Problem $4$

As more and more components are placed on a single integrated circuit $($chip$),$ the amount of heat that is dissipated continues to increase. However, this increase is limited by the maximum allowable chip operating

$($a$)$ Sketch the equivalent thermal circuit for the pintemperature, which is approximately $75C.$ To maxichip$-$board assembly, assuming one$-$dimensional, mize heat dissipation, it is proposed that a $44$ array steady$-$state conditions and negligible contact re sistance between the pins and the chip. In variableof copper pin fins be metallurgically joined to the outer form, label appropriate resistances, temperatures, surface of a square chip that is $12\mathrm{.}7$ mm on a side. and heat rates.

$($b$)$ For the conditions prescribed in Problem $3\mathrm{.}27,$ what is the maximum rate at which heat can be dissipated in the chip when the pins are in place? That is$,$ what is the value of $q_c$ for $T_c=75C?$ The pin diameter and length are $D_p=1\mathrm{.}5mm$ and $L_p=15mm.$