GATE ME 2014 Set 3 — Question 22
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Heat Transfer → Conduction → 1D Steady Conduction
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Question
Consider a long cylindrical tube of inner and outer radii, and , respectively, length, and thermal conductivity, . Its inner and outer surfaces are maintained at and , respectively (). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is
Correct answer
(C) (1)/(2π kL) ln((rₒ)/(rᵢ))
Solution
The steady-state heat conduction through a cylindrical wall is governed by Fourier's Law in cylindrical coordinates:where is the surface area at radius . Substituting :Separating variables and integrating from the inner radius to the outer radius :Thermal resistance () is defined as the ratio of temperature difference to the heat flow rate:This corresponds to option (C).
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