Question

Problem 2: A circular fin of length Land diameter D extends between the upper and lower walls of an air duct, which are both held at a constant temperature of Tp. Hot air flows over the fin with a freestream temperature T>Tp and a convection coefficient h. (a) Starting with an appropriate differential control volume in the fin, derive an equation for the temperature variation T(x) through the fin. Clearly indicate your control volume and the various terms inthe energy balance. (b) Sketch the temperature variation T(x) through the fin, and indicate any locations where the conduction heat flux through the fin would be maximum.

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