$1.$ A plane wall $($k $=2$ W$/$m$.$K$,$ $=9\mathrm{.}9107$ m$2/$s$)$ of thickness $30$ cm is initially at a temperature of

$293$ K$.$ One side of the wall is insulated. At t $=0,$ the other side of the wall is exposed to a hot gas at $780$K$.$ Estimate the time for the insulated surface to reach $600$ K if the average convection heat transfer coefficient between the wall and the hot gas is:

$($a$)50$ W$/$ m$2.$K

$($b$)500$ W$/$m$2.$K$.$