Aspect ratio effect on natural convection in water near its density maximum temperature

The effect of the aspect ratio on natural convection in water subjected to density inversion has been investigated in this study. Numerical simulations of the two-dimensional, steady state, incompressible flow in a rectangular enclosure with a variety of aspect ratios, ranging from 0.125 to 100, have been accomplished using a finite element model. Computations cover Rayleigh numbers from 10³ to 10⁶. Results reveal that the aspect ratio, A, the Rayleigh number, Ra, and the density distribution parameter, R, are the key parameters to determine the heat transfer and fluid flow characteristics for density inversion fluids in an enclosure. A new correlation for predicting the maximum mean Nusselt number is proposed in the form of , with the constants a and b depending on density distribution number R. It is demonstrated that the aspect ratio has a strong impact on flow patterns and temperature distributions in rectangular enclosures. The stream function ratio Ψ_inv/|Ψ_reg| is introduced to describe quantitatively the interaction between inversional and regular convection. For R=0.33, the density inversion enhancement is observed in the regime near A=3.