Flow and heat transfer regimes in inclined differentially heated cavities

The natural convection in long inclined cavities with differentially heated end walls is analytically and numerically studied. The dimensionless axial temperature gradient at the core region, K, is calculated and it is used to determine the frontiers: of the flow regimes (conductive. transition and boundary layer regimes) in the space of parameters. For horizontal cavities (alpha = 90 degrees) these frontiers have been found at A(2)Ra similar or equal to 10(2) and A(2)Ra similar or equal to 10(4), and confirm the results of B. Boehrer (Convection in a long cavity with differentially heated end walls, int. J, Heat Mass Transfer 40 (17) (1997) 4105-4114). Fur 0 < x < 90 degrees (heated-from-below cavities) the frontiers are found at values of the group parameter ARa cos(alpha)/R-0 of order 1 and 10. If the cavity is heated from above the flow always remains in the conductive regime if cc is made large enough (typically alpha > 100 degrees). The boundary layer regime (BLR) are alpha < 90 is also studied, If the cavity is inclined, no stagnant region is formed at the center of the cure, but instead a region with approximately constant shear. In the BLR, the maximum cross-stream and axial velocities scale, respectively, with Ra-1 (4) and Ra-4 7 and the transport of heat in the core, governed by the axial advection, grows like Nu similar to Ra-2 '7. Numerical calculations of the flow in a closed geometry carried out by a Chebyshev-collocation method confirm the theoretical predictions: and are used to investigate the structure of the flow at large Rayleigh number. (C) 2001 Elsevier Science Ltd. All rights reserved.