A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m · K, p = 7850 kg/m3, c = 430 J/kg · K) and is of thickness L = 10 mm. To protect it from the corrosive effects of the furnace combustion gases, one surface of the wall is coated with a thin ceramic film that, for a unit surface area, has a thermal resistance of R"t,f: = 0.01 m2 · K/W. The opposite surface is well insulated from the surroundings.
At furnace start-up the wall is at an initial temperature of Tj = 300 K, and combustion gases at T8 = 1300 K enter the furnace, providing a convection coefficient of h = 25 W/m2 · K at the ceramic film. Assuming the film to have negligible thermal capacitance, how long will it take for the inner surface of the steel to achieve a temperature of Ts.i = 1200 K? What is the temperature Ts.o of the exposed surface of the ceramic film at this time?