A $3-$D cube $0$ x $$ a$,0$ y $$ a$,0$ z $$ a is initially at temperature T $=$ xyz $+$ T$.$ For times t $>0,$ the boundaries at x $=0,$ y $=0,$ and z $=0$ are insulated, and the boundaries at x $=$ a$,$ y $=$ a$,$ and z $=$ a all dissipate heat by convection into an environment with fluid temperature T and with identical heat transfer coefficients h at all three boundaries. Obtain an expression for the temperature distribution T $($x$,$ y$,$ z$,$ t$)$ in the region.