Derive the expression for heat conduction through a cylinder

Question

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

03 Mar 2025

Answer :

Word Count : 413

To derive the expression for heat conduction through a cylinder, we consider a hollow cylinder with inner radius \( r_1 \) and outer radius \( r_2 \), and length \( L \). The temperatures at the inner and outer surfaces are \( T_1 \) and \( T_2 \), respectively, where \( T_1 > T_2 \), indicating heat transfer radially outward.

### Fourier’s Law of Heat Conduction
For steady-state conduction, Fourier’s law states:
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