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.

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.

Temperature and Concentration Effects on Oscillatory Flow for Variable Viscosity Carreau Fluid through an Inclined Porous Channel

The aim of this paper is to study the combined effects of the concentration and the thermo-diffusion on the unsteady oscillation flow of an incompressible Carreau fluid through an inclined porous channel. The temperature is assumed to affect exponentially the fluid's viscosity. We studied fluid flow in an inclined channel under the non-slip condition at the wall. We used the perturbation series method to solve the nonlinear partial differential equations. Numerical results were obtained for velocity distribution, and through the graphs, it was found that the velocity of fluid has a direct relation with Soret number, Peclet number, and Grashof number, while it has a reverse variation with chemical reaction, Schmidt number, frequency of oscillation, and Froude number.

Thermo-Diffusive Flow of Chemically Reacting Fluid in a Saturated Porous Medium for Radiative Heat Flux

A theoretical investigation has been made for a radiating and chemically reacting viscous-fluid of a conducting gas over a vertical porous surface immerse in a saturated porous medium for the impact of magnetic drag-force, buoyancy forces and thermal-diffusion (Soret) order under oscillatory suction and heat absorption. The analytical solutions have been derived for the physical variables related to the governing equations under the appropriate boundary conditions. It is found that the velocity profiles increase with the increasing values of Soret number (S0) and higher Soret number (S0 = 5) shows the large temperature difference. It is noticed that increasing radiation parameter (R) elevated the velocity profiles near the plate. In the effects of Soret number (S0) the velocity profiles are an increasing function for both the cases of M = 0 and M = 10. The validity and accuracy of the flow model is presented and found suitable to proceed the work. In this study, the findings would be useful in many practical areas such as diffusion operations, which involved molecular diffusion of species with molar concentration.

MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions

This work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

Two-Dimensional Flow Through the Uniformly Porous Horizontal Pipe with Thermal Radiation and Cross-Diffusion Effects

This paper is dedicated to the mathematical analysis of an axisymmetric, steady Newtonian fluid flow through a horizontal pipe within the occurrence of radiation, Dufour, and Soret effects. The flow is exposed to associate outwardly functional constant suction above the pipe along Z-direction. The homotopy analysis methodology (HAM) is utilized to get semi-analytical solutions for the coupled differential equations. The results of diverse rising constraints on velocities, thermal and solutal are discussed and pictured. The flow is studied through streamlines, isotherms and pressure contours area unit likewise shown as pictured. It is identified that the temperature can increase with an increase in Dufour parameter but decelerates with an improvement in the radiation parameter. For the given increase within the Soret number, the concentration decelerates.

Numerical Investigation of Heat and Mass Transport in the Flow over a Magnetized Wedge by Incorporating the Effects of Cross-Diffusion Gradients: Applications in Multiple Engineering Systems

The flow over a wedge is significant and frequently occurs in civil engineering. It is significant to investigate the heat and mass transport characteristics in the wedge flow. Therefore, the analysis is presented to examine the effects of preeminent parameters by incorporating the cross-diffusion gradients in the energy and mass constitutive relations. From the analysis, it is perceived that the temperature drops against a higher Prandtl number. Due to concentration gradients in the energy equation, the temperature rises slowly. Moreover, it is examined that the mass transfer significantly reduces due to Schmidt effects and more mass transfer is pointed against the Soret number. The shear stresses increase due to stronger magnetic field effects. The local thermal performance of the fluid enhances against more dissipative fluid, and DuFour effects reduced it. Furthermore, the mass transport rate drops due to higher Soret effects and increases against multiple Schmidt number values.

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.