Question

A hot surface at 125°C is to be cooled by attaching 8 cm long, 0.8 cm in diameter aluminum pin fins(k = 237 W/m-°C and a = 97.1 X 106 m²/s) to it. The temperature of the surrounding medium is 17°C, and the heat transfer coefficient on the surfaces is 38 W/m²-°C. Initially, the fins are at a uniform temperature of 29°C, and at time t=0, the temperature of the hot surface is raised to 125°C.Assuming one-dimensional heat conduction along the fin and taking the nodal spacing to be Ax = 2.0 cm and a time step to be At = 1.5 s, determine the nodal temperatures after 5 minutes by using the explicit finite difference method. Also determine how long it will take for steady conditions to be reached.

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