A spherical shell having inner radius $$ and outer radius $,$ azimuth span $$ and

elevation angle $$ has no internal energy generation and a constant thermal

conductivity.

A$)$ Derive an expression for the steady state temperature distribution of the

shell beginning from the generalized heat equation. Comment on the

behavior of the temperature distribution and show a plot of the result.

B$)$ Determine the heat flux distribution. Again, comment on the result and

plot it$.$ What is the source of the variation?

C$)$ Determine the heat flow distribution and determine an expression for

the thermal resistance. Show your formulation collapses to the typical

definition for a spherical shell that has full span in both azimuth and

elevation angle $($i$.$e$.,$ a full sphere rather than a sector$).$