Numerical Study of Natural Convection between Two Concentric Ellipses with Different Shapes and Imposed Temperatures

In this work, the laminar natural convection problem for a Newtonian fluid confined between two concentric ellipses is solved numerically. Two cases of heating are assumed, an inner wall at high temperature (TH ) and an external one at low temperature (TC ), then the opposite. Starting from the case of two circles (ellipses with equal diameters) and arriving at two ellipses, 25 geometries are studied for each type of heating, which gives 50 geometries in total. The effects of Rayleigh number (Ra), aspect ratio in addition to the ellipses orientations are investigated. The dynamic and thermal fields as well as the geometry average Nusselt number calculation (Nuavg=(Nuavo+Nuavi)/2) are analyzed. Nuavg values are ranked at the end in a descending order to show which geometry offers the largest heat exchange rate and vice versa, that is something very useful in practice. It should be noted that a good choice of the geometry shape may lead to have a more homogeneous thermal field, a result which goes against the stratifying effect of natural convection that has sometimes to be avoided.

Keywords: Aspect ratio, Concentric ellipses, Heating type, Natural convection, Nusselt number, Rayleigh number.