A hemi-spherical heat source of radius $r_o = 1$ mm is embedded in a very large silicon substrate at
$T_\infty = 25$ °C with thermal conductivity, $k = 50$ W/m-K and dissipates heat at a rate of $q = 35$ W. Its
top surface is well insulated.
insulator
k
1) Obtain a general expression for the silicon substrate temperature, $T(r)$ as a function of $T_s$
(surface temperature of heat source), $r_o$, and $T_\infty$. [15 pts]
2) What is the temperature of hemi-spherical heat source surface, $T_s$? [15 pts]