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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.

The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects.

In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled.

Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase.

The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

The purpose of this paper is to deal with unsteady double diffusive natural convection in a square enclosure filled with a porous medium with various boundary condition effects in the presence of heat source or sink.

Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, amplitude wave length ratio, dimensionless time parameter, Darcy number, buoyancy parameter and heat generation/absorption parameter on the streamlines, temperature and concentration contours, as well as Nusselt number and Sherwood number, were considered.

The sinusoidal variations of the temperature and concentration remove the singularities which appear in the case of fixed temperature and concentration.

The paper's results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.

The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100Ra_T100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers.

A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides.

It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter.

The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc.

An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc.

Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.

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 investigation is to determine the nature of the flow field, temperature distribution and heat and mass transfer in a triangular solar collector enclosure with a corrugated bottom wall in the unsteady condition numerically.

Non-linear governing partial differential equations (i.e. mass, momentum, energy and concentration equations) are transformed into a system of integral equations by applying the Galerkin weighted residual method. The integration involved in each of these terms is performed using Gauss’ quadrature method. The resulting non-linear algebraic equations are modified by the imposition of boundary conditions. Finally, Newton’s method is used to modify non-linear equations into the linear algebraic equations.

Both the buoyancy ratio and thermal Rayleigh number play an important role in controlling the mode of heat transfer and mass transfer.

Calculations are performed for various thermal Rayleigh numbers, buoyancy ratios and time periods. For each specific condition, streamline contours, isotherm contours and iso-concentration contours are obtained, and the variation in the overall Nusselt and Sherwood numbers is identified for different parameter combinations.

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 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.

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.

This study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.

The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.

A strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

The purpose of this paper is to study the boundary layer flow and heat transfer of a power-law non-Newtonian nanofluid over a non-linearly stretching sheet.

The governing equations describing the problem are transformed into a nonlinear ordinary differential equations by suitable similarity transformations. The resulting equations for this investigation are solved numerically by using the variational finite element method.

It was found that the local Nusselt number increases by increasing the Prandtl number, stretching sheet parameter and decreases by increasing the power-law index, thermophoresis parameter and Lewis number. Increases in the stretching sheet parameter, Prandtl number and thermophoresis parameter decrease the local Sherwood number values. The effects of Brownian motion and Lewis number lead to increases in the local Sherwood number values.

The work is relatively original as very little work has been reported on non-Newtonian nanofluids.