$2.\backslash ((20\backslash \%)\backslash )$

Consider steady heat conduction in a long cylinder of radius $\backslash ($ r$\_\{$o$\}\backslash )$ with uniform heat generation $\backslash ($ g$^\{\backslash$prime $\backslash$prime $\backslash$prime$\}\backslash ).$ The cylinder is made of material with thermal conductivity $\backslash ($ k $\backslash )$ and subject to constant surface temperature $\backslash ($ T$\_\{0\}\backslash ).$

a$).$ Find the governing equation.

b$).$ Find the relevant boundary conditions in the cylinder.

c$).$ Solve for the temperature profile in the cylinder.

d$).$ Evaluate the heat flux at the outer surface of the cylinder.

e$).$ Find the governing equation and the relevant boundary conditions for a sphere of equal radius $\backslash ($ r$\_\{$o$\}\backslash )$ made of the same material under the same thermal condition.

f$).$ Solve for the temperature profile in the sphere.

g$).$ Evaluate the heat flux at the outer surface of the sphere.