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.
