A large steel plate having a thickness of L = 4 in, thermal conductivity of k = 7.2 Btu/h...

A large steel plate having a thickness of L = 4 in, thermal conductivity of k = 7.2 Btu/h · ft °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at Tx = 90°F with an average heat transfer coefficient of h = 12 Btu/h · ft2 °F as well as by radiation with the open sky with an equivalent sky temperature of Tsky = 480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the Variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0.