Natural convection in tilted square cavities with differentially heated opposite walls

Natural convection in air-filled, tilted square enclosures with two adjacent walls heated and the two opposite walls cooled is numerically studied. A computational model based on the SIMPLE algorithm is used for solving the mass, momentum, and energy transfer governing equations. Simulations are performed for different values of the Rayleigh number in the range 10(4) <= Ra <= 10(6), and of the tilting angle of the cavity in the range 0 degrees <= gamma <= 360 degrees. The influence of Ra and gamma on the flow pattern, on the local temperature distribution, and on the heat transfer rates across the enclosure are analysed and discussed. The results obtained for the overall heat transfer in the range of gamma between 45 degrees and 225 degrees may be expressed through the semi-empirical dimensionless correlation-equation Nu = 1.2Ra(0.135)[1 + (sin gamma)/2](0.405). For any tilting angle gamma < 45 degrees, the heat transfer rate is the same as that for angle (90 degrees - gamma). For any tilting angle gamma > 225 degrees, the heat transfer rate is the same as that for angle (450 degrees - gamma). In addition, the occurrence of hysteresis phenomena around gamma = 45 degrees is documented within a range of y whose extent decreases from nearly 20 degrees to nearly 4 degrees as the Rayleigh number increases from 10(4) to 10(6). (c) 2005 Elsevier SAS. All rights reserved.