Conduction comparison across geometries: thick sphere versus thick cylinder Assess the statement: Heat transfer by conduction through a thick spherical wall is the same as through a thick cylindrical wall. Choose the correct truth value.
Mechanical Engineering
Heat Transfer, Refrigeration and Air Conditioning
Difficulty: Easy
Choose an option
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ATrue (same functional form and result)
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BFalse (different area variation and formula)
Answer
Correct Answer: False (different area variation and formula)
Explanation
Concept/ApproachIn steady radial conduction, the governing area for heat flow varies with radius: Acyl = 2πrL (cylinder) versus Asph = 4πr² (sphere). This leads to different analytical forms for thermal resistance and heat rate.
ConsequencesFor a cylinder: Q = 2πkL (T1 − T2) / ln(r2/r1). For a sphere: Q = 4πk (T1 − T2) / (1/r1 − 1/r2).
Final AnswerFalse — the conduction relations are different for thick spheres and thick cylinders.