Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0 ≤ m ≤ 10), the flow behaviour index (0.6 ≤ n ≤ 1.4), and the Rayleigh number (0 < Ra ≤ 10 5 ), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

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Two-dimensional steady laminar natural convection of a viscoelastic fluid represented by generalized second-grade fluid model in a square enclosure is studied. The cavity is submitted at its vertical sides to a uniform density of heat flux while the horizontal walls are insulated, without slipping conditions at all the solid boundaries. The governing conservation and constitutive equations with the corresponding boundary conditions are solved by finite volume method in a collocated grid system. The contributions of shear rate dependent and elastic characteristics of the viscoelastic fluid are investigated on momentum and heat transport. The effects of elastic number (E) in the range 0 - 1 on heat transfer and fluid motion are interpreted for a power-law index (n) in the range 1.4 - 0.6 and nominal values of Rayleigh number (Ra) range of 103 to 105.

The current study explores numerically mixed convection of thermo-dependent power-law fluids in a square lid-driven enclosure, including the thermal radiation effect. The vertical sidewalls are sustained at both hot and cold temperatures. On the other hand, the cavity is insulated from the horizontal walls. The upper wall is moving along the x-axis. The main governing equations that the Boussinesq approximation is used for are solved using the finite difference method. The simulations focus on the effects of multiple pertinent parameters, including the Richardson number. (Ri = 0.1, 1, 10 and 100), thermal radiation parameter (Rd = 0 and 10), power-law index (0.6 ≤ n ≤ 1.4) and the Pearson number (0 ≤ m ≤ 6). The findings reveal that improving the Richardson number reduces heat transfer. Then, increasing Rd results in a domination of heat conduction for a fluid having a higher thermal conductivity. Also, the growth in the power law-index reduces heat transfer while improving convective flow. Finally, increasing the Pearson number improves the convective flow rate and also the average Nusselt number.

The present paper investigates double-diffusive mixed convection inside a horizontal rectangular cavity both numerically using the finite volume method to solve the governing equations and analytically based on the parallel flow approximation developed for the case of shallow enclosures A≫1. Uniform heat and mass fluxes are applied to the short vertical walls, while the horizontal ones are insulated and impermeable, with top wall sliding from left to right. The results show good agreement between both solutions for a wide range of controlling parameters: Peclet number, Pe, Lewis number, Le, the buoyancy ratio, N, and thermal Rayleigh number, RaT. In order to highlight how the convective regimes influence the effect of controlling parameters on flow and heat and mass transfer characteristics, the parameter RaT/Pe 3.0 is established to delineate the zones where natural, mixed, and forced convections dominates the heat and mass transfer. Effects of governing parameters on flow intensity and heat and mass transfer rates are illustrated and discussed in terms of the stream function, Ψ, the average Nusselt number, ̅̅̅̅ , the average Sherwood number ℎ ̅̅̅ , for the three separated convective regimes.