Aplane wall of a furnace is fabricated from plain carbon steel ( 60 w/m·k, 7850 kg/m3, 430 j/kg·k) and is of thickness 30 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 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 300 k, and combustion gases at ∞ 1300 k enter the furnace, providing a convection coefficient of 25 w/m2·k at the ceramic film. (a) how long will it take for the inner surface of the steel to achieve a temperature of ts, i = 1200 k? (b) what is the temperature ts, o of the exposed surface of the ceramic film at this time?