Numerical study of laminar natural convection in a half ellipsoid of revolution subjected to heat flux of constant density

Abstract

In this article, we numerically study the natural convection in a half-eliipsoid of revolution filled with a Newtonian fluid (air). The ellipsoid wall is isothermal which is maintained at a heat flux of constant density. The equations that govern the flow and heat transfer are described by the so-called Navier-Stokes equation of motion accompanied by the so-called Fourier equation of heat. The finite element method is used to solve the system of equations.  We consider the effect of the shape factor of the elliptical wall and the Grashof number on the results obtained in the form of streamlines, and mean Nusselt numbers.  The Nusselt numbers for natural convection inside a system formed by a rectangular geometry and for a curved shape are comparer and analyzed each other. We find that this number is quite higher for a curved system than that of a planar shape. It shows the importance of the form factor, particularly, in circular shape which is much more advantageous compared to the straight shape.

In terms of inertia, the geometry of rounded shape ensures the best distribution of energy. In fact, the half ellipsoidal greenhouse with a circular base studied during this research offers a better distribution for the flow of the convection currents from the bottom to the top of the system.