Electrical components mounted to each of two isothermal plates are cooled by passing atmospheric air between the plates, and an in-line array of aluminum pin fins is used to enhance heat transfer to the air.

The pins are of diameter D = 2 mm, length L = 100 mm, and thermal conductivity k = 240 W/m ∙ K. The longitudinal and transverse pitches are S_L = S_T = 4 mm, with a square array of 625 pins (N_T = N_L = 25) mounted to square plates that are each of width W = 100 mm on a side. Air enters the pin array with a velocity of 10 m/s and a temperature of 300 K.

(a) Evaluating air properties at 300 K, estimate the average convection coefficient for the array of pin fins.

(b) Assuming a uniform convection coefficient over all heat transfer surfaces (plates and pins), use the result of part (a) to determine the air outlet temperature and total heat rate when the plates are maintained at 350 K.

Components Section A-A Plate Air ... O Pin fins D, L V, T, O... O W- ...