Chapter 4, Problem 4.28P

An aluminum heat sink $\left(k=240\text{W/m}\cdot \text{K}\right),$ used to coolan array of electronic chips, consists of a square channelof inner width $w=25\text{mm,}$ through which liquidflow may be assumed to maintain a uniform surfacetemperature of $T_1=20°\text{C}\text{.}$ The outer width and lengthof the channel are $W=40\text{mm}$ and $L=160\text{mm,}$ respectively.

If $N=120$ chips attached to the outer surfaces of theheat sink maintain an approximately uniform surfacetemperature of $T_2=50°\text{C}$ and all of the heat dissipatedby the chips is assumed to be transferred to the coolant,what is the heat dissipation per chip? If the contact resistancebetween each chip and the heat sink is $R_{t,c}=0.2\text{K/W,}$ what is the chip temperature?