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A spherical body with surface A1 is completely enclosed by another hollow body with inner surface A2. The shape factor of A2 with respect to A1 is
- a)0
- b)0.5
- c)1
- d)π
Correct answer is option 'A'. Can you explain this answer?
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A spherical body with surface A1 is completely enclosed by another hol...
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The shape factor relates the radiation heat transfer between two surfaces to the geometrical configuration and orientation of the surfaces. It is defined as the ratio of the actual radiation heat transfer between the two surfaces to the radiation heat transfer that would occur if both surfaces were black and at the same temperature.
In this case, the spherical body with surface A1 is completely enclosed by the hollow body with inner surface A2. Since A2 completely surrounds A1, it intercepts all the radiation that A1 emits. Therefore, the radiation heat transfer between A1 and A2 is equal to the radiation emitted by A1.
If both surfaces were black and at the same temperature, the radiation heat transfer between them would be given by the Stefan-Boltzmann law:
q = σ(T1^4 - T2^4) A1
where q is the radiation heat transfer, σ is the Stefan-Boltzmann constant, T1 is the temperature of A1, T2 is the temperature of A2, and A1 is the surface area of A1.
Since A2 completely surrounds A1, it intercepts all the radiation that A1 emits. Therefore, the effective area of A2 that receives radiation from A1 is equal to A1. Hence, the shape factor of A2 with respect to A1 is:
F12 = q / (σT1^4 A1) = 1
Therefore, the answer is (c) 1.
The shape factor relates the radiation heat transfer between two surfaces to the geometrical configuration and orientation of the surfaces. It is defined as the ratio of the actual radiation heat transfer between the two surfaces to the radiation heat transfer that would occur if both surfaces were black and at the same temperature.
In this case, the spherical body with surface A1 is completely enclosed by the hollow body with inner surface A2. Since A2 completely surrounds A1, it intercepts all the radiation that A1 emits. Therefore, the radiation heat transfer between A1 and A2 is equal to the radiation emitted by A1.
If both surfaces were black and at the same temperature, the radiation heat transfer between them would be given by the Stefan-Boltzmann law:
q = σ(T1^4 - T2^4) A1
where q is the radiation heat transfer, σ is the Stefan-Boltzmann constant, T1 is the temperature of A1, T2 is the temperature of A2, and A1 is the surface area of A1.
Since A2 completely surrounds A1, it intercepts all the radiation that A1 emits. Therefore, the effective area of A2 that receives radiation from A1 is equal to A1. Hence, the shape factor of A2 with respect to A1 is:
F12 = q / (σT1^4 A1) = 1
Therefore, the answer is (c) 1.
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A spherical body with surface A1 is completely enclosed by another hollow body with inner surface A2. The shape factor of A2 with respect to A1 isa)0 b)0.5c)1 d)πCorrect answer is option 'A'. Can you explain this answer?
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A spherical body with surface A1 is completely enclosed by another hollow body with inner surface A2. The shape factor of A2 with respect to A1 isa)0 b)0.5c)1 d)πCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical body with surface A1 is completely enclosed by another hollow body with inner surface A2. The shape factor of A2 with respect to A1 isa)0 b)0.5c)1 d)πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical body with surface A1 is completely enclosed by another hollow body with inner surface A2. The shape factor of A2 with respect to A1 isa)0 b)0.5c)1 d)πCorrect answer is option 'A'. Can you explain this answer?.
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