Problem $2(4$ points$)$: A silicon chip of thickness $t=1mm$ is shaped as a rectangular plate of length $L=2cm$ and width $w=1\mathrm{.}5cm.$ When the chip is used within a computer, energy generation takes place within the chip since electrical energy is converted to heat energy, thereby heating the chip. Energy generation within the volume of the chip is to the tune of $q_g^{}=0\mathrm{.}5K\frac{W}{m^3}.$ The lower surface of the chip is placed on a ceramic insulating board $($hatched lines on the lower surface indicate insulation$),$ whereas top surface of the chip is exposed to air blowing from the CPU fan, with the air at $T_{}=15C$ flowing past the top surface of the chip. The convective heat transfer coefficient between top surface of the chip and air flowing past it is $h=30\frac{W}{m^2}-K.$ The top surface is exposed to very large surroundings at a temperature of $T_{\text{s}\text{u}\text{r}}=20C.$ The emissivity of the top surface is $0\mathrm{.}25.$ You are asked to assume the surface of the silicon chip is opaque$-$gray. The thermal conductivity of silicon is $k_s=150\frac{W}{m}K.$ Neglecting heat transfer from the edges and bottom surface of the chip, determine surface temperature $T_s$ of the top surface of the chip. Assume large surroundings.