Repeat Prob. 5–32E by disregarding radiation heat transfer from the upper surface.

Data from problem 32

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 ε = 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·°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 k_soil = 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

(b) Determine the top and bottom surface temperatures of the plate by solving those equations.

Transcribed Image Text:

Radiation & Plate Soil Tsky Convection h, T 0 2345 ¡> 1 in *** 9. 10+ VX 0.6 ft