Abstract: A semi-analytical methodology is developed for solving time-dependent 2D heat conduction problems in heterogeneous media [1]. This method combines the nodal scheme with lumped analysis and Laplace transform technique. The nodal method is initially applied: the partial differential equation is transverse-integrated in one of the space variables [2]. The next step is the lumped analysis: temperatures at the top and at the bottom boundaries are approximated by their average values. This procedure furnishes a set of one-dimensional differential equations. The solution for the averaged fluxes is obtained by numerical Laplace transform inversion, using the Gaussian quadrature [3]. From the author knowledge, the combined approach, that means the nodal and the Laplace transform methods, have not yet be applied in the solution of the two-dimension diffusion equation in a multi-component plates. The proposed method is applied in the simulation of the temperature distribution and heat flux for a multi-component plate. Numerical results and comparisons with solutions from the literature are reported.

References

[1] I. B. Aseka, M. T. Vilhena, P. O. Byer, M. V. A. Bianchi; Solution of transient heat conduction equation in multicomponent plates, Brazilian Congress on Thermal Engineering and Sciences, Proc. in CD-Rom, ISBN 85-85769-04-0 (2000).

[2] J. Zabadal, M. T. Vilhena, L. B. Barichello; An analytical Solution for the two-dimensional discrete ordinates problem in a convex domain, Progress in Nuclear Enginnering, Vol. 31, 225-228 (1997).

[3] A. H. Stroud, D. Secrest; Gaussian Quadrature Formulas, Prentice Hall, New Jersey (1966).