To enhance heat transfer from a silicon chip of width W = 4 mm on a side, a copper pin fin is brazed to the surface of the chip. The pin length and diameter are L = 12 mm and D = 2 mm, respectively, and atmospheric air at V = 10 m/s and T_∞ = 300 K is in cross flow over the pin. The surface of the chip, and hence the base of the pin, are maintained at a temperature of T_b = 350 K.

(a) Assuming the chip to have a negligible effect on flow over the pin, what is the average convection coefficient for the surface of the pin?

(b) Neglecting radiation and assuming the convection coefficient at the pin tip to equal that calculated in part (a), determine the pin heat transfer rate.

(c) Neglecting radiation and assuming the convection coefficient at the exposed chip surface to equal that calculated in part (a), determine the total rate of heat transfer from the chip.

(c) Independently determine and plot the effect of increasing velocity (10 < V< 40 m/s) and pin diameter (2 < D < 4 mm) on the total rate of heat transfer from the chip. What is the heat rate for V = 40 m/s and D = 4 mm?

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Pin Air fin To Chip, T, -W-/ 11