Effects of the aspect ratio on the optimal tilting angle for maximum convection heat transfer across air-filled rectangular enclosures differentially heated at sides

Natural convection in air-filled rectangular cavities inclined with respect to gravity, so that the heated wall is facing upwards, is studied numerically under the assumption of two-dimensional laminar flow. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum and energy transfer governing equations. Simulations are performed for height-to-width aspect ratios of the enclosure from 0.25 to 8, Rayleigh numbers based on the length of the heated and cooled walls from 102 to 107, and tilting angles of the enclosure from 0° to 75°. The existence of an optimal tilting angle is confirmed for any investigated configuration, at a location that increases as the Rayleigh number is decreased, and the height-to-width aspect ratio of the cavity are increased, unless the value of the Rayleigh number is that corresponding to the onset of convection or just higher. Dimensionless correlating equations are developed to predict the optimal tilting angle and the heat transfer performance of the enclosure.