Investigation of thermal energy transport from an anisotropic central heating element to the adjacent channels: A multipoint flux approximation

Abstract The problem of heat transfer from a central heating element pressed between two clad plates to cooling channels adjacent and outboard of the plates is investigated numerically. The aim of this work is to highlight the role of thermal conductivity anisotropy of the heating element and/or the encompassing plates on thermal energy transport to the fluid passing through the two channels. When the medium is anisotropic with respect to thermal conductivity; energy transport to the neighboring channels is no longer symmetric. This asymmetry in energy fluxes influence heat transfer to the coolant resulting in different patterns of temperature fields. In particular, it is found that the temperature fields are skewed towards the principal direction of anisotropy. In addition, the heat flux distributions along the edges of the heating element are also different as a manifestation of thermal conductivity anisotropy. Furthermore, the peak temperature at the channel walls change location and magnitude depending on the principal direction of anisotropy. Based on scaling arguments, it is found that, the ratio of width to the height of the heating system is a key parameter which can suggest when one may ignore the effect of the cross-diagonal terms of the full conductivity tensor. To account for anisotropy in thermal conductivity, the method of multipoint flux approximation (MPFA) is employed. Using this technique, it is possible to find a finite difference stencil which can handle full thermal conductivity tensor and in the same time enjoys the simplicity of finite difference approximation. Although the finite difference stencil based on MPFA is quite complex, in this work we apply the recently introduced experimenting field approach which construct the global problem automatically.