Numerical simulation of natural convection with density inversion in a square cavity

Water has its density maximum at 4 degrees C, and natural convection around the temperature is complicated. In this study, natural convection with density inversion in a two-dimensional vertical square cavity is investigated numerically. To express the average Nusselt number nondimensionally, some parameters are chosen by observing the calculated flow-temperature fields. Then a simple expression of heat transfer correlation as a function of Galilei number, wall temperature ratio, and density function is proposed. The present correlation has a deviation of about 10%.