Question

4. A silicon chip is attached with a copper pin fin in order to enhance the heat transfer. The square shape silicon chip has a width of W=10 mm on each side. The length and diameter of the copper pin are L=20 mm and D=4 mm, respectively. During the operation, the surface of the chip, as well as the base of the pin, are maintained at the temperature of To=375 K. The thermal conductivity of the copper pin fin is 399 W/mK. In the meantime, air at atmospheric pressure is blowing at a speed of V=5 m/s with temperature at To= 275 K, which is in cross flow over the pin. (30 pts) Adiabatic tip V.T. Fin Silicon chip w Tь W (a) Assuming the chip to have a negligible effect on flow over the pin and the film temperature for the pin to be Tfilm=(Tb+ T.)/2, what is the average convection coefficient, ñ, for the surface of the pin? (b) Neglecting radiation and assuming the fin tip is insulated (adiabatic tip), 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 whole chip.

Answer 1

solution: 0 Given that, W = 10 mm To = 315 k K: 399 W/mK L.20 mm Too = 275k. D = 4 mm V-5 ms V, Too de J 4 Tь i a. Talm: Tht Too 375 + 275 325 K 2 2 S=1.0864 kg/m3 -6 V: 18.154 x 10 m2/S Por = 0.6976 K = 0.0284 Wimk VD Re e = 1101.685 (5) x (48103) 18.154X106 29 from the heat heat foransfer dada book 0.333 Nio - 0.466 0.683 (Reno) (290) 0.333 0.466 0.683 (1101.685) (0.6976) PUD - 15.84.6 NUD hD =hs e aud) к 0.0284 x 15.846 4x10 3 h = 112. 5066 wim?.k

= 80 + b, for Insulated tip 2) Q: Thekac lanh (m) 6 Oo : Tb - TW 375 -275 = 100 P lo (3.14) (0.004) 0.01256 m Aca T02 : 1. 256x16 "m? ma 112.5066x 0.01256 hp KA 16.9 399 x 61.256x10-5 (119.5066) (0.06256) (390) C 1. 256810-5) tan (mL) (100) Os = 2.7257 colm 2 C, for end. convection, we can take cognieded length Le LA A Lt D = 21 mm 4 Lo = 21 mm SAPKÁC tanh (c) 20 ar - 2.8515 Wima .
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