Soluções híbridas de difusão e convecção-difusão com transformações integrais e diferenças finitas

Abstract

The present article addresses several hybrid solutions (numerical-analytical) for conjugate diffusion-convection heat transfer problems and conduction. Four heat transfer cases with internal flow are discussed, going through different aspects, ranging from smooth, corrugated and sinuous channel flows, as well as a microchannel problem taking into account slip flow and temperature jump effects in the solid-liquid interface, which are typically despised at the macroscale. Still considering the internal flow in smooth channel, specifically in the eigenvalue problem, a problem that incorporates convective effects was also addressed, in addition to the classic formulation of Sturm Liouville. A final case study involves a heat conduction problem with an irregular geometry. A fictitious domain encompassing the entire original domain is created to avoid explicit treatment. The conjugated and conduction problems are solved using the Generalized Integral Transform Technique (GITT), with a single-domain formulation. This formulation could be used due to the approach of the coefficient with spatial variations introduced in the energy equation, thus allowing the non explicit treatment of the wall-fluid interaction regions, enabling the treatment of complex geometries. The auxiliary eigenvalue problem, generated from the application of integral transformations, is solved through the Finite Differences Method, while the generated ordinary differential equation system is solved analytically, thus making it a hybrid technique. The solutions obtained by GITT are compared throughout the work with results from the COMSOL Multiphysics® platform. Thus, the hybrid methodology was able to solve the proposed problems correctly, taking the COMSOL solutions as a reference. In addition, the numerical solutions of the eigenvalue problems proved to be advantageous in relation to the solutions with integral transformations already presented in the literature.