The outer surface of an engine is situated in a place where oil leakage can occur. When leaked oil comes in contact with a hot surface that has a temperature above its autoignition temperature, the oil can ignite spontaneously. Consider an engine cover that is made of a stainless steel plate with a thickness of 1 cm and a thermal conductivity of 14 W/m∙K. The inner surface of the engine cover is exposed to hot air with a convection heat transfer coefficient of 7 W/m²∙K at 333°C. The outer surface is exposed to an environment where the ambient air is 69°C with a convection heat transfer coefficient of 7 W/m²∙K. To prevent fire hazard in the event of oil leak on the engine cover, a layer of thermal barrier coating (TBC) with a thermal conductivity of 1.1 W/m∙K is applied on the engine cover outer surface. Would a TBC layer of 4 mm in thickness be sufficient to keep the engine cover surface below autoignition temperature of 200°C to prevent fire hazard?

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7 W/m².K 69°C Engine cover k = 14 W/m-K 7 W/m².K 333°C TBC