Thermodynamics HW Solutions 408

Thermodynamics HW Solutions 408 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-25 A long triangular fin attached to a surface is considered. The nodal temperatures, the rate of heat transfer, and the fin efficiency are to be determined numerically using 6 equally spaced nodes. Assumptions 1 Heat transfer along the fin is given to be steady, and the temperature along the fin to vary in the x direction only so that T = T ( x ). 2 Thermal conductivity is constant. Properties The thermal conductivity is given to be k = 180 W/m ⋅ °C. The emissivity of the fin surface is 0.9. Analysis The fin length is given to be L = 5 cm, and the number of nodes is specified to be M = 6. Therefore, the nodal spacing Δ x is m 01 . 1- 6 m 05 . 1 = = − = Δ M L x The temperature at node 0 is given to be T = 200°C, and the temperatures at the remaining 5 nodes are to be determined. Therefore, we need to have 5 equations to determine them uniquely. Nodes 1, 2, 3, and 4 are interior nodes, and the finite difference formulation for a general interior node...
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