A hot surface at 120°C is to be cooled by attaching 8 cm long, 0.8 cm in diameter aluminum pin fins (k = 237 W/m · K and α = 97.1 × 10^-6 m²/s) to it with a center-to-center distance of 1.6 cm. The temperature of the surrounding medium is 15°C, and the heat transfer coefficient on the surfaces is 35 W/m² · K. Initially, the fins are at a uniform temperature of 30°C, and at time t = 0, the temperature of the hot surface is raised to 120°C. Assuming one-dimensional heat conduction along the fin and taking the nodal spacing to be Δx = 2 cm and a time step to be Δt = 0.5 s, determine the nodal temperatures after 10 min by using the explicit finite difference method. Also, determine how long it will take for steady conditions to be reached.

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