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 (α=90°) these frontiers have been found at A2Ra≃102 and A2Ra≃104, 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). For 0<α<90° (heated-from-below cavities) the frontiers are found at values of the group parameter ARacos(α)/R0 of order 1 and 10. If the cavity is heated from above the flow always remains in the conductive regime if α is made large enough (typically α>100°). The boundary layer regime (BLR) for α<90° is also studied. If the cavity is inclined, no stagnant region is formed at the center of the core, but instead a region with approximately constant shear. In the BLR, the maximum cross-stream and axial velocities scale, respectively, with Ra1/4 and Ra4/7 and the transport of heat in the core, governed by the axial advection, grows like Nu∼Ra2/7. 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.