A computer CPU chip, $18mm$ square, generates heat at a rate of $50$ Watts. The chip is mounted to a $8mm$ thick substrate PCB board with glue. Forced convection cools a pattern of $2mm$ square copper pins.

a$)$ Determine the minimum amount of square copper pins needed to get the chip surface temperature at or below $60C.$ Assume the pins are perfectly attached to a copper base. Assume copper base on top of the chip is thin and has negligible conduction through the thickness. Don't forget sanity checks: number of pins must be an integer & will that many pins fit on the chip?

b$)$ What is the total $q$ for all cooling mechanisms?

c$)$ What is an individual fin efficiency?

$(30$ Points$)$

$T_{}=25C$

$h=900\frac{W}{m^2(K)}$

$T_{}=25C$

$h=35\frac{W}{m^2(K)}$

$t_{\text{s}\text{u}\text{b}\text{s}\text{t}\text{r}\text{a}\text{t}\text{e}}=8mm$

$K_{\text{s}\text{u}\text{b}\text{s}\text{t}\text{r}\text{a}\text{t}\text{e}}=2\mathrm{.}5\frac{W}{mK}$

$K_{\text{C}\text{o}\text{p}\text{p}\text{e}\text{r}}=450.\frac{W}{mK}$

$L_n=20mm$

Glue:

$R_{tc}=0\mathrm{.}005\frac{m^2(K)}{W}$