Thermodynamics HW Solutions 407

Thermodynamics HW Solutions 407 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-24 A uranium plate is subjected to insulation on one side and convection on the other. The finite difference formulation of this problem is to be obtained, and the nodal temperatures under steady conditions are to be determined. Assumptions 1 Heat transfer through the wall is steady since there is no indication of change with time. 2 Heat transfer is one-dimensional since the plate is large relative to its thickness. 3 Thermal conductivity is constant. 4 Radiation heat transfer is negligible. Properties The thermal conductivity is given to be k = 28 W/m °C. Analysis The number of nodes is specified to be M = 6. Then the nodal spacing Δ x becomes m 01 . 0 1 - 6 m 05 . 0 1 = = = Δ M L x This problem involves 6 unknown nodal temperatures, and thus we need to have 6 equations to determine them uniquely. Node 0 is on insulated boundary, and thus we can treat it as an interior note by using the mirror image concept. Nodes 1, 2, 3, and 4 are interior nodes, and thus for them we can use the general
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