Consider a long, homogeneous, hollow cylinder with internal and external radii r$1$ and r$2,$ respectively. The temperature is kept constant at the cylinder walls as Ts$1$ and Ts$2.$ a$)$ Starting from the heat conduction equation in cylindrical coordinates, and using the thermal diffusivity D $=$ k $/(\backslash$rho Cp$)$ as the only parameter of interest, develop the steady state solution for temperature T$($r$)$ for r$1$ r $$ r$2.$

b$)$ For Ts$1=0$ and Ts$2=$ To plot the solution.

c$)$ With the solution in part b$)$ as initial condition, and assuming Ts$1=0$ and

Ts$2=0$ develop and plot the transient solution for T$($r$,$ t$).$ Use $\backslash$epsi $=$ r$2/$ r$1=1\mathrm{.}2.$