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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.

Non‐linear reaction‐diffusion processes with cross‐diffusion in two‐dimensional, anisotropic media are analyzed by means of an implicit, iterative, time‐linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross‐diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cross‐diffusion deform the reaction front and affect the front velocity, and the magnitude of these effects increases as the magnitude of the off‐diagonal components of the heat and species diffusivity tensors is increased. It is also shown that the five types of boundary conditions employed in this study produce similar results except when there is either strong anisotropy in the species or heat diffusivity tensors and there are no Soret and Dufour effects, or the species and heat diffusivity tensors are isotropic, but the anisotropy of the Soret and Dufour effects is important. If the species and heat diffusivity tensors are isotropic, the effects of either the Soret or the Dufour cross‐diffusion effects are small for the cases considered in this study. The time required to achieve steady state depends on the anisotropy of the heat and diffusivity tensors, the cross‐diffusion effects, and the boundary conditions.

The purpose of this paper is to study the effects of chemical reaction, thermal radiation and Soret and Dufour effects of heat and mass transfer by natural convection flow about a truncated cone in porous media.

The problem is formulated and solved numerically by an accurate implicit finite-difference method.

It is found that the Soret and Dufour effects as well as the thermal radiation and chemical reaction cause significant effects on the heat and mass transfer charateristics.

The problem is relatively original as it considers Soret and Dufour as well as chemical reaction and porous media effects on this type of problem.

The purpose of this paper is to analyse the buoyancy flow, mass and heat transfer in coaxial duct under Soret and Dufour effect. The combined effects of the thermal-diffusion and diffusion-thermo coefficients, as well as the Schmidt number, on natural convection in a heated lower coaxial curve were explored using the proposed physical model. The Dufour and Soret effects are taken into consideration in the energy and concentration equations, respectively.

The dominating mathematical models are converted into a set of non-linear coupled partial differential equations, which are solved using a numerical approach. The controlling non-linear boundary value problem is numerically solved using the penalty finite element method with Galerkin’s weighted residual scheme over the entire variety of essential parameters.

It was observed that different parameters were tested such as heat generation or absorption coefficient, buoyancy ratio, Soret coefficient, Dufour coefficient, Lewis number and Rayleigh number. Effect of Rayleigh number, absorption/generation and Dufour coefficient on isotherm are significantly reported. For greater values of Lewis number, maximum mass transfer in duct in the form of molecular particles is produced. Buoyancy ratio parameter decreases the average rate of heat flow and increases its mass transfer.

The main originality of this work is to make an application of Soret and Dufour effects in a coaxial duct in the presence of source sink.

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.

The purpose of this study is to investigate the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction.

The similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Then, they are solved numerically by the fourth-order Runge–Kutta–Gill method along with the shooting technique and the Newton–Raphson method. In addition, the ordinary differential equations are also analytically solved by the homotopy analysis method.

The results for dimensionless velocity, temperature, solutal concentration and nanoparticle volume fraction profiles, as well as local skin friction coefficient and local Nusselt and local Sherwood numbers are presented through the plots for various combinations of pertinent parameters involved in the study. The heat transfer rate increases on increasing the Soret parameter and it decreases on increasing the Dufour parameter. The mass transfer behaves oppositely to heat transfer.

In engineering applications, a wedge is used to hold objects in place, such as engine parts in the gate valves. A gate valve is the valve that opens by lifting a wedge-shaped disc to control the timing and quantity of fluid flow into an engine.

No such investigation is available in literature, and therefore, the results obtained are novel.

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 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.

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.