GATE ME 2024 Set 1 — Question 50
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Heat Transfer → Radiation → Radiation Exchange
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Question
Consider a hemispherical furnace of diameter m with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300 K and 1200 K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is ________kW (rounded off to the nearest integer).Use Stefan-Boltzmann constant = W/(m K)
Correct answer
2720 to 2740
Solution
Given:
The net rate of radiation heat transfer from the dome (2) to the base (1) in a two-surface enclosure is:Since the base is a blackbody (), the third term in the denominator is zero:Substituting the numerical values:Rounding to the nearest integer, the rate of radiation heat transfer is 2727 kW.
- Diameter of the hemispherical furnace, m Radius, m.
- Surface 1: Flat base (blackbody), K, .
- Surface 2: Dome (hemispherical), K, .
- Stefan-Boltzmann constant, W/(m K).
- Area of the flat base, m
- Area of the hemispherical dome, m
- For a flat base in a hemispherical enclosure, all radiation leaving the base must strike the dome: .
- By reciprocity: .
The net rate of radiation heat transfer from the dome (2) to the base (1) in a two-surface enclosure is:Since the base is a blackbody (), the third term in the denominator is zero:Substituting the numerical values:Rounding to the nearest integer, the rate of radiation heat transfer is 2727 kW.
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