In an annealing process, a $50-$mm$-$thick stainless steel plate $(\backslash$rho $=8238$ kg$/$m$^3,$ Cp $=468$ J$/$kg$$c$,$ k $=13\mathrm{.}4$ W$/$m$$c$,$ and $\backslash$alpha $=3\mathrm{.}48$ x $10$ m$^2/$s$)$ was reheated in a furnace from an initial uniform temperature of $236\backslash$deg C$.$ The ambient temperature inside the furnace is at a uniform temperature of $1000\backslash$deg C and has a convection heat transfer coefficient of $215$ W$/$m$^2$K$.$ If it is left for $200$ seconds to cool, determine the temperature at the center and the extremities of the plate.