THREE DIMENSIONAL NATURAL CONVECTION OF THE WATER LAYER IN A VERTICAL CAVITY WITH THE MAXIMUM DENSITY

This paper is concerned with the three dimensional heat transfer in a vertical water layer that is calculated numerically by the PHOENICS Code. The thickness of the water layer is 2.5 cm , and the length and depth are both 25 cm . The vertical warm plate generates heat per unit volume $Q\left[\mathrm{~W} / \mathrm{m}^3\right]$ to set the mean temperature of its plate $T_h$, and the temperature of the cold plate $T_c$ is fixed at $0^{\circ} \mathrm{C}$ considering the melting of ice. The Nusselt number, Nu, of 3D is generally larger than Nu of 2 D in a range of $T_h \lesssim 40^{\circ} \mathrm{C}$. However, the ratio of $\mathrm{Nu}_{3 \mathrm{D}} / \mathrm{Nu}_{2 \mathrm{D}}$ increases with decreasing $T_h$, and marks the maximum of about 2.38 at $T_h \approx 8^{\circ} \mathrm{C}$. The ratio decreases with decreasing $T_h$ from $T_h \approx 8^{\circ} \mathrm{C}$ to $T_h \approx 0^{\circ} \mathrm{C}$. Received: May 15, 2024Accepted: June 8, 2024