IMPACT OF THE NON-NEWTONIAN OSWALD–DE WAELE FLUID ON HEAT AND MASS TRANSFER WITH SORET AND DUFOUR IN ANISOTROPIC POROUS MEDIA

In this paper, thermo-diffusion (Soret effect) and diffusion-thermo (Dufour effect) effects on double-diffusive natural convection induced in a horizontal Brinkman porous layer with a stress-free upper boundary are investigated. The cavity is filled with a binary fluid and subjected to uniform fluxes of heat and mass on its long sides. An analytical solution based on the parallel flow approximation is developed for the problem considered in order to allow prompt determination of the thresholds of stationary and finite amplitude solutions and also heat and mass transfer characteristics. The analytical solution is validated numerically by using a finite difference method. The combined effects of the Soret and Dufour parameters, the thermal Rayleigh number, the buoyancy ratio, and the Darcy number on the flow intensity and heat and mass transfer are illustrated graphically, and some particular behaviors observed are discussed. The analytical solution proves the existence of different regions in the buoyancy ratio-Dufour parameter plane, corresponding to different parallel flow behaviors. The number, the location, and the extent of these regions, which are impossible to predict numerically, depend strongly on Soret and Dufour parameters. The effect of thermo-diffusion and diffusion-thermo on flow intensity and heat and mass transfer is found to be important.

Simulation of double diffusive natural convection and entropy generation of power-law fluids in an inclined porous cavity with Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

This work investigates unsteady free convection heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects. The bounding walls and the specie are considered to have ramped temperature and ramped concentration respectively. Perturbation method is first used to decouple the governing equations that arise from the model due to the presence of combined Soret and Dufour effects. Laplace transform technique is then used to obtain an analytical solutions for the temperature, concentration and velocity. In order to cross check the accuracy of the proposed analytical method, numerical solutions are obtained using PDEPE in MATLAB. The influences of the two effects as well as the ramped boundary conditions on the fluid flow are graphically presented and discussed. The results show that these two effects and the imposed boundary conditions affect the fluid temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and wall Skin friction. Moreover, it is found that the solutions obtained by the authors Jha and Gambo correspond to the results of the present work when Soret effect is absent.

A study on heat and mass transfer behaviour on porous medium embedded in a square annulus is conducted. The inner surface wall is considered to have a cool temperature T c while the outer surface is exposed to a hot temperature T h . Finite element method (FEM) is used to solve the governing partial differential equations. The results present the influences of the Dufour and Soret effects on the heat and mass transfer of a square annulus. The effects of various physical parameters on the temperature and concentration profiles together with the local Nusselt and Sherwood numbers are presented graphically. It is found that when Dufour parameter is increased, Nusselt number increases. Dufour effect has more influences on velocity profile, while it has no significant effect on the concentration and can be deemed negligible. It is observed that the local Nusselt number is highest at the bottom wall for low values of Dufour parameter; however, the top wall Nusselt number is highest for higher values of Dufour parameter. Soret effect tends to make more significant contribution to the concentration profile than Dufour effect.

This research presents an analytical solution of unsteady free convection and mass transfer flow past a vertical plate with Soret and Dufour effects. The dimensionless system of governing equations is solved analytically with appropriate initial and boundary conditions. The accuracy of the analytical method is ensured by obtaining numerical solutions with PDEPE of MATLAB and comparing with the analytical results. Perturbation method is first adopted to decouple the system of equations that arise as a result of coupling Soret and Dufour effects. Laplace Transform Technique is then applied to solve the system. The expressions for velocity, temperature, concentration, Skin-friction, Nuselt and Sherwood numbers are obtained. In the course of discussions, the effects of main parameters are described. It is observed that increase in Soret number reduces the temperature while increasing the velocity and concentration. Moreover, Soret effect is more significant on the concentration than on the temperature. Similarly, the Dufour parameter causes the temperature and velocity to increase while the concentration decreases and the effect is more significant on the temperature than on the concentration. However, there is no significant difference on the effects of Dufour and Soret parameters on the velocity. The velocity, temperature and concentration profiles are presented graphically for $$Pr = 0.71$$ and $$Sc = 0.78$$ as well as for arbitrary values of other parameters.

Double diffusive flow in a cavity has attracted lots of attention due to its importance in many engineering fields such as ocean circulation, crystal growth, pollution transportation in air, metal manufacturing process and so on. When heat and mass transfer occur simultaneously in the double diffusive flow, the fluid flow is not only driven by the temperature gradient but also by the concentration gradient as well. In some cases, the Dufour and Soret effects will play a significant role in the double diffusive flow process. The energy flux created by the concentration gradient is called Dufour effect and the temperature gradient can cause the mass flux which is Soret effect. When taking the Soret and Dufour effects into account, the temperature and concentration equations become coupled with each other. However, the coupling diffusivities matrix can be diagonalized. The coupled system can then be transformed to two uncoupled diffusion-advection equations of two independent species. The temperature and concentration can be obtained by the inverse transformation of these two independent species. As a numerical method developed in the past two decades, lattice Boltzmann method (LBM) is powerful in simulating complex heat transfer and fluid mechanics problems. In the current study, a lattice Boltzmann model was developed and implemented for the double-diffusive convection with Soret and Dufour effects. Three distribution functions were used to compute the fluid velocity, specie 1, and specie 2, respectively. Specifically, a rectangular enclosure with horizontal temperature and concentration gradients was investigated. On the other hand, the graphics processing units (GPU) computing becomes popular since the advent of the NVIDIA’s CUDA platform, which includes both hardware components and software programming environment. The developed LBM code was adapted on the CUDA platform to accelerate the computation for parametric studies. The GPU is responsible for the parallel tasks while CPU tackles the sequential steps in the computation. To verify the improvement on computation ability by using GPU, the ratio of the computational time between CPU code and CUDA code is presented by simulating the classical natural convection process in a cavity. The computational speed can be accelerated by more than 20 times when large number of nodes is used. The fluid flow, temperature field and concentration field are presented for different Rayleigh numbers, buoyancy ratios, Prandtl numbers, Lewis numbers, aspect ratios, as well as Soret and Dufour coefficients. In addition, the results of Nusselt and Sherwood numbers are shown for different parametric conditions. As a result, lattice Boltzmann method was demonstrated as a good option to study the complex double-diffusive convection with Soret and Dufour effects in a vertical cavity.

Numerical study of double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on GPU

Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)

Transient natural convention heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects: An analytical approach

Newtonian fluid is ideal for lubrication purposes because the viscosity of this fluid remains as a function of the shear. Besides, the heat and mass transfer are an important study area in fluid dynamics due to its vast applications in industrial processes. The heat-mass transfer can be defined as the Soret and Dufour effect, which implemented in many industrial applications such as in chemical engineering and geosciences field. In addition, the fluid flow over an extending/compressing sheet has significant industrial applications such as the cooling of continuous strips, glass fibre production, the extrusion of plastic sheets from a die, etc. As a response, this study aims to investigate the impacts of Soret and Dufour parameters on the Newtonian fluid flow over an inclined stretching/shrinking sheet. The methodology of this mathematical model are stated as follow: 1) the transformation of partial differential equations (PDEs) to the ordinary differential equations (ODEs), and 2) The ODEs are solved using bvp4c solver in MATLAB software. The bvp4c solver is a MATLAB program directory that solves general form and multi-point boundary layer problems. The main sections of bvp4c are: 1) The solution of the ODEs, 2) The related boundary conditions that can produce the expected results, and 3) An initial guess to run the bvp4c solver. As a result, the numerical and graphical results show that the Soret effect increases the concentration profile whereas decreases the temperature profile. The vice versa occurrence is true for Dufour effect. The convective mass transfer caused by a temperature gradient is known as thermal-diffusion (Soret) effect. The convective heat transfer produced by concentration differences is known as diffusion-thermo (Dufour) effect. However, since the process of heat and mass transfers are related to each other, the Soret and Dufour effects are able to influence both of this process simultaneously. In conclusion, the convective heat transfer is enhanced by increasing Soret and Dufour number while the convective mass transfer is declined by increasing the two numbers.

This article investigates numerically the effects of Hall current and rotation effects on radiating and chemically reacting unsteady MHD natural convection flow past an accelerated infinite vertical permeable plate in the presence of Soret and Dufour effects. The dimensionless coupled non-linear governing partial differential equations of the problem are solved numerically by employing finite element method. The influence of various physical parameters influencing the flow on the primary velocity, secondary velocity, temperature and the species concentration are displayed graphically whilst the numerical results of the primary skin friction, secondary skin-friction, Nusselt number and the Sherwood number are presented in tabular form. Results reveals that magnetic parameter, radiation parameter and chemical reaction rate tends to depreciate both primary and secondary velocity components whilst Hall, Soret and Dufour effects have reverse trend. Rotation parameter tends to retard fluid flow in the primary flow direction and accelerate fluid flow in the secondary flow direction. Thermal boundary layer thickness decreases with increasing radiation parameter whilst the reverse trend is noticed with increasing Dufour effect. Thermal diffusion effect causes to improve concentration boundary layer thickness whilst chemical reaction rate has reverse impact. These parameters have similar effect on the primary and secondary skin-frictions whilst opposite effect was noticed on the Nusselt and Sherwood numbers. This model problem finds an important in engineering and industrial application such as MHD generators, food processing, heat exchangers devices and internal rotation rate of the sun. HIGHLIGHTS The problem investigate the effects of Hall current and rotation effects on radiating and reacting on unsteady magnetohydrodynamics (MHD) natural convection heat and mass transfer flow over an infinite vertical porous plate embedded in a uniform porous medium taking Soret and Dufour effects into account The resulting partial differential equations governing the fluid flow are solved numerically using the finite element method. In order to determine the effects of various pertinent parameters and to investigate the important flow features, the numerical calculations for fluid velocity, temperature and species concentration are computed and shown graphically whereas skin friction, Nusselt number and Sherwood number at the plate are evaluated and depicted in tabular form The model problem finds an important in engineering and industrial application GRAPHICAL ABSTRACT

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate.

Purpose – 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. Design/methodology/approach – 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. Findings – 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. Originality/value – 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.

A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.