Thermodynamics HW Solutions 401

Thermodynamics HW Solutions 401 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-10 A plane wall with variable heat generation and constant thermal conductivity is subjected to insulation at the left (node 0) and radiation at the right boundary (node 5). Using the finite difference form of the 1st derivative, the finite difference formulation of the boundary nodes is to be determined. Assumptions 1 Heat transfer through the wall is steady since there is no indication of change with time. 2 Heat transfer is one-dimensional since the plate is large relative to its thickness. 3 Thermal conductivity is constant and there is nonuniform heat generation in the medium. 4 Convection heat transfer is negligible. Analysis The boundary conditions at the left and right boundaries can be expressed analytically as At x = 0: 0 ) 0 ( or 0 ) 0 ( = = dx dT dx dT k Insulated Δ x g ( x ) 1 ε 0 2 3 4 5 T surr Radiation At x = L : ] ) ( [ ) ( 4 4 surr T L T dx L dT k = εσ Replacing derivatives by differences using values at the
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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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