Solution of Multiphase Heat Conduction Problems via the Generalized Integral Transform Technique with Domain Characterization through the Indicator Function
Humberto Araujo Machado1; Heidi Korzenowisk2; Newton Galvão de Campos Leite3; Élcio Nogueira3
1 IAE; 2 UNIVAP; 3 UERJ
doi:10.20906/CPS/COB-2015-0234
Resumo
The Generalized Integral Transform Technique (GITT) has appeared in the literature as an alternative to conventional discrete numerical methods for partial differential equations in heat transfer and fluid flow. Its hybrid numerical-analytical structure permits the automatic control of the global error in the simulation, which avoids the need for several computer program runs to inspect for the convergence on the final results, yielding codes that automatically work towards user prescribed accuracy targets. This method is also easy to program, since there is no need for a discretization mesh and its adaptive refinement according to the potential field and physical situation to be calculated. The method has being constantly improved in order to solve convection-diffusion problems with increasing complexity. However, there still a vast number of practical problems that has not being solved satisfactory by the method due its need for a previous algebraic treatment of the equations. In several brands of engineering, the transport equations have to be solved for a combination of different phases or materials or inside irregular domains. In this case, the simple application of the well-known discrete numerical methods demands some specific treatment that adds some residual error to final results. In this case, the mathematical resource of the Indicator function, as defined in the Interface Tracking Method can be employed. This function is a representation of the phases or parts of the domain with the numbers 0 and 1 for each phase. According to the method, the Indicator Function is defined by Poisson's equation, which is added to the system of the transport equations. An integral is done along the curve that defines the interface that will generate the source term in Poisson' equation used to calculate the Indicator Function distribution. The solution of the system of equations is done using the common GITT approach. Then, an analytical expression for each transformed potential of the indicator function and the other
Palavras-chave: Integral transforms; Irregular geometries; Heat conduction