Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation

We consider unsteady laminar natural convection flow of water subject to density inversion in a rectangular cavity formed by isothermal vertical walls with internal heat generation. The top and bottom horizontal walls are considered to be adiabatic, whereas the temperature of the left vertical wall is assumed to be greater than that of the right vertical wall. The equations are non-dimensionalized and are solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of both heat generation and variations in the aspect ratio on the streamlines, isotherms and the rate of heat transfer from the walls of the enclosure are presented. Investigations are performed for water taking Prandtl number to be Pr=11.58 and the Rayleigh number to be Ra=10⁵.