Question

It's a heat transfer question.

The chip is square with dimensions 15mm by 15mm and 5mm thickness with constant temperature T_c = 87 degrees C at the bottom of the chip. At the top surface, 20 pin fins with convective ends are attached to the chip. Above the chip, we have the 20 fins plus we also have the exposed board area, which is total area of the chip minus the base area of the 20 fins. The diameter of each fin, D_p = 1.5 mm, the length of each fin, L_p = 15 mm, and the thermal conductivity K_p = 400W/mK (For chip and fins). There is no thermal resistance between the fins and the chip. The convection coefficient, h = 50 W/(m²·K), and fluid temperature of T_∞ = 300K. Plot the temperature distribution along the center axis line (T vs x). Calculate the maximum heat that can be dissipated.

Answer 1

Cinnen haso male k: 400 cymle Tos 15 h Ndx ) Ck to "T Te Bop Dp=1.5mm Lp=15mm T = 876= 360k Tos = 300k LP Thxaod - m- Trif Y TCAIS 164 1/2 50*480 PIS Varox1.5x183 = 2.236 and mL = 2.236*0.015 = 8.633541 The general solution is o Ce-mx 4 C2 tnx at berundary condition XO O = 0, ocas, o = C+C₂ and at nal O2 = ceme teeme from @ & Tempo distribution 0 = 0, sinh [mel-n)] + O2 Sinh (ma) sinh (me) O = 02

) 11 (366 ~300) in, [ 2.33 (0-015-21 (340 3) ၇l (2234) »n (0 - 09 ) 0 - 188 55, - (၀-၄-၆၇, (ဂ) ၄)