Thermodynamics HW Solutions 406

Thermodynamics HW Solutions 406 - unknowns T 1 and T 2 ,...

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Chapter 5 Numerical Methods in Heat Conduction 5-23 A pin fin with negligible heat transfer from its tip is considered. The complete finite difference formulation for the determination of nodal temperatures is to be obtained. Assumptions 1 Heat transfer through the pin fin is given to be steady and one-dimensional, and the thermal conductivity to be constant. 2 Convection heat transfer coefficient is constant and uniform. 3 Heat loss from the fin tip is given to benegligible. Convectio T 0 h , T 0 1 2 D Δ x T surr Radiation ε Analysis The nodal network consists of 3 nodes, and the base temperature T 0 at node 0 is specified. Therefore, there are two
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Unformatted text preview: unknowns T 1 and T 2 , and we need two 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 finite difference formulations become Node 1 (at midpoint): ) ( ) )( 2 / ( 4 1 4 surr 1 1 2 1 = − + − Δ + Δ − + Δ − ∞ T T A T T x p h x T T kA x T T kA εσ Node 2 (at fin tip): ) )( 2 / ( ) )( 2 / ( 4 2 4 surr 2 2 1 = − Δ + − Δ + Δ − ∞ T T x p T T x p h x T T kA where is the cross-sectional area and 4 / 2 D A π = D p = is the perimeter of the fin. 5-9...
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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