Effects of the Heated Surface on the Unsteady Two Dimensional Natural Convection in Enclosures Bounded by Two Paraboloids of Revolution


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Abstract


Using a paraboloidal coordinates system and a vorticity- stream function formulation, the authors study numerically the two-dimensional unsteady natural convection of a Newtonian fluid confined between two paraboloids of revolution with vertical axes. A certain portion of the opening upward surface is heated up with a constant temperature and the rest remains thermally isolated. The upper surface downwardly open is completely cooled. A spatial discretization based on finite volume method is used to approximate the dimensionless equations. 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 parameters like the Rayleigh number and the heat factor   (ratio between heated surface and total surface of the upwardly open paraboloid) on the dynamic of the system. Local results are presented in the form of streamline and isotherm plots as well as the variation of the average Nusselt number and the friction coefficient on the lower wall. The analysis of these figures showed that for the three values of e, 1/2, 3/4, 1 observed flows are very different
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Keywords


Convection; Finite Volume; Rayleigh Number; Heat Factor

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