Thermodynamics HW Solutions 506

Thermodynamics HW Solutions 506 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-117 A hot surface is to be cooled by aluminum pin fins. The nodal temperatures after 5 min are to be determined using the explicit finite difference method. Also to be determined is the time it takes for steady conditions to be reached. Assumptions 1 Heat transfer through the pin fin is given to be one- dimensional. 2 The thermal properties of the fin are constant. 3 Convection heat transfer coefficient is constant and uniform. 4 Radiation heat transfer is negligible. 5 Heat loss from the fin tip is considered. Convectio h , T 0 2 4 D Δ x 3 1 Analysis The nodal network of this problem consists of 5 nodes, and the base temperature T 0 at node 0 is specified. Therefore, there are 4 unknown nodal temperatures, and we need 4 equations to determine them. Using the energy balance approach and taking the direction of all heat transfers to be towards the node under consideration, the explicit transient finite difference formulations become
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