The outer surface of an engine is situated in a place where oil leakage can occur. Some oils have autoignition temperatures of approximately above 250°C. When oil comes in contact with a hot engine surface that has a higher temperature than its autoignition temperature, the oil can ignite spontaneously. Treating the engine housing as a plane wall, the inner surface (x = 0) is subjected to 6 kW/m² of heat. The engine housing (k = 13.5 W/m ∙ K) has a thickness of 1 cm, and the outer surface (x = L) is exposed to an environment where the ambient air is 35°C with a convection heat transfer coefficient of 20 W/m² ∙ K. To prevent fire hazard in the event the leaked oil comes in contact with the hot engine surface, the temperature of the engine surface should be kept below 200°C. Determine the variation of temperature in the engine housing and the temperatures of the inner and outer surfaces. Is the outer surface temperature of the engine below the safe temperature?

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h, T T(L) < 200°C Engine housing k = 13.5 W/m-K 1 1 1 1 90 = 6 kW/m² X L 0