Optimal inclination for maximum convection heat transfer in differentially-heated enclosures filled with water near 4 degrees C

Natural convection in water-filled square cavities inclined with respect to gravity, having one wall cooled at 0°C and the opposite wall heated at a temperature ranging between 4°C and 30°C, is studied numerically for cavity widths spanning from 0.02 m to 0.1 m in the hypothesis of temperaturedependent physical properties, with the main aim to determine the optimal tilting angle for maximum heat transfer. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Once the vertical configuration, in which the cavity is differentially heated at sides, is identified by the zero tilting angle, and positive angles denote configurations with the heated wall facing upwards, it is found that the optimal tilting angle is positive if the heating temperature is equal or higher than 8°C, whereas it is negative whenever the heating temperature is lower than 8°C. Moreover, the optimal tilting angle is found to increase as the cavity width is decreased and the temperature of the heated wall is either decreased or increased, according as it is higher or lower than 8°C. Sets of dimensionless correlating equations are developed for the prediction of both the optimal tilting angle and the heat transfer rate across the enclosure.