Problem

A large steel plate having a thickness of L = 5 in, thermal conductivity of k = 7.2 Btu/h∙...

A large steel plate having a thickness of L = 5 in, thermal conductivity of k = 7.2 Btu/h∙ft∙oF, and an emissivity of e = 0.6 is lying on the ground. The exposed surface of the plate exchanges heat by convection with the ambient air at T∞ = 80°F with an average heat transfer coefficient of h =3.5 Btu/h·ft2.°Fas well as by radiation with the open sky at an equivalent sky temperature of Tsky =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 = 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.