Thermodynamics HW Solutions 463

Thermodynamics HW Solutions 463 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction Transient Heat Conduction 5-63C The formulation of a transient heat conduction problem differs from that of a steady heat conduction problem in that the transient problem involves an additional term that represents the change in the energy content of the medium with time. This additional term represent the change in the internal energy content during t in the transient finite difference formulation. A xC T T t m i m i ( ) + 1 / 5-64C The two basic methods of solution of transient problems based on finite differencing are the explicit and the implicit methods . The heat transfer terms are expressed at time step i in the explicit method, and at the future time step i + 1 in the implicit method as Explicit method: & & Q G V C T T t i m i m i All sides element i element + = + 1 Implicit method: & & Q G V C T T t i m i m i + + + = 1 1 All sides element i+1 element 5-65C The explicit finite difference formulation of a general interior node for transient heat conduction in a...
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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