Numerical Simulation of Natural Convection Between Two Elliptical Cylinders: Influence of Rayleigh Number and Prandtl Number

This paper reports the numerical study of the phenomenon of the natural convection in a space annulus, situated between two horizontal confocal elliptic cylinders. This space is filled by a Newtonian fluid. The Prandtl number and the Rayleigh number vary. By using the Boussinesq approximation and the vorticity-stream function formulation, the flow is modeled by the differential equations with the derivative partial: continuity and momentum equations are expressed in a frame of reference known as “elliptical”, to facilitate the writing of the boundary conditions and to transform the curvilinear field into a rectangular one. The two cylindrical walls of the enclosure are kept isotherms, T1 for the internal wall and T2 for the external wall, with T1>T2. A computer code was developed, the latter uses finite volumes, for the discretization of the equations and in order to show its reliability, the resulting results from the latter are compared with other similar results existing in the literature and the effect of the values of Rayleigh and Prandtl numbers on the results obtained that it is qualitatively or quantitatively, is examined.