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 104⩽Ra⩽106, and of the tilting angle of the cavity in the range 0°⩽γ⩽360°. The influence of Ra and γ 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 γ between 45° and 225° may be expressed through the semi-empirical dimensionless correlation-equation Nu=1.2Ra0.135[1+(sinγ)/2]0.405. For any tilting angle γ<45°, the heat transfer rate is the same as that for angle (90°−γ). For any tilting angle γ>225°, the heat transfer rate is the same as that for angle (450°−γ). In addition, the occurrence of hysteresis phenomena around γ=45° is documented within a range of γ whose extent decreases from nearly 20° to nearly 4° as the Rayleigh number increases from 104 to 106.