Chapter 4, Problem 4.28P

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

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