Thermodynamics HW Solutions 414

Thermodynamics HW Solutions 414 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-28 A plate is subjected to specified heat flux on one side and specified temperature on the other. The finite difference formulation of this problem is to be obtained, and the unknown surface temperature under steady conditions is to be determined. Assumptions 1 Heat transfer through the base plate is given to be steady. 2 Heat transfer is one- dimensional since the plate is large relative to its thickness. 3 There is no heat generation in the plate. 4 Radiation heat transfer is negligible. 5 The entire heat generated by the resistance heaters is transferred through the plate. Properties The thermal conductivity is given to be k = 20 W/m °C. Analysis The nodal spacing is given to be Δ x =0.2 cm. Then the number of nodes M becomes 4 1 cm 2 . 0 cm 6 . 0 1 = + = + Δ = x L M The right surface temperature is given to be T 3 =85 ° C. This problem involves 3 unknown nodal temperatures, and thus we need to have 3 equations to determine them uniquely. Nodes 1, 2, and 3 are interior
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