Eventos Anais de eventos
COBEM 2017
24th ABCM International Congress of Mechanical Engineering
Integral Transformation of Multidimensional Heat Conduction Problems in Heterogeneous Media
Submission Author:
Anderson Pereira de Almeida , RJ
Co-Authors:
Carolina Palma Naveira Cotta, Renato Machado Cotta, Anderson Pereira de Almeida
Presenter: Anderson Pereira de Almeida
doi://10.26678/ABCM.COBEM2017.COB17-1906
Abstract
The integral transform method is applied in the analytical solution of three-dimensional transient heat conduction problems in heterogeneous media, with the heterogeneities being represented by arbitrarily space variable coefficients. The Generalized Integral Transform Technique (GITT) is employed in the solution of the multidimensional Sturm-Liouville eigenvalue problem, by adopting a simpler auxiliary eigenvalue problem and proposing an expansion for the original eigenfunctions. Also, in combination with a single domain reformulation strategy, the proposed solution also handles multiregion and multiscale problem formulations. The methodology is demonstrated for a couple of test cases. The first example is related to Functionally Graded Materials (FGM), with multiscale variations of thermal conductivity and capacitance in a three-dimensional domain. The second example involves abrupt variations of thermophysical properties simulating the interfacing among multiple materials. The computational simulations here presented have been obtained in the symbolic-numeric Mathematica platform, version 10.2. Simulations in COMSOL Multiphysics, version 4.4, are also employed for critical comparisons against the GITT solutions.
Keywords
heat conduction, Integral Transforms, GITT, heterogeneous media, FGM, Eigenvalue Problem
