A hypothetical solid sphere $0$ r $1$m is initially at temperature T $=201$C$.$ For times t $>0,$ the boundary surface at r $=1$ m is maintained at a constant temperature of $200$C$.$ In addition, the sphere is subjected to uniform internal energy generation of $60$ W$/$m$3.$ The thermal conductivity of the solid sphere is $10$ W$/$m$-$K$.$ Its thermal diffusivity is $1$ m$2/$s $($a$)(15$ pts$)$ Obtain an expression for the temperature distribution T $($r$,$ t$)$ in the sphere for times t $>0.($b$)(20$ pts$)$ Estimate the temperature at r $=0\mathrm{.}5$ m after $10$ minutes. For the thermophysical properties of the solid sphere $($Aluminum$),$ refer to any heat transfer or thermodynamics textbook you can get access to$.$ Make sure to cite your source properly.