Effects of Dufour and thermal diffusion on unsteady MHD free convection and mass transfer flow through an infinite vertical permeable sheet

In this paper, the effects of Dufour and thermal diffusion and on unsteady MHD (magnetohydrodynamic) free convection and mass transfer flow through an infinite vertical permeable sheet have been investigated numerically. The non-dimensional governing equations are solved numerically by using the superposition method with the help of “Tec plot” software. The numerical solution regarding the non-dimensional velocity, temperature, and concentration variables against the non-dimensional coordinate variable has been carried out for various values of pertinent numbers and parameters like the suction parameter $$\left( {v_{0} } \right)$$ v 0 , Prandtl number $$\left( {P_{r} } \right)$$ P r , magnetic parameter $$\left( M \right)$$ M , Dufour number $$\left( {D_{f} } \right)$$ D f , Soret number $$\left( {S_{0} } \right)$$ S 0 , Schmidt number $$\left( {S_{c} } \right)$$ S c , and for constant values of modified local Grashof number $$\left( {G_{{\text{m}}} } \right)$$ G m and local Grashof number $$\left( {G_{r} } \right)$$ G r .The velocity field decreases for increasing the suction parameter which is focusing on the common fact that the usual suction parameter stabilizing the effect on the boundary layer growth. The thermal boundary layer thickness becomes thinner for rising values of the Dufour and Soret numbers. The skin friction enhances for uplifting values of Soret number and Dufour number but reduces for moving suction parameter, Magnetic force number, Prandtl number, and Schmidt number. The heat transfer rate increases for increasing the suction parameter, Dufour number, Prandtl number, and Soret number. The mass transfer rate increases for enhancing the values of suction parameter, Magnetic force number, Soret number, and Prandtl number but decreases for Dufour number and Schmidt number.

Micropolar Fluid Flow Along with an Inclined Riga Plate Through a Porous Medium

This study presents the one-dimensional unsteady micropolar fluid flow set in a porous medium along with an inclined infinite Riga plate. This Riga plate is created an electric and magnetic field, where a transverse Lorentz force is generated that contributes a flow along with the plate. The explicit finite difference method is used to find the solution of the non-dimensional form of the governing equations and estimated results are analyzed in terms of Microrotation parameter, Suction parameter, thermal Grashof number, mass Grashof number, Permeability parameter, Hartmann number, Dufour number, Soret number, Schmidt number. Also, the effects of the pertinent parameters on the local and average shear stress, Nusselt number, and Sherwood number are reported numerically as well as graphically.

Physical impact of thermo-diffusion and diffusion-thermo on Marangoni convective flow of hybrid nanofluid (MnZiFe2O4–NiZnFe2O4–H2O) with nonlinear heat source/sink and radiative heat flux

The objective of this study is to illustrate the influence of Marangoni convection, nonlinear heat sink/source, thermal radiation, viscous dissipation, activation energy, Soret and Dufour effects on magnetohydrodynamics flow of nanofluid generated by rotating disk. Further, the entropy generation equation is derived as a function of velocity, concentration, and thermal gradients. The governing equations of the model along with associated boundary constraints are reduced to ordinary differential equations by adopting suitable similarity transformation. Later, these equations are tackled numerically by means of shooting technique. The whole examination is performed by using two distinctive nanoparticles of ferrites in particular, manganese zinc ferrite (MnZnFe2O4) and nickel zinc ferrite (NiZnFe2O4) in a carrier liquid [Formula: see text]. The physical characteristics of velocity, thermal, concentration entropy generation, skin friction, and Nusselt number against numerous pertinent parameters are discussed in detail and deliberated graphically. Result reveals that thermal gradient shows substantial enhancement for advanced values of heat sink/source parameter. The entropy production increases with an augmentation in the Brinkman number and Marangoni ratio values. The escalation in Marangoni ratio and Dufour number improves the rate of heat transference.

Onset of Linear and Nonlinear Thermosolutal Convection with Soret and Dufour Effects in a Porous Collector under a Uniform Magnetic Field

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.

Double-diffusive convection of a nanofluid in a porous cavity containing rotating hexagon and circular cylinders: ISPH simulations

Purpose The purpose of this study is to apply an incompressible smoothed particle hydrodynamics (ISPH) method to simulate the Magnetohydrodynamic (MHD) free convection flow of a nanofluid in a porous cavity containing rotating hexagonal and two circular cylinders under the impacts of Soret and Dufour numbers. Design/methodology/approach The inner shapes are rotating around a cavity center by a uniform circular motion at angular rate ω. An inner hexagonal shape has higher temperature Th and concentration Ch than the inner two circular cylinders in which the temperature is Tc and concentration is Cc. The performed numerical simulations are presented in terms of the streamlines, isotherms and isoconcentration as well as the profiles of average Nusselt and Sherwood numbers. Findings The results indicated that the uniform motions of inner shapes are changing the characteristics of the fluid flow, temperature and concentration inside a cavity. An augmentation on a Hartman parameter slows down the flow speed and an inclination angle of a magnetic field raises the flow speed. A rise in the Soret number accompanied by a reduction in the Dufour number lead to a growth in the concentration distribution in a cavity. Originality/value ISPH method is used to simulate the double-diffusive convection of novel rotating shapes in a porous cavity. The inner novel shapes are rotating hexagonal and two circular cylinders.

Soret and Dufour Effects on MHD Nonlinear Convective Flow of Tangent Hyperbolic Nanofluid Over a Bidirectional Stretching Sheet with Multiple Slips

The purpose of the present analysis is to investigate the Soret and Dufour effects on steady and incompressible MHD nonlinear convective flow of tangent hyperbolic nanofluid over a permeable stretching surface with multiple slip conditions at the wall. Also, nonlinearly varying thermal radiation, heat generation and chemical reaction along with a vanishing nanoparticle mass flux condition at the surface are taken into account. Further, Rosseland’s approximation for an optically thick and grey medium is used to approximate heat flux due to radiation. Suitable similarity transformations are employed to transform governing PDEs into a system of ODEs. The resulting nonlinear equations are then solved numerically using the shooting technique based on the Runge-Kutta Cash-Karp method. The upshots of various physical parameters on velocity, temperature and concentration distributions are illustrated and displayed through figures. The variations in coefficients of local skin friction, Nusselt and Sherwood numbers are explained and presented in tabular form. The obtained results are validated with the previously reported results for a particular case of the present fluid flow problem, and an outstanding correlation is noticed from the comparison. Graphical results reveal that the nonlinear convection parameters for both temperature and concentration accelerate the primary flow. However, the Dufour number diminishes the fluid temperature near the wall, and the Soret number uplifts the concentration profile within the boundary layer.

Exploration of Aluminum and Titanium Alloys in the Stream-Wise and Secondary Flow Directions Comprising the Significant Impacts of Magnetohydrodynamic and Hybrid Nanofluid

This exploration examines the nonlinear effect of radiation on magnet flow consisting of hybrid alloy nanoparticles in the way of stream-wise and cross flow. Many experimental, as well as theoretical explorations, demonstrated that the thermal conductivity of the regular liquid increases by up to 15 to 40% when nanomaterials are mixed with the regular liquid. This change of the thermal conductivity of the nanoliquid depends on the various characteristics of the mixed nanomaterials like the size of the nanoparticles, the agglomeration of the particles, the volume fraction, etc. Researchers have used numerous nanoparticles. However, we selected water-based aluminum alloy (AA7075) and titanium alloy (Ti6Al4V) hybrid nanomaterials. This condition was mathematically modeled by capturing the Soret and Dufour impacts. The similarity method was exercised to change the partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). Such nonlinear ODEs were worked out numerically via the bvp4c solver. The influences of varying the parameters on the concentration, temperature, and velocity area and the accompanying engineering quantities such as friction factor, mass, and heat transport rate were obtained and discussed using graphs. The velocity declines owing to nanoparticle volume fraction in the stream-wise and cross flow directions in the first result and augment in the second result, while the temperature and concentration upsurge in the first and second results. In addition, the Nusselt number augments due to the Soret number and declines due to the Dufour number in both results, whereas the Sherwood number uplifts due to the Dufour number and shrinks due to the Soret number in both results.

Dufour, Soret and radiation effects with magnetic dipole on Powell-Eyring fluid flow over a stretching sheet

Purpose This paper aims to investigate the effect of Powell–Eyring fluid induced by a stretched sheet. Heat and mass transfer under the influence of magnetic dipole over a stretching sheet are taken into account. Design/methodology/approach Nonlinear coupled governing equations are solved using the optimal homotopy asymptotic technique, and a computer software package BVPh 2.0 is used for numerical computations. Findings Impact of significant quantities is graphically examined. It is seen that the heat transfer deceases for higher values of viscous dissipation parameter, radiation parameter, Dufour number, whereas it increases for bigger values of Prandtl number. The numerical results have been validated through comparison with existing literature as a special case of proposed model and perceived that the Soret number has reining role to increase the rate of heat transfer. Originality/value To the best of the authors’ knowledge, this study is reported for the first time.

MHD Free Convection-Radiation Interaction in a Porous Medium - Part II: Soret/Dufour Effects

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium by taking into account of the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. Increasing the Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing the Soret number and simultaneously reducing the Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study of the previously published and present results in a limiting sense is made and an excellent agreement is found between the results.

Effects of Some Flow Parameters on Unsteady MHD Fluid Flow Past a Moving Vertical Plate Embedded in Porous Medium in the Presence of Hall Current and Rotating System

This paper is on the numerical study of the effects of some flow parameters like Hall current, rotation, thermal diffusion (Soret) and diffusion thermo (Dufour) on unsteady magnetohydrodynamic natural convective heat and mass transfer of a viscous, rotating, electrically conducting and incompressible fluid flow past an impulsively moving vertical plate embedded in porous medium. The fundamental governing dimensionless coupled boundary layer partial differential equations are solved by the method of lines (MOL). Computations are then performed to determine the effects of the governing flow parameters. The results show that an increase in Soret number, Dufour number and Hall current parameter, causes an increase in the primary and secondary velocities of the fluid flow. As rotating parameter increases, the primary velocity of the flow decreases. Similarly, as Dufour and Soret numbers increase, the temperature and concentration profiles of the fluid flow increase. The effects of the flow parameters on primary and secondary velocity, temperature and concentration fields for externally cooling of the plate are shown graphically.