Rayleigh-Bénard double-diffusive mixed convection in two-dimensional rectangular cavities filled with non-Newtonian fluids

Abstract

The present work investigates numerically and analytically Rayleigh-Bénard double-diffusive mixed convection inside horizontal rectangular cavities filled with non-Newtonian fluids and subjected to uniform heat and mass fluxes along the sliding horizontal walls, while the vertical ones are considered insulated and impermeable. The problem is found to be governed by: Peclet number Pe, thermal Rayleigh number RaT, Lewis number Le, buoyancy ratio N, and power-law behavior index n. Both solutions show a good agreement for inclusive ranges of governing parameters; thus, validating the analytical approach and the numerical code. To gain further insight into convection phenomena, the dominance regions of convective regimes, namely natural, mixed, and forced convection are defined, where ratios RaT/Pe1.57, RaT/Pe1.92, and RaT/Pe2.27 accurately delineate the three regimes for n = 0.6, n = 1.0, and n = 1.4, respectively. As a result, the effects of governing parameters are amply discussed in each governing regime. Increasing Peclet number enhances flow intensity while heat and mass transfer rates increase only until reaching a higher plateau. For thermal Rayleigh number, increasing it intensifies fluid circulation while heat and mass transfer increase only for a given range of Pe values, where after a critical value Pecr the opposite happens as shear and buoyancy forces compete driving the transfer rates down. Such results are due to Pe strengthening forced convection contribution in the overall convection and RaT enhancing natural convection. As for Lewis number, a given range correlated with n strongly enhances natural regime contribution, which increases flow intensity while the outcome on heat transfer depends on the associated shear force magnitude. Further, increasing Le enhances mass transfer until reaching a higher plateau due to boosted forced convection contribution. In contrast, buoyancy ratio is found to strengthen natural convection leading to similar outcomes as for RaT. Finally, the rheological behavior of non-Newtonian fluids leads to some unforeseen effects on flow characteristics directly related to the dominant convective regime. The critical Peclet number Pecr signaling the change in n effect and leading to buoyancy forces reducing transfer rates instead of enhancing them is presented as a function of the remaining governing parameters RaT, Le, N, and n.