Double-diffusive mixed convection in rectangular cavities filled with non-Newtonian fluids

Abstract

• Double-diffusive mixed convection in a double-lid driven rectangular cavity filled with non-Newtonian fluids is investigated analytically and numerically. • Analytical solution based on the parallel flow assumption agrees perfectly with the numerical solution for a wide range of governing parameters. • Mixed convection parameter is established to separate the dominance zones of natural, mixed and forced convective regimes for pseudo-plastic, Newtonian and dilatant fluids. • Increasing thermal Rayleigh number or Peclet number enhances fluid circulation and heat and mass transfer, by strengthening the buoyancy force and shear effect, respectively. • Increasing Lewis number/buoyancy ratio promotes the contribution of forced/natural regime. Also, forced convection affects strongly the rheological behavior of fluids as it abolishes its effect on flow characteristics observed in natural regime. The present study investigates numerically and analytically double-diffusive mixed convection in a closed rectangular cavity filled with non-Newtonian power-law fluid and subjected to uniform heat and mass fluxes from its vertical short sides, while the horizontal ones are insulated and impermeable and moving in opposite directions. The finite volume method is used to solve governing equations numerically, while the analytical solution is developed based on the parallel flow assumption valid in the case of a shallow cavity. A good agreement is found between both solutions for a wide range of governing parameters, namely, thermal Rayleigh number Ra T , Peclet number Pe , Lewis number Le , buoyancy ratio N , and power-law behavior index n . The effects of mentioned governing parameters on flow intensity and heat and mass transfer rates were illustrated and discussed in terms of the stream function Ψ, the average Nusselt number N u ¯ , the average Sherwood number S h ¯ , streamlines, isotherms, and iso-concentrations along with velocity, temperature, and concentration profiles. A mixed convection parameter is introduced to separate the zones where natural, mixed, and forced convective regimes dominate the convection, allowing to examine the effects of governing parameters for each separated regime. As a result, the ratios Ra T / Pe 2.6 , Ra T / Pe 3.0 and Ra T / Pe 3.4 are found to outline the limit between the predominance regions of the three convective regimes for n = 0.6, n = 1.0, and n = 1.4, respectively. It is found that increasing thermal Rayleigh number or Peclet number enhances heat and mass transfer, as the first strengthen the buoyancy force responsible for natural convection while the second promotes the contribution of shear effect accountable for forced convection. As for Le and N , interesting results are found, where increasing Le boost the contribution of forced convection while buoyancy ratio N produces an opposite effect, as increasing it leads to a more pronounced effect of natural regime on the convection. On the other hand, and while it is common knowledge that decreasing the power law-index enhances flow characteristics in the natural regime, the forced convection is found to affect strongly the rheological behavior of non-Newtonian fluids as it cancels the effect of n on flow characteristics.