Thermodynamics HW Solutions 417

Thermodynamics HW Solutions 417 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 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 The thermal contact resistance at the plate-soil interface is negligible. 4 Radiation heat transfer 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 and 6, 7, 8, and 9 in the soil are interior nodes, and thus for them we can use the general finite difference relation expressed as ) 0 (since 0 2 0 2 1 1 2 1 1 = = + = + Δ
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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.

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