Chapter 5 Numerical Methods in Heat Conduction 5-30E A large plate lying on the ground is subjected to convection and radiation. Finite difference formulation is to be obtained, and the top and bottom surface temperatures under steady conditions are to be determined. Assumptions 1 Heat transfer through the plate is given to be steady and one-dimensional. 2 There is no heat generation in the plate and the soil. 3 Thermal contact resistance at plate-soil interface is negligible. Properties The thermal conductivity of the plate and the soil are given to be k plate = 7.2 Btu/h ⋅ ft ⋅ °F and k soil = 0.49 Btu/h ⋅ ft ⋅ °F. Analysis The nodal spacing is given to be Δ x 1 =1 in. in the plate, and be Δ x 2 =0.6 ft in the soil. Then the number of nodes becomes 11 1 ft 0.6 ft 3 in 1 in 5 1 soil plate = + + = + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = x L x L M The temperature at node 10 (bottom of thee soil) is given to be T 10 =50 ° F. Nodes 1, 2, 3, and 4 in the plate
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.