A fire clay brick slab with $=5\mathrm{.}4{10}^{-7}\frac{m^2}{sec}$ and $K=1$ watts $\frac{?}{m}C,$ has a thickness of $5$ cm and initially at a uniform temperature of $350C.$ Suddenly one of its surfaces is subject to $40C.$ The other surface is insulated.

a$.$ sketch a diagram of the given scenario.

b$.$ Plot the temperature profile on your diagram.

c$.$ Calculate the centerline temperature one hour after the start of cooling.