Análise de convecção interna conjugada em microcanais utilizando a técnica da transformada integral

Abstract

The rise of electronic devices across sectors poses a thermal management challenge. Smaller, more potent devices highlight the need for better heat dissipation. Microchannel technology, with hydraulic diameters ranging from 1 micrometer to 1 milimeter, offers improved heat transfer, compactness, and integration without much space increase. Within this framework, the present work considers an extended Graetz problem with conjugated internal convection in a parallel plate microchannel, which is modeled as two-dimensional and steady-state across two distinct regions: the solid wall and the fluid, where the convection-diffusion equations are applied. The mentioned equations account for heat diffusion effects in both the wall and fluid domains, crucial for flows with small Péclet numbers. Thermal properties are assumed to be constant within each of the regions, while the flow is considered hydrodynamically developed but thermally developing. Moreover, slip flow and temperature jump conditions are also considered. A semi-analytical solution is presented based on the Generalized Integral Transform Technique (GITT) which offers a methodical approach for solving steady-state and time-dependent boundary value heat transfer problems. Therefore, using the matrix exponential method, the coupled ordinary differential equations system resulting from the GITT is analytically solved. Several previous research efforts on conjugated internal convection, have been developed employing a single-domain and single-region formulation. However, this work introduces a novel methodology for a single-domain, two-region formulation using piecewise-defined eigenfunctions and a preliminary parametric analysis to investigate the influence of various combined parameters on the performance of the system. The results of this investigation provided the temperature profile in both regions and characterized the behavior of the Nusselt number as a function of the Péclet and Knudsen numbers, the conjugate effect of the solid region, and the thermal conductivity ratio. Furthermore, these results were validated against previous studies.