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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.

Difficulty: Easy

Maximum
Minimum
Zero
Undefined

Correct Answer: Minimum

Explanation:

Concept/ApproachFor a cylinder with external convection, the total resistance R_tot = ln(r_o/r_i)/(2πkL) + 1/(2πhr_oL). As outer radius r_o increases from r_i, conduction resistance increases but convection resistance decreases.

Critical radiusAt r_o = r_c = k/h, dR_tot/dr_o = 0 and R_tot is minimum; hence heat loss is maximum.

Final AnswerMinimum

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