperature, C K
Low temperature absorptivity (emissivity),
Stefan-Boltzmann constant, W/m-KAt radiation equilibrium, the energy absorbed by the plate equals the energy emitted by radiation to the surroundings:Converting to Celsius:Rounding to the nearest integer, the radiation equilibrium temperature is C.According to the official answer key, the acceptable range is 210 to 225.
Solar flux absorbed, W/m
Ambient temperature, C K
Low temperature absorptivity (emissivity),
Stefan-Boltzmann constant, W/m-KAt radiation equilibrium, the energy absorbed by the plate equals the energy emitted by radiation to the surroundings:Converting to Celsius:Rounding to the nearest integer, the radiation equilibrium temperature is C.According to the official answer key, the acceptable range is 210 to 225.
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