Consider the bomb calorimeter as shown in the figure. The inner and outer radius of the bomb calorimeter are $R_1$ and $R_2,$ respectively. An exothermic reaction takes place in the inner cylinder of radius $R_l$ and results in a uniform heat generation of $q_{\text{g}\text{e}\text{n}}(W).$ The ambient temperature is $T_0$ and the convection coefficient between the environment and the bomb calorimeter is $h_0.$

a$)$ Select a convenient control volume and make a shell balance for the steady state onedimensional heat conduction to derive the temperature profile in radial direction for the cylinder wall $R_1-R_2.$

b$)$ Write the boundary conditions to solve the differential equation from part $($a$).$

c$)$ Obtain the temperature profile in radial direction.

Hint: Answer : $,T(r)=(\frac{q_{\text{g}\text{e}\text{n}}}{2kL})[ln{(}_2^{R_2})+\frac{k_h}{r}]+T_0$