Abstract

Using a paraboloidal coordinate system and a vorticity- stream function formulation, the authors studied numerically the two-dimensional unsteady natural convection of a Newtonian fluid confined between two paraboloids of revolution with vertical axes. The opening on the upward surface is heated up with a constant temperature, while the rest remains thermally isolated. The downward opening on the upper surface is completely cooled. A spatial discretization based on finite volume method is used to approximate the dimensionless equations of vorticity, heat and stream function. A fully implicit scheme is adopted for time discretization and algebraic systems obtained are solved by a successive under relaxation method. The authors analyzed the effects of the control parameter like the Rayleigh number on the dynamics of the system. The results obtained are related to Rayleigh numbers between 10⁵ and 10⁷.

Key words: Convection, paraboloid, paraboloidal coordinate system, finite volume method.