$[$Total $20$ points$]$ Consider a long sold tube $($hollow tube$),$ insulated at the inner radius $r$ and cooled at the outer radius $17,$ with uniform heat generation $g^{\text{'}}(\frac{W}{m^3})$ within the solid. Assume that only $T_{\text{m}\text{a}\text{t}}($temperature at the inner radius$)$ is known $($T pa is unknown$).(a,10$ points$)$ Obtain the general solution for the temperature distribution $T($I$)$ in the fube, $($b$,5$ points$)$ Detormine the heat removal rate per unit length of the tube $($assume Lis the length of the tube$)($c$,5$ points$)$ If the lemperature of the surrounding fuid is $T_h,$ obtain an expression for the convection coefficient to allow for operation at prescribed values of $T_2,1$ and $q^{\text{'}}.$