A solid sphere $0$ r $$ b is initially at temperature T $=1+$r$.$ For times t $>0,$ the boundary surface at r $=$ b is maintained at a constant temperature of T$1.$ In addition, the sphere is subjected to uniform internal energy generation g$0($W$/$m$3).$ Obtain an expression for the temperature distribution T $($r$,$ t$)$ in the sphere for times t $>0.$