Aplane wall of a furnace is fabricated from plain carbon steel (k = 60w m-1k-1 , ? = 7850 kg m-3 , c = 430 j kg-1k-1 ) 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 m2kw-1 . the opposite surface is well insulated from the surroundings. at furnace start-up the wall is at an initial temperature of ti = 300 k, and combustion gases at ti = 1300 k enter the furnace, providing a convection coefficient of h = 25w m-2k-1 at the ceramic film. assume that the film has negligible thermal capacitance.