IGNOU MRW 2 2026 - Derive the expression for heat conduction through a cylinder. Assume s

Question

Derive the expression for heat conduction through a cylinder. Assume suitable dimension of the cylinder and the temperature difference across the cylinder.

23 Apr 2026

Answer :

Word Count : 380

Heat conduction through a cylindrical surface is an important case of steady-state heat transfer encountered in pipes, cables, and insulation systems. Consider a hollow cylinder of length (L), inner radius (r_1), and outer radius (r_2). Let the inner surface be maintained at temperature (T_1) and the outer surface at temperature (T_2), where (T_1 > T_2). Heat flows radially outward under steady-state conditions, and the thermal conductivity of the material is (k), assumed constant. For radial heat flow in a cylinder, the area through which heat flows is not constant but varies with radius. At any radius (r), the area normal to heat flow is the lateral surface area of the cylinder, given by: [ A = 2\pi r L ] According to

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