The wall (thickness L) of a furnace, with inside temperature 800 C, is comprised of brick material [thermal conductivity = 0.02 W m-1 K-)). Given that the wall thickness is 12 cm, the atmospheric temperature is 0 C, the density and heat capacity of the brick material are 1.9 gm cm-3 and 6.0 J kg K- respectively, estimate the temperature profile within the brick wall after 2 hours. Solve the partial differential equation T T = pc, dx subject to the initial condition T(x,0) = 800 sin 2L and boundary conditions at the inner (x = L) and outer (x = 0) walls of T = 0 at x = 0 and T at x = L Find the temperature profile at T = 7200 seconds = 2 hours.