A large steel plate having a thickness of L.= 5 in. thermal conductivity of k =

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A large steel plate having a thickness of L.= 5 in. thermal conductivity of k = 7.2 Btu/h ft degree F. and an emissivity of epsilon. = 0.6 is lying on the ground. The exposed surface of the plate exchanges heal by convection with the ambient air at T infinity = 80 degree F with an average heat transfer coefficient of h = 3.5 Btu/h ft: degree F as well as by radiation with the open sky at an equivalent sky temperature of T = 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 degree F at that location. The thermal conductivity of the soil can be taken to be 0.49 Btu/h ft degree 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 I in in the plate and 0.6 ft in the ground, obtain the finite difference formulation for all II nodes shown in Figure P5-32E and determine the top and bottom surface temperatures of the plate by solving those equations. Note: One problem in english units to mix it up. Everything should be done the same way as if the units were SI. Leave number substitutions for the end.

Explanation / Answer

A large steel plate having a thickness of L.= 5 in. thermal conductivity of k =

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