A large steel plate having a thickness of L = 5 in, thermal conductivity of k = 7.2 Btu/h·ft·°F, and an emissivity of e 5 0.6 is lying on the ground. The exposed surface of the plate exchanges heat by convection with the ambient air at T` 5 80°F with an average heat transfer coefficient of h = 3.5 Btu/h·ft2·°F as well as by radiation with the open sky at an equivalent sky temperature of T_sky = 510 R. The ground temperature below a certain depth (say, 3 ft) is not affected by the weather conditions outside and remains fairly constant at 50°F at that location. The thermal conductivity of the soil can be taken to be ksoil 5 0.49 Btu/h·ft·°F, and the steel plate can be assumed to be in perfect contact with the ground. Assuming steady one-dimensional heat transfer and taking the nodal spacings to be 1 in in the plate and 0.6 ft in the ground, (a) obtain the finite difference formulation for all 11 nodes shown in Figure P5–32E and (b) determine the top and bottom surface temperatures of the plate by solving those equations.