Thermodynamics HW Solutions 462

Thermodynamics HW Solutions 462 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-62 A rectangular block is subjected to uniform heat flux at the top, and iced water at 0 ° C at the sides. The steady finite difference formulation of the problem is to be obtained, and the unknown nodal temperatures as well as the rate of heat transfer to the iced water are to be determined. Assumptions 1 Heat transfer through the body is given to be steady and two-dimensional. 2 There is no heat generation within the block. 3 The heat transfer coefficient is very high so that the temperatures on both sides of the block can be taken to be 0°C. 4 Heat transfer through the bottom surface is negligible. Properties The thermal conductivity is given to be k = 23 W/m °C. Analysis The nodal spacing is given to be Δ x = Δ x = l =0.1 m, and the general finite difference form of an interior node equation for steady 2-D heat conduction is expressed as 0 4 0 4 node bottom right top left 2 node node bottom right top left = + + + = + + + + T T T T T k l g T T T T T &
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