Please solve and show how calculations for each step.

A radioactive waste container is stored in a cylindrical container made of stainless steel.

Thermal energy is generated uniformly throughout the waste material. The rate of this generation per

unit volume is equal to $3$xx$10^(4)$W$//$m$^(3).$ The container is stored in water at $298$ K $,$ with a convection

coefficient of $1000$W$//$m$^(2)$K$.$ The circular ends of the container are insulated.

Important Information:

Conductivity of stainless steel, k$\_($s$)=15$W$//$mK

Conductivity of the waste, k$\_($w$)=20$W$//$mK

Inside diameter of the container, $1\mathrm{.}2$ m

Outside diameter of container, $1\mathrm{.}5$ m

A$.$ Use the Poisson equation to determine the temperature profile in the waste.

B$.$ Determine an expression for the q in the r direction for the waste using Fourier's rate equation and

dT$//$dr from part A$.$ Calculate the q$//$L$.$ Note that L is the height of the cylinder.

C$.$ Use the LaPlace equation to determine the temperature profile in the stainless steel container.

D$.$ Use the resistance model for the conduction in the container and the convection in the water

outside to develop an expression for q$//$L$.$

E$.$ Determine the steady state temperatures at the inner and outer surfaces of the stainless steel.

F$.$ What is the steady state temperature at the center of the waste?