Effect of density inversion on Bénard convection of water

Bénard convection in a water layer heated from below is studied numerically for cases with and without density inversion. Calculations were carried out for varying the temperature difference between the top and bottom walls. Moreover, for the case where density inverses, the aspect ratio was also incorporated into parameters. When density inversion occurs, the number of cells takes a maximum value at the commencement of the convection, which equals double the inverse of the aspect ratio, and exhibits a tendency to decrease as the Rayleigh number increases. The Nusselt number for the case with density inversion is smaller than that for no density inversion because a stagnant region forms at the top of the cavity behaves as a thermal resistance. However, the difference in the Nusselt number decreases as the Rayleigh number increases. Further, an approximate model is proposed to predict the heat transfer rate and the critical Rayleigh number for the case with the density-inverting system. The predicted critical Rayleigh number shows good agreement with numerical one.