A circular (annular) fin of radius r₂ is attached to a pipe of radius r₁. The fin is exposed to an ambient fluid at temperature T_∞ having heat transfer coefficient h and the fin base is maintained at temperature T_b. The fin thickness (t) is small compared to the fin length and the heat loss from the fin tip can be considered negligible compared with that from the top and bottom surfaces of the fin. Derive the differential equation and the boundary conditions for this fin by writing an energy balance around a differential volume element. Write your assumptions in detail. Do not solve the differential equation.

 

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