MHD flow in a rotating vertical cone through a porous medium

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.

The triple-diffusive convection with the involvement of non-Newtonian fluid has many applications in the science and technology field, industrial processes, and also in research works. Therefore, the mathematical model of the triple-diffusive convection of Casson fluid by the mathematical approach is investigated. In addition, a mathematical model for the triple-diffusive convection of Casson fluid flow beyond a nonlinear compressing sheet has been formulated and solved by numerical approach, where this is the main objective of this study. This model is subjected to mass transfer and heat transfer, known as Soret and Dufour effect (Soret-Dufour). The Soret effect is occurred when the temperature gradient is produced, whereas the differences in mass cause the Dufour effect. The model is formed by the continuity equation, momentum equation, energy equation, and concentration equations of component 1 and 2, together with the boundary conditions. They have been reduced to ordinary differential equations, and subsequently, they have been implemented in bvp4c programme provided by MATLAB software to get the numerical solutions. The solutions obtained were profiles of velocity, temperature and concentration of both components. Next, the effect of Casson parameter, Soret parameter, and Dufour parameter have been investigated by changing their values of inside the coding in MATLAB and observing the behaviour of the related profiles due to these parameters. The main results from this study were: The velocity of the Casson fluid reduced as the Casson parameter enhanced, increment in both Soret and Dufour parameters caused the temperature to decrease, and the fluid concentration was higher for the increasing Soret number.

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 II: entropy generation)

An analytical and numerical study on the influence of flow indices of a non-Newtonian fluid in the presence of Soret and Dufour effects during heat and mass transfer, in the absence of the thermal Rayleigh number, is conducted in a saturated anisotropic porous layer. The Darcy model, the Boussinesq approximation, and the Oswald-de Waele model were used. Heat and mass fluxes are constant on the horizontal walls, while the vertical walls are assumed to be adiabatic and impermeable. The analytical investigation is based on the parallel flow approximation in the horizontal cavity, while the numerical method involves solving the nonlinear equation using the Newton-Raphson method in MATLAB. We observed that the numerical solution admits real solutions for n < 1 and n > 1 when the thermal Rayleigh number is zero. A parametric study is conducted to show the effect of a non-Newtonian fluid with Soret and Dufour parameters, in the absence of thermal Rayleigh number, on the stream function at the center of gravity, speed, temperature, concentration, as well as the Nusselt and Sherwood numbers. The results highlight the predominant role of Soret and Dufour effects in heat and mass transfer, even in the absence of the thermal Rayleigh number, and emphasize the importance of these mechanisms for the optimal design of systems involving non-Newtonian fluids in anisotropic porous media.

Analysis of boundary layer MHD Darcy-Forchheimer radiative nanofluid flow with soret and dufour effects by means of marangoni convection

Double-diffusive laminar natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder (Part II: Entropy generation)

The primary intent of this paper is to examine the influence of radiation, Soret, and Dufour on the laminar flow of a rotating fluid through a permeable plate undergoing a chemical reaction. The Soret effect, for example, has been employed to differentiate isotopes and to combine gases of different molecular weights. Many real-world applications, including geosciences and chemical engineering, comprise the Soret and Dufour effects. Using similarity variables, the governing equations and allied boundary conditions (BCs) are simplified to a dimensionless form and then solved using the finite element method (FEM). In order to get the numerical approximations of velocity, temperature, and concentration, dimensionless parameters of the flow were utilized, and the consequences were envisioned visually. The most significant results of this research are that raising the Soret and Dufour parameters causes an upsurge in the velocity profile and enhancing the radiation factor causes an upsurge in the temperature distribution. Enhancing the values of permeability causes a reduction in skin friction. Enhancing the accuracy of heat absorption factor estimations leads to an increase in the values of the Nusselt number. A comparison case study has been made among the outcomes of well-existing repository literature with the current solutions and detected a great correlation.

Magnetoconvection in an enclosure of water near its density maximum with Soret and Dufour effects

This work is devoted to study the combined effects of thermal radiation and thermophoresis on heat and mass transfer by mixed convection over a vertical rotating cone in a fluid saturated porous medium. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method and Newton–Raphson method. The numerical results are compared and found to be approximately better than previously published results, Hering and Grosh (ASME J Heat Transf 85:29–34, 1963) and Himasekhar et al. (Int Commun Heat Mass Transf 16:99–106, 1989) as special cases of the present work. The local tangential and azimuthal skin friction coefficients, dimensionless wall thermophoretic velocity, local Nusselt and Sherwood numbers are presented graphically for different values of Darcy number, thermophoretic coefficient, thermal radiation parameter, and discussed to depict interesting features of the solutions.

Purpose The purpose of this study is to explore the impact of Joule heating, slip conditions, Dufour and Soret effects on three-dimensional magneto-convection of nanoliquid over a rotating surface in the existence of thermal radiation, viscous dissipation and internal heat generation/absorption. Design/methodology/approach The considered physical system is modelled by a set of partial differential equations (PDEs) with conditions at surface. Then, the nonlinear PDEs are altered into a system of ordinary differential equations and they are solved numerically by the Runge−Kutta−Fehlberg method. Plotting the collected velocity, temperature and solute concentration characteristics allows one to see how relevant parameters affect the results. Calculations are made for skin friction and the rate of heat and mass transfer. Findings The outcomes are portrayed in the form of tables and graphs with a wide range of parameter involved in the study. It is observed that the local thermal energy transfer rate enriches on increasing the value of both thermal and solute slips. The solutal slip parameter suppresses the solute transport rate and thermal slip supports the solute transport. Practical implications Combining the Dufour and Soret effects is used in oil reservoirs, binary alloy solidification and isotope separation in mixtures of gases. Heat exchangers, nuclear reactors and thermal engineering can all benefit from the usage of nanofluid with Joule heating. Social implications This study is mainly useful for thermal sciences and chemical engineering. Originality/value The investigation of the effects of slip circumstances and Joule heating on magnetohydrodynamic rotating nanoliquid stream with thermal radiation and cross-diffusion makes this work unique. The discoveries produced are valuable and distinctive, and they have applications in many areas of thermal science and technology.

This research investigates the influence of thermodiffusion (Soret effect) and diffusion-thermo (Dufour effect) on transient Magneto-Hydro-Dynamic (MHD) free convective flow adjacent to a heated, inclined plate within a porous medium. The analysis incorporates thermal radiation as a key heat transfer mechanism, accounting for time-dependent variations in both velocity and temperature distributions. The porous structure introduces hydraulic resistance, altering fluid motion and thermal transport properties, while the plate's inclination modifies buoyancy-driven convection patterns. The applied magnetic field further complicates the dynamics through Lorentz force interactions. By addressing the coupled Soret and Dufour effects— frequently overlooked in basic models—the study enhances understanding of multispecies heat and mass transfer. The governing nonlinear partial differential equations are solved numerically via the finite difference method.Graphical results demonstrate how critical parameters affect velocity, temperature, and concentration profiles. This computational framework elucidates the complex interdependencies among electromagnetic, thermal, and hydrodynamic phenomena in porous media flows. Major Findings: Soret and Dufour effects significantly influence MHD free convection near an inclined plate in a porous medium. Radiation, magnetic field, and inclination modify flow and heat transfer. Numerical results show complex velocity, temperature, and concentration profiles.

Soret and Dufour effects on double-diffusive convection in a salinity gradient solar pond

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subject to variable viscosity are numerically analyzed, by taking into account the diffusion‐thermo (Dufour) and thermal‐diffusion (Soret) effects. The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge‐Kutta‐Gill method along with shooting technique. The parameters of the problem are variable viscosity, buoyancy ratio, Lewis number, Prandtl number, Dufour effect, Soret effect, and Schmidt number. The velocity, temperature, and concentration distributions are presented graphically. The Nusselt number and Sherwood number are also derived and discussed numerically.

PurposeThe present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects.Design/methodology/approachA numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type.FindingsThe influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids.Research limitations/implicationsConsider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable.Practical implicationsThe flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs.Social implicationsIn the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks.Originality/valueThe motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

The Soret and Dufour Effects in Non-thermal Equilibrium Packed Beds with Forced Convection and Endothermic Reactions