Problem $3(10$ points$)$: A brick of thickness $t=4mm$ and thermal conductivity $k_b=0\mathrm{.}05\frac{W}{m}-K,$ is shaped as a cuboid of length $L=3cm$ and width $w=2\mathrm{.}5cm.$ The top surface of the brick is exposed to ambient air $T_{}=15C.$ Convective heat transfer coefficient between top surface of the brick and air flowing past it is $h_T=25\frac{W}{m^2}-K.$ Emissivity of the top surface of the brick is ${}_T=0\mathrm{.}2,$ and emissivity of the bottom surface of the brick is ${}_B=0\mathrm{.}5.$ Top surface of the brick is exposed to surroundings at a temperature $T_{\text{s}\text{u}\text{r}\text{,}T}.$ Treat the brick as opaque, gray, and small compared to surroundings. Heat transfer takes place through thickness $(y)$ direction. Don't assume ambient and surrounding temperature to be same.

Case $1(4$ points$)$: Assume bottom surface