The 150-mm-thick wall of a gas-fired furnace is constructed of fire-day brick (k = 1.5 W/m ∙ K. p = 2600 kg/m ∙ c p = 1000 J/kg ∙ K) and is well insulated at its outer surface. The wall is at a uniform initial temperature of 20°C, when the burners are fired and the inner surface is exposed to products of combustion for which T_∞, = 950°(' and h = 100 W/m² ∙ K.

(a) How long does it take for the outer surface of the wall to reach a temperature of 750°C?

(b) Plot the temperature distribution in the wall at the foregoing time, as well as at several intermediate times.