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DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.80
15 pages

Mikhail D. Mikhailov
Applied Mathematics Center, PO Box 384, Sofia, Technical University, Sofia, Bulgaria; and Mechanical Engineering Department—EE/COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68.503, Rio de Janeiro, RJ, 21945-970, Brasil


Some new perspectives for generalized integral transform method(GITT)and finite difference method(FDM), when using the Mathematica software system are demonstrated. First, the GITT is applied to find the transient temperature distribution in a slab with temperature dependent thermal conductivity. The corresponding system of ordinary differential equations (ODE) is derived in non-expanded form which permitted efficient generation of the truncated ODE system. The coupling integrals are solved exactly by using a new approach. It consists of obtaining an algebraic system for the unknown integrals by using an integral identity and some properties of the eigenfunctions. Next, the Laplace equation is solved by generating non uniform finite difference templates that include the boundary conditions. In order to obtain optimal finite difference formulae, exact polynomial solutions of the Laplace equation are used. An efficient rule for generation of such polynomials is given. The final Mathematica finite difference solution gives numerical value for any specified location in the solution domain. The technique developed is applicable to many other problems and makes FDM comparable to FEM in dealing with irregular geometry.

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