Heat transfer correlations for natural convection in inclined enclosures filled with water around its density-inversion point

Natural convection in tilted square cavities filled with water, having one side cooled at 0 °C and the opposite side heated at a temperature ranging between 8 °C and 40 °C, is studied numerically for different cavity widths in the hypothesis of temperature-dependent physical properties, exploring the full range of inclination angles. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. It is found that, as the inclination angle is increased starting from the cooling-from-below configuration, the heat transfer rate keeps substantially constant until the breakdown of the upper fluid stratification occurs. Thereafter, the heat transfer performance increases steeply up to reaching a peak at an optimal tilting angle, which increases with decreasing both the cavity width and the temperature of the heated wall. Furthermore, when the combination of the cavity width and the temperature of the heated wall is such that at small tilting angles the buoyancy force in the water layer confined between the cooled bottom wall and the density-inversion isotherm is that required for the onset of convection, or just higher, the asymptotic solution is periodical. A number of dimensionless correlations are developed for the prediction of both the optimal tilting angle and the heat transfer rate across the enclosure.