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This article deals with the effects of thermophoresis on thermosolutal mixed convection in a vertical wavy porous cavity. Three distinct flow features are chosen by changing the directions of the moving horizontal borders. A nonuniform temperature, as well as concentration distributions, are introduced to the bottom wall while keeping cold temperature and low concentration for the other walls. The governing equations are modeled to describe thermosolutal phenomena. These equations are solved by reconstructing a recently developed compact scheme. Furthermore, the significance of well-defined parameters influencing the fluid rotation and thermosolutal transfer, namely Richardson number ( 0.01 ≤ Ri ≤ 100 ), Buoyancy ratio (N = 1), number of undulations ( 0 ≤ d ≤ 2 ) of the wavy walls, Lewis number ( 1 ≤ Le ≤ 10 ), thermophoretic coefficient ( 0.0 ≤ K T ≤ 1.0 ), Darcy number ( 0.001 ≤ Da ≤ 0.1 ), and porosity of the porous medium ( 0.1 ≤ ε ≤ 1.0 ) are performed generously. Results are displayed in terms of streamlines, isotherms, iso-concentrations, Nusselt, and Sherwood numbers to evoke the thermosolutal phenomena for various physical parameters. It is observed that thermophoresis is effective in certain circumstances. In addition, heat and mass transfer enhancement is noted with decreasing Richardson number while heat and mass transfer reduction is noted with increasing undulation number of the wavy walls. We have noticed that for the change in Le from 1 to 10, heat transfer is diminished up to 2.91% in Case-1, 3.03% in Case-2, and 2.20% in Case-3 while mass transfer is enhanced by 162.85% in Case-1, 164.05% in Case-2, and 87.03% in Case-3. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann simulations of double-diffusive convection in a rectangular cavity differentially heated and salted are conducted in the presence of internal heat generation and Dufour and Soret effects. The study is performed for an aspect ratio A = 2, an external Rayleigh number RaE = 105, a Lewis number Le = 2, a buoyancy ratio N = -1, and a Prandtl number Pr = 0.71: The study focuses mainly on the effect of Dufour number (Du = 0 and 0.5) to measure its impact on the ranges of steady/unsteady solutions reported in a previous study for the Soret parameter ranging from -0.5 to 0.5 and internal to external Rayleigh numbers ratio ranging from 0 to 80. Compared to Du = 0, the results obtained show that the presence of Dufour mechanism with a positive value leads to a destabilizing effect by widening the ranges of instability observed for the considered values of Sr: The combinations (Sr, Du) the most stabilizing/destabilizing are identified and discussed in this study. [ABSTRACT FROM AUTHOR]

AbstractThermosolutal natural convection originates in a fluid when the density changes due to the presence of two distinct components with varying rates of diffusion. This convection is driven by buoyancy resulting from concurrent temperature and concentration gradients. This study focuses on the thermosolutal free convection flow within a parallelogrammic enclosure. The functioning fluid under consideration is non-Newtonian and formulated by the viscosity model (power-law). The top and bottom walls of the chamber are adiabatic and are assumed to be impermeable. The temperature and concentration on the left side are maintained at a high level, while the conditions on the right side are cold and low. The controlling parameters for the present case include Rayleigh number (105≤Ra≤106), Lewis number (Le = 5, 10), Prandtl number (Pr = 6.2), buoyancy ratio (N = 0.8, −0.8) along with power-law index (n = 0.6, 1, 1.4). The results obtained from this numerical study are validated with existing results and indicate the correctness of the code. The output of the study is shown in terms of velocity and temperature profiles, streamlines, isotherms, and iso-concentrations, the average rate of heat and mass transmission in terms of the average Nusselt number (Nu¯) and the average Sherwood number (Sh¯). The correlation equation derived from the RSM approach demonstrates the relationship between the output responses and the input parameters. It concludes that n negatively affects both heat and mass transfer, while Ra affects positively. The findings of this study could be helpful for understanding of thermosolutal natural convection behavior of non-Newtonian (power-law) fluid in an enclosure and therefore accelerate the industrial application of such fluid in the relevant field, such as HVAC (heating, ventilation, and air conditioning) system. [ABSTRACT FROM AUTHOR]

We examine the initial layer problem and the infinite Prandtl number limit of the thermosolutal convection, which is applicable to magma chambers. We derive the effective approximating system of the Boussinesq system at large Prandtl number using two time scale approach [M. Holmes,Introduction to Perturbation Methods, Springer, New York, 1995, A. Majda,Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lecture Notes in Mathematics, Vol. 9, New York, American Mathematical Society, Providence, RI, 2003]. We show that the effective approximating system is nothing but the infinite Prandtl number system with initial layer terms. We also show that the solutions of the Boussinesq system converge to solutions of the effective approximating system with the convergence rate ofO(ϵ). [ABSTRACT FROM AUTHOR]

A three phase volume averaging model has been developed to simulate globular equiaxed solidification, the three phases being liquid, solid and air. The basic conservation equations of mass, momentum and enthalpy have been solved for each phase, and the thermal and mechanical (drag force) interactions among the phases have been considered. Grain nucleation, growth rate (mass exchange), solute partitioning at the liquid/solid interface and solute transport have also been accounted for. Due to its low density, the air phase floats always at the top region, forming a definable air/liquid melt interface, i.e. free surface. By tracking this free surface, the shrinkage cavity in an open casting system can be modelled. As the temperature and concentration dependent density and solidification shrinkage are explicitly included, the thermosolutal convection, together with feeding flow and grain movement can be taken into account. This paper focuses on the model description; preliminary results on a benchmark ingot casting (Al–4Cu) are presented and discussed. [ABSTRACT FROM AUTHOR]