Critical radius of insulation: effect on thermal resistance/heat flow For cylindrical/spherical insulation with external convection, at the critical insulation radius the thermal resistance to heat flow is at what condition? Choose the correct condition.
Mechanical Engineering
Heat Transfer, Refrigeration and Air Conditioning
Difficulty: Easy
Choose an option
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AMaximum
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BMinimum
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CZero
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DUndefined
Answer
Correct Answer: Minimum
Explanation
Concept/ApproachFor a cylinder with external convection, the total resistance Rtot = ln(ro/ri)/(2πkL) + 1/(2πhroL). As outer radius ro increases from ri, conduction resistance increases but convection resistance decreases.
Critical radiusAt ro = rc = k/h, dRtot/dro = 0 and Rtot is minimum; hence heat loss is maximum.
Final AnswerMinimum