Inconel® refers to a class of nickel-chromium-based superalloys that are used in high-temperature applications, such as gas turbine blades. For further improvement in the performance of gas turbine engine, the outer blade surface is coated with ceramic-based thermal barrier coating (TBC). Consider a flat Inconel® plate, with a thickness of 12 mm, is coated with a layer of TBC, with a thickness of 300 mm, on its surface. At the interface between the Inconel® and the TBC, the thermal contact conductance is 10,500 W/m²∙K. The thermal conductivities of the Inconel® and the TBC are 25 W/m∙K and 1.5 W/m∙K, respectively. The plate is in a surrounding of hot combustion gasses at 1500°C, and the convection heat transfer coefficient is 750 W/m²∙K. Determine the temperature at the mid-plane of the Inconel® plate, if the outer surface temperature is 1200°C.