$2.$ A $1$ cm$\backslash$times $2$ cm ceramic strip with k $=3\mathrm{.}0$ W$/$m$$C is embedded in a high$-$thermal conductivity

material so that the sides $($both left and right$)$ are maintained at a constant temperature

of $300$C$.$ The bottom surface of the ceramic is insulated and the top surface is exposed

to a convection environment with h $=200$ W$/$m$2$

$.$

$$C and T$\backslash$infty $=50$C$.$ At time t $=0,$ the

ceramic is at a uniform temperature of $300$C$.$ For ceramic material, given $\backslash$rho $=1600$ kg$/$m$3$

and cp $=0\mathrm{.}8$Kj$/$kg$.$C$.$ For $$x $=$y $=0\mathrm{.}5,$ estimate and analyze the temperatures of

different nodes inside the ceramic material at time t $=12$ sec using

$($a$)$ Explicit scheme of numerical method $(10)$

$($b$)$ Analytical solution $($assuming one$-$dimensional heat conduction$)$