A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer surfaces are Tn and Ti, respectively. The thermal conductivity of the material of which the cylinder is made is k. Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation assuming that the thickness of the cylinder d is much smaller than the its inner radius R.

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Atomic diffusion in solids

In material science, diffusion can take place in solid, liquid, and gases. In solids, atomic diffusion can take place with the help of thermally activated and randomly vibrating atoms. The atomic diffusion in solids is complex and very slow in comparison to atomic diffusion in liquids and gases because the interatomic distance between the atoms is smaller in solids as compared to liquids and gases.