$(24$pts$)$ Electronics Cooling: A Credo BGA chip package with $T_{\text{j}\text{m}\text{a}\text{x}}=105C,$ is attached as shown to a heatsink. You can assume that all of the heat dissipated is transferred to the heatsink $($if applied$),$ and the heatsink base is isothermal. Also, Tambient$=55$C$,v_{\text{a}\text{i}\text{r}}=2\mathrm{.}5{10}^{-5}\frac{m^2}{sec,P{r}_{\text{a}\text{i}\text{r}}}=0\mathrm{.}72,k_{\text{a}\text{i}\text{r}}=0\mathrm{.}028\frac{W}{m}C$ and

Chip Package

$$jc$=0\mathrm{.}4$C$/$W

$$ca$=8\mathrm{.}0$C$/$W@$1\mathrm{.}5$m$/$sec

$P=30W$

Heatsink Information

Overall Dimensions $=72mm$ wide $x30mm$ tall fins $x100mm$ long $(x,y,z)$

Fins$=28-1\mathrm{.}0$mm Thick $30mm$ Tall, Evenly Spaced

$-$interface $=0\mathrm{.}04\frac{C}{W}$

Material: T$6061$ Aluminum, k$=205$W$/$mC

Surfaces Outlined in Blue Exposed to

Airflow in z$-$direction at $V=1\mathrm{.}5\frac{m}{sec}$

$1\mathrm{.}63$ mm between fins $($not correct fin number$)$

Show work!

a$)$ If the chip package has $jc=\mathrm{.}08\frac{C}{W}$ and $($no heatisnk$)$ is Tjunction$(($:$C$