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The thermal-diffusion (Soret) and the diffusion-thermo (Dufour) effects play a crucial role in double diffusive mixed convection in a lid-driven cavity; but they have not been studied properly by researchers. The purpose of this paper is to investigate effects of Soret and Dufour parameters on double diffusive laminar mixed convection of shear-thinning and Newtonian fluids in a two-sided lid-driven cavity.

Finite Difference Lattice Boltzmann method (FDLBM) has been applied to solve the complex problem. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.00062-1), power-law index (n=0.2-1), Soret parameter (Sr=−5-5) as Dufour number effects have been investigated from Dr=−5 to 5 at Buoyancy ratio of N=1 and Lewis number of Le=5.

Results indicate that the augmentation of Richardson number causes heat and mass transfer to decrease. The fall of the power-law index declines heat and mass transfer at Ri=0.00062 and 0.01 in various Dufour and Soret parameters. At Ri=1, the heat and mass transfer rise with the increment of power-law index for Dr=0 and Sr=0. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri=1. The positive Dufour numbers augment the heat transfer gradually as the positive Soret numbers enhance the mass transfer. The Dr=−5 and Sr=−5 provokes the negative average Nusselt and Sherwood numbers, respectively, to be generated. The least magnitude of the average Nusselt and Sherwood numbers were obtained at Dr=−1 and Sr=−1, respectively.

Soret and Dufour effects in double diffusive mixed convection has not been studied in a lid-driven cavity. In addition. this study has been conducted also for shear-thinning fluids.

A study on heat and mass transfer behavior for an anisotropic porous medium embedded in square cavity/annulus is conducted using incompressible smoothed particle hydrodynamics (ISPH) method. In the case of square cavity, the left wall has hot temperature T_h and mass C_h and the right wall have cool temperature T_c and mass C_c and both of the top and bottom walls are adiabatic. While in the case of square annulus, the inner surface wall is considered to have a cool temperature T_c and mass C_c while the outer surface is exposed to a hot temperature T_h and mass C_h. The paper aims to discuss these issues.

The governing partial differential equations are transformed to non-dimensional governing equations and are solved using ISPH method. The results present the influences of the Dufour and Soret effects on the fluid flow and heat and mass transfer.

The effects of various physical parameters such as Darcy parameter, permeability ratio, inclination angle of permeability and Rayleigh numbers on the temperature and concentration profiles together with the local Nusselt and Sherwood numbers are presented graphically. The results from the current ISPH method are well-validated and have favorable comparisons with previously published results and solutions by the finite volume method.

A study on heat and mass transfer behavior on an anisotropic porous medium embedded in square cavity/annulus is conducted using Incompressible Smoothed Particle Hydrodynamics (ISPH) method. In the ISPH algorithm, a semi-implicit velocity correction procedure is utilized, and the pressure is implicitly evaluated by solving pressure Poisson equation (PPE). The evaluated pressure has been improved by relaxing the density invariance condition to formulate a modified PPE.

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

The purpose of this paper is to analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

The purpose of this paper is to address the heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions. Mass transfer is considered in the presence of first order chemical reaction. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. Convergent series solutions to the resulting non-linear problems are developed. Effects of Biot and Deborah numbers on the Sherwood number are decreasing. Local Nusselt reduces with an increase in Eckert numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt number are increasing while Sherwood number decreases with an increase in Prandtl number.

The involved partial differential systems are reduced to the ordinary differential systems using appropriate transformations. Series solutions by homotopy analysis method are constructed and analyzed. Graphical results are presented and examined in detail.

It is found that roles of Deborah and Biot parameters on the Nusselt number are opposite. However, the Sherwood number is qualitative similar for both Biot and Deborah numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt and Sherwood numbers are similar.

The purpose of present communication is to investigate the three-dimensional flow of Maxwell fluid over a stretching surface with convective condition. Analysis has been carried out in the presence of mass transfer with first order chemical reaction and Soret and Dufour effects.

The purpose of this paper is to study the heat and mass transfer with Soret-Dufour effects for the magnetohydrodynamic three-dimensional flow of second grade fluid in the rotating frame of reference.

Series solution is obtained by homotopy analysis method.

Increase in Soret number, Schmidt number and Dufour number, the heat transfer increases and mass transfer decreases. Effects of Prandtl and Eckert numbers are qualitatively similar as they assist the temperature profile and reduce the concentration of species. Increase in the length of the channel versus height increases the temperature profile but decreases the concentration field. Increase in the second grade fluid parameter causes reduction in both the temperature and concentration fields. The heat flux values at the lower plate are smaller than the values at the upper plate, whereas the situation is opposite in the case of mass transfer.

These findings will be useful for the fluid flow in porous channel.

The purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.

The ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.

The resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.

A novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

The boundary layer flow and heat transfer of second grade fluid in a region of the stagnation point over a stretching surface has been examined. Thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects combined with melting heat transfer are also considered. Suitable transformations are employed to convert the partial differential equations representing the conservation of mass, momentum, energy and diffusion into the system of ordinary differential equations. The series solutions for the flow quantities of interest are presented. Interpretation to velocity, temperature and concentration is assigned. Numerical values of the local Nusselt and Sherwood numbers have been computed. The paper aims to discuss these issues.

Analytic approach homotopy analysis method (HAM) is used to find the convergent solution of melting heat transfer in a boundary layer flow of a second grade fluid under Soret and Dufour effects.

In this article the main findings are as second grade fluid; melting heat transfer; Soret and Dufour effects; mass transfer; stretching sheet. It is noted that melting heat transfer enhances the flow. Moreover, the effects of Soret and Dufour parameters have opposite effects on the temperature and concentration fields.

The performed computations show that the behaviors of Prandtl number Pr and Schmidt number Sc on the dimensionless temperature and concentration fields are similar in a qualitative sense.

In this paper the effects of viscous dissipation and ohmic heating on the fluid flow and resulting heat and mass transfer caused by vertically moving rotating disk are explored with magnetic field acting perpendicular to disk rotation. The flow regime is also under the influence of Dufour and Soret effects.

An approach of similarity transformation is used to transform the governing set of equations into non-linear ordinary differential equations. Numerical simulations are carried out in Maple software to study the influence of incorporated non-dimensional parameters viz. disk movement parameter (−0.3 < S < 0.2), magnetic parameter (0.1 < M < 0.4), Eckert number (0.1 < Ec < 1), Schmidt number (0.1 < Sc < 1), Soret parameter (0.1 < Sr < 1) and Dufour number (0.1 < Du < 1) on velocity, temperature and concentration profiles.

The upward/downward motion of the disk along with rotation set up a three-dimensional flow over the disk surface and exerts the same effects as injection/suction through the wall. It is also observed that incorporated parameters along with disk movement greatly affect the flow regime and associated heat and mass transfer.

The present study examines the heat and mass transfer characteristics of incompressible Newtonian fluid over an impermeable rotating disk moving vertically. The effect of viscous dissipation and ohmic heating is considered. To the best of the authors’ knowledge, such consideration is yet to be published in the literature.

The purpose of this paper is to emphasize on the impact of endoscope in MHD peristaltic flow of Carreau fluid. Heat and mass transfer phenomena are comprised of Soret and Dufour effects. Influences of mixed convection and viscous dissipation are also accounted. Wall properties and convective boundary conditions are used.

The Navier–Stokes and energy equations used the lubrication approach. The reduced system of equations is executed numerically. The graphical illustration of velocity, temperature, concentration and heat transfer coefficient for various emerging parameters is discussed.

The response of Weissenberg number and power law index is decaying toward velocity and temperature. Moreover impression of Soret and Dufour number on temperature is quite reverse to that of concentration.

The titled problem with the various considered effects has not been solved before, and it is of special importance in various industries. The problem is original.