Soret Number Research Articles

Modeling and measurements of Soret and Dufour effects on the water vapor transfer in membrane-based desiccant solution dehumidification dual-chamber system

In order to study the mutual influences of temperature gradient and concentration gradient in the coupled heat and mass transfer process of membrane-based desiccant solution dehumidification, an air-solution dual-chamber system was built. The reduced heat of transfer without concentration gradient is defined, qm2∗=-rmmrmq, to derive thermal diffusivity DSr, and then derive the corresponding Onsager coefficients rqm2(rmq2) and rmm2. The expression of the total entropy production with respect to temperature gradient and chemical potential varying with concentration is given as σ=-λ2Jm2∙T2∙dTdx3+[λJm12∙(dlnT)2+∂μ/∂cT∙Dm]∙Jm1∙Jm1+Jm2. There should be a certain temperature gradient to enable the thermal diffusion process to occur by qualitative analysis. The hydrophilic-hydrophobic alumina porous ceramic membrane grafted with fluoroalkylsilane (FAS) was prepared. The improved time lag method was applied in air-solution compartments to obtain the water vapor diffusivity in large temperature difference. The thermal conductivities of the membrane under different temperature gradients were measured. The Soret number and the Dufour number are calculated by the discretization method. A transient two-dimensional mathematical model was established to describe the Soret term affecting the mass transfer process and the Dufour term affecting the heat transfer process. In model validation section, the deviation in the latter part is explained from the perspective of the intrinsic resistance of the membrane material influenced by air inlet temperature. The phenomenon of the occurrence of additional mass flux caused by the temperature gradient in the coupled heat and mass transfer process was revealed by the simulation results of water vapor concentration and temperature distribution.

Numerical study on thermal enhancement in magnetohydrodynamic micropolar liquid subjected to motile gyrotactic microorganisms movement and Soret and dufour effects

Motile gyrotactic organism activity in micropolar fluid subjected to simultaneous heat and mass transfer in the presence of thermal diffusion and diffusion thermo effects is modeled. The base fluid is taken as kerosene oil. The immersion of nano-sized particles of C u − T i O 2 kerosene oil makes its rheological characteristics of micropolar fluid because nano-sized particles serve as micro-structures. In this case couple stress, vortex and spin gradient viscosities become significant and simultaneously linear and angular momenta become equally remarkable. So, micropolar theory is the best to model the immersion of nano-structures in the fluid. Similarity variables are used to transform the problems into their dimensionless forms. The mathematical models are solved numerically by applying the finite element method (FEM). The results are validated and numerical experiments are performed to analyze the key parameters of the unknown field variables. In order to analyze the impact of physical parameters on field variables, numerous simulations are performed. The micro-rotation of microparticles and nanoparticles due to fluid deformation motivates fluids particles to rotate faster. Therefore, linear motion is observed to be increased for higher values of vortex viscosity. The curvature parameter has significantly impacted the linear motion of the fluid particles. The impact of the curvature parameter on the movement of nanofluid is lesser than the impact of the curvature parameter on the motion of hybrid nanoparticles. Concentration gradient supports the diffusion of heat in the fluid regime and numerical experiments with variation of Dufour (that measures the effects of concentration gradient on heat diffusion) have shown that concentration gradient is more effective in the case of hybrid nanofluid relative to the mono nanofluid. The angular motion of fluid particles increases when vortex viscosity is increased. Numerical simulations have predicted that the angular motion of particles of hybrid nanofluid has a lesser angular speed than that of the angular motion of particles of mono nanofluid. The Soret number determines the impact of temperature gradient on the diffusion of solute in the fluid. Simulations for various values of Soret number have predicted that the impact of temperature gradient on the diffusion of solute in hybrid nanofluid is stronger than the impact of temperature gradient on the diffusion of solute in mono nanofluid.

Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect

In this paper, the thermal instability of rotating convection in a bidispersive porous layer is analyzed. The linear stability analysis is employed to examine the stability of the system. The neutral curves for different values of the physical parameters are shown graphically. The critical Rayleigh number is evaluated for appropriate values of the other governing parameters. Among the obtained results, we find: the Taylor number has a stabilizing effect on the onset of convection; the Soret number does not show any effect on oscillatory convection, as the oscillatory Rayleigh number is independent of the Soret number; there exists a threshold, Rc* ∈ (0.45, 0.46), for the solute Rayleigh number, such that, if RC > Rc*, then the convection arises via an oscillatory mode; and the oscillatory convection sets in and as soon as the value of the Soret number reaches a critical value, (∈(0.6, 0.7)), and the convection arises via stationary convection.

FEM to study the radiation, Soret, Dufour numbers effect on heat and mass transfer of magneto-Casson fluid over a vertical permeable plate in the presence of viscous dissipation

In this paper, the impact of Dufour number along with viscous dissipation on the non-steady stream of heat together with the mass transfer of Casson fluid, on vertical permeable laminate is studied with chemical reaction. Dimensionless governing equations of temperature, velocity as well as concentration have been resolved by the finite element method (FEM). The tables of skin friction, Sherwood along with the Nusselt number are explained numerically in the tables. Effects of various physical quantities such as Dufour, Soret numbers, Eckert number, radiation, chemical reaction parameters, and so on are discussed in detail through figures and tables. A comparison with previously published work reveals extremely excellent agreement.

Thermal Radiation Effect on Unsteady Magneto-Convective Heat-Mass Transport Passing in a Vertical Permeable Sheet with Chemical Reaction.

The unsteady magneto-convective heat-mass transport passing in a vertical porous sheet with the thermal radiation and the chemical reaction effects has been examined numerically. The governing PDEs have been transferred into ODEs by applying the local similarity transformation. The nondimensional governing equations including the boundary conditions are solved by applying the superposition method with the help of the “MATLAB ODE45” software numerically. The influence of emerging nondimensional numbers/parameters, for example, the Prandtl number (Pr), thermal radiation parameter (R), Schmidt number (Sc), and chemical reaction parameter (Kr), on fluid velocity, concentration, and thermal radiation within the boundary layer has been examined. The outcomes indicate that enhancing values of the Soret and Dufour numbers reduce the thermal boundary layer thickness. Uplifting values of the thermal radiation (0.5-3.5) enhance the local skin friction coefficient and mass transfer rate by approximately 15% and 78% but decrease the heat transfer rate by 47%. The local skin friction coefficient enhances about 21%, and the mass transfer rate reduces about 64% due to an increase in the chemical reaction parameter (0.5-2.0). Finally, we compared our numerical results with previously published literature and observed them to have a good agreement.

Unsteady thermally radiative Prandtl fluid flow past a magnetized inclined porous stretching device with double-diffusion, viscous dissipation, and Joule heating

The extensive applications and complex nature of non-Newtonian fluids inspire researchers to explore them so it serves more precisely humankind. In this scenario, the Prandtl fluid over the inclined porous surface has been explored and formulated the mathematical model considering the magnetic, thermal radiation, and double diffusion effect. Also, the viscous dissipation and joule heating effect are taken into account to explore more features of the flow situation. The mathematical model of flow is renovated with the effective implementation of similarity invariants. The numerical investigation is carried out using the Runge–Kutta method and the results obtained are interpreted graphically. The effects of physical parameters such as Dufour and Soret number, radiation parameter, magnetic parameter, etc., on non-dimensional quantities, are graphically illustrated with MATLAB. The thermal boundary layer gets elevation for rising values of Eckert number, magnetic parameter, unsteadiness parameter, Dufour number, and thermal radiation.

Significance of cross diffusion and uneven heat source/sink on the variable reactive 2D Casson flowing fluid through an infinite plate with heat and Ohmic dissipation

ABSTRACT This research work is focused on nonlinear mathematical model of non-Newtonian Casson fluid using Runge-Kutta method via shooting technique. The solutions to the momentum velocity profiles, heat transfer energy and mass transfer concentration profiles are carried out. Applying similarity transformations, the partial derivative model is transmuted to ordinary derivative equations and then solved utilizing shooting scheme combined with Runge-Kutta integration technique by a mathematical software MAPLE. The graphical results are plotted for various physical parameters under different effects. Also, the computed outcomes are compared with earlier published works and found that there is a good correlation between them. The outcomes show that radiation and magnetic field increased heat distribution and reaction index induced Casson reacting species. An enhancement in the Dufour number leads temperatures to accelerate and also leads to system blow-up if not appropriately managed. Further the Soret number yields higher distributions of solutal density. The recent research explores the cumulative aspects of various physical applications on the non-Newtonian Casson liquid over a vertical surface, which has impressive technical and industrial science characteristics.

Soret and Dufour aspects of the third-grade fluid due to the stretching cylinder with the Keller box approach

The convective transport of the third-grade fluid with thermo-diffusion features has to be worked out. The impact of the Soret and Dufour properties, as well as the radiative phenomena, is noticed. The assumed flow is due to the stretched cylinder. The partial differential equations indicating the flow model are first worked out into the dimensionless nature using similarity variables. The most effective numerical technique (the Keller Box method) has been used to solve nonlinear ODEs for obtaining the numerical data. The solution accuracy is validated using already claimed studies. The exploration subject to the flow pattern against parameters is presented. The simultaneous increase in Dufour and Soret numbers assists the temperature and concentration in the boundary layer region around the cylinder. With the increasing fluctuation in Dufour and reducing Soret numbers, the revised change in heat and mass transportation phenomenon is depicted. Furthermore, the radiation effects are elucidated by varying the effective Prandtl number.

Free Convective MHD Radiative Flow Past a Porous Vertical Plate in a Porous Medium with Chemical Reaction

An analytical solution for two-dimensional steady, viscous, incompressible hydromagnetic free convective flow past a uniformly moving vertical porous plate embedded in a porous medium in the presence of the Soret effect and chemical reaction is investigated in this paper. A uniform magnetic field is applied perpendicular to the plate and directed into the fluid region. The asymptotic series expansion method is used to solve the non-dimensional governing equations. The effects of thermal diffusion, magnetic field, thermal radiation, Grashof number, and chemical reaction are mainly focused on discussing the present problem. One of the significant findings of this study includes that an upsurge in the chemical reaction causes a downfall in the fluid temperature. It is seen that the Soret number enhances the velocity and temperature. Further, the fluid's velocity, concentration, and temperature decrease with an increase in the magnetic field parameter. In most works dealing with convective MHD flow, ohmic dissipation and viscous dissipation are neglected. In this work, these two effects are considered. Further, the Soret effect and the effect of first-order chemical reactions are also considered.

Thermal diffusion effect on unsteady MHD free convective flow past a semi-infinite exponentially accelerated vertical plate in a porous medium

The objective of the present work was to obtain an exact solution to the problem of a free convective, radiative, viscous, chemically reacting, heat-absorbing, incompressible, and unsteady magnetohydrodynamic flow past an exponentially accelerated moving vertical plate embedded in a porous medium. The fluid was assumed to be optically thick and nongray. A magnetic field was applied in the transverse direction of the flow. Effects of arbitrary ramped temperature and thermal diffusion were also considered. The Rosseland approximation method was used to describe the radiative heat flux that appears in the energy equation. Analytical solutions of the nondimensional governing equations were obtained by adopting a closed form of the Laplace transformation technique. The influence of various physical parameters on flow and transport characteristics was analyzed with suitable graphs. From the investigation, it was observed that increasing the Soret number increased both the concentration and velocity fields. Increasing the radiation parameter caused an upsurge in the Nusselt number but reduced the Soret number.

Thermosolutal convection of a sloshing wavy rod in a partial layer porous cavity mobilized by a nanofluid

This work discusses the dual diffusion of a sloshing wavy rod in a nanofluid-filled cavity. The top zone of a cavity is suspended by a porous medium. The boundary treatment in the ISPH method employs a kernel renormalization function. The wavy rod sloshes by an excitation frequency [Formula: see text] and it carries [Formula: see text] and [Formula: see text]. The rigid cavity walls are fixed, adiabatic (horizontal walls), and [Formula: see text] and [Formula: see text] (vertical walls). The measurements of pertinent parameters are the Soret number ([Formula: see text] Sr [Formula: see text]), nanoparticles parameter ([Formula: see text]), Rayleigh number ([Formula: see text] Ra [Formula: see text]), sinusoidal function ([Formula: see text]), Dufour number ([Formula: see text] Du [Formula: see text]), a slope angle of a magnetic field ([Formula: see text]), Hartmann number ([Formula: see text]), and Darcy parameter ([Formula: see text] Da [Formula: see text]). The performed simulations revealed that the nanofluid flow is accelerated by the Sort number, the sloshing of the rod, and the sinusoidal wavy of the rod. Besides, the dual convection is enhanced by the sinusoidal wavy function and the sloshing of the rod. There is almost no nanofluid flow in a top porous zone of a cavity when Da [Formula: see text].

Joule heating and thermal radiation impact on MHD boundary layer Nanofluid flow along an exponentially stretching surface with thermal stratified medium

The current investigation leads to the characterisation of the flow phenomena of hydromagnetic nanofluid thermal stratified through permeable medium due to the influence of the radiative heat energy. Additionally, the behaviour of chemical reaction, viscous as well as Joule dissipations enriches the flow profiles. The embedded system for the governing equation comprised of partial differential equations is distorted to nonlinear ordinary with the help of the similarity transformations. MATLAB software is used to implement numerical schemes such as the Runge-Kutta-Fehlberg methodology in conjunction with the shooting method. The effects of several non-dimensional factors on flow phenomena are shown graphically, and the simulated results for the rate coefficients are presented in tabular form. The results established are extremely closed and excellent concurrence with published work. The thermal boundary surface thickness is enhanced due to frictional heating with rising values of Eckert number. A rise in Dufour number leads to a reduction in temperature profile. In contrast, a rise in concentration leads to higher values of the Soret number.

Numerical investigation of a squeezing flow between concentric cylinders under the variable magnetic field of intensity

The ongoing research aims to examine the mass and heat transmission phenomena of squeezing flow between two concentric cylinders under the effect of heat sources and magnetic fields. The impacts of the Lorentz force on the behavior of the liquid flow are elucidated via a magnetic field incorporated in the momentum equation. Furthermore, within concentric cylinders, the expression Q = frac{Q_0}{1-beta t} has been employed as a source/sink. The proposed model of PDEs formulates the physical phenomena of time-dependent incompressible two-dimensional squeezing flow via modified Navier-Stokes equation, energy equation, and mass transfer equation, and variable magnetic field. The proposed model involved a highly nonlinear system of PDEs, which has been reduced into a system of ODEs via Lie group of similarity transformation and subsequently solved numerically in MATLAB by Parametric Continuation Method. The direct impact of the squeezing parameter on the profile of temperature and concentration has been observed. The results shown that an increment in the heat source indicates a decline in the liquid temperature profile, that an increment in the heat source indicates a decline in the liquid temperature profile. An increment in the heat source indicates a decline in the liquid temperature prof. At the same time, an inverse relationship is observed for the concentration profile. Therefore, we have witnessed a significant increase in the velocity profiles of the flow, mainly as a result of the heat absorption coefficient. In addition, the declining effect of the Soret number on the concentration profile is noticed. It has been found that it enhanced the entropy generation rate for Pr, Omega, and Ec, while an opposite impact has been noticed at the Bejan number. The numerical outcomes of the proposed model that explain fluid flow characteristics and fluid flow characteristics are quantitatively elucidated by tables and displayed graphically. The comparison of two numerical results in the cases are found to be in good agreement, as shown in Tables.

Theoretical study of transport of MHD peristaltic flow of fluid under the impact of viscous dissipation

ABSTRACT This article studies irreversibility analysis in the peristaltic transport of a non-Newtonian fluid. Jeffrey fluid is treated as the blood transport through a flexible artery/vessel. A peristaltic wave travels on the porous opposite wall of the inclined channel under the magnetic environment. Heating effects cause the shear thinning in the viscosity of the base liquid, transferring tiny particles. The efficiency of peristalsis is improved by reducing the irreversibility factor by means of entropy generation. The perturbation technique is applied to understand the nonlinear flow dynamics of heat and mass transfer with Jeffrey fluid with the help of convective boundary conditions. Comparative analysis is carried out with the available literature for the limiting case and found to have complete coherence. A detailed parametric study is carried out to comprehend the contribution of significant parameters which reveals that magnetic fields and slippery walls induce a resistive force on the nanoflow. The motion of the base liquid expedites subject to variation in Darcy number and shear-thinning effects. The energy is contributed to the nanofluid system in response to the Brinkman number. More, the number density of nanospecies reduces in the region of higher concentration subject to the Soret number and Schmidt number, respectively.

Soret and Dufour effects on MHD squeezing flow of Jeffrey fluid in horizontal channel with thermal radiation.

The fluid flow with chemical reaction is one of well-known research areas in the field of computational fluid dynamic. It is potentially useful in the modelling of flow on a nuclear reactor. Motivated by the implementation of the flow in the industrial application, the aim of this study is to explore the time-dependent squeeze flow of magnetohydrodynamic Jeffrey fluid over permeable medium in the influences of Soret and Dufour, heat source/sink and chemical reaction. The presence of joule heating, joule dissipation and radiative heat transfer are analyzed. The flow is induced due to compress of two surfaces. Conversion of partial differential equations (PDEs) into ordinary differential equations (ODEs) is accomplished by imposing similarity variables. Then, the governing equations are resolved using Keller-box approach. The present outcomes are compared with previously outcomes in the literature to validate the precision of present outcomes. Both outcomes are shown in close agreement. The tabular and graphical results demonstrate that wall shear stress and velocity profile accelerate with the surfaces moving towards one another. Moreover, the concentration, temperature and velocity profiles decreasing for the increment of Hartmann numbers and Jeffrey fluid parameters. The impacts of heat generation/absorption, joule dissipation and Dufour numbers enhance the heat transfer rate and temperature profile. In contrast, the temperature profile drops and the heat transfer rate boosts when thermal radiation increases. The concentration profile decelerates, and the mass transfer rate elevates with raise in Soret number. Also, the mass transfer rate rises for destructive chemical reaction and contrary result is noted for convective chemical reaction.

A computational study on the MHD Casson fluid flow with thermal radiation and variable physical properties under the influence of Soret and Dufour effects

AbstractThis research study discusses the flow of a magnetohydrodynamic Casson fluid under the influence of Soret, Dufour, and thermal radiation. Nonlinear partial differential equation (PDE) of governing equations is transformed into a dimensionless version of the modified PDEs presented in terms of dimensionless parameters. The solution of coupled PDEs is obtained by the finite difference method with a combination of the quasilinearization technique. The effects of various dimensionless parameters are shown graphically, such as buoyancy force (), concentration buoyancy force , Casson parameter (), magnetic parameter (), thermal radiation (), Darcy parameter (), Forchheimer (fr), Dufour (), Soret (Sor), Brownian motion (), thermopohersis (), and Lewis number (). Prevention of heat transfer in the industrial system is critical, the velocity behavior (), thermal variation (), and concentration profile () are more prominent in the roles of coal, gas, and solar thermal collectors.

Natural convective flow past a suddenly started vertical plate with uniform mass and heat flux in the presence of radiation, thermal diffusion

AbstractAn attempt has been made to investigate the problem of a natural convective radiative flow past an impulsively moving vertical plate with uniform mass and heat flux in the existence of the thermal diffusion effect. The resulting governing equations are solved by the Laplace transform technique in closed form. Effects of radiation, Prandtl number, Soret number, Grashof number, modified Grashof number, and Schmidt number are studied on temperature field, concentration field, velocity field, plate temperature, plate concentration, skin friction, and are demonstrated through graphs. The present study reveals that an intensification of the thermal radiation effect causes a downfall in the fluid temperature, plate temperature, and skin friction, but a contradictory outcome is spotted for plate concentration. One of the significant findings of this study includes that the increasing thermo‐diffusion effect hikes the concentration and frictional resistance of the field.

MHD free convective non-Newtonian Casson fluid flow over an oscillating vertical plate

The goal of this investigation is to examine magnetohydrodynamic​ natural convective, mass and heat transfer, performing non-Newtonian Casson fluid flow through an oscillating straight up permeable plate with the existence of thermal diffusion (Soret). Finite element approach (FEM) is implemented to overcome non-dimensional PDEs for distribution of velocity, temperature & concentration of Casson fluid by the impact of different dimensional variables. Local skin-frication, heat and mass transfer rate are often extracted as well as analyzed by graphical ways. The analysis shows that the concentration and velocity of Casson fluid are increased as an enhancement of Soret number. Velocity of Casson fluid increased as an increment of Grashof numbers for heat and mass transfer. Additionally, the flow velocity decreases with the rising values of Casson fluid, phase angle and magnetic field parameters however it enhances with the rising of permeability parameter. Furthermore, the temperature profiles diminished with the growing of Prandtl number. The solutions of the present investigation have been compared with the existing literature in certain circumstances and great agreement were achieved.

Significance of melting heat transfer in bio-convective thixotropic nanofluid

This work studies bio-convective thixotropic nanomaterial flow due to stretchable surface. Importances of bio-convection and melting impact are examined. Nanofluid significance through thermophoresis and Brownian diffusion is considered. Radiation, magnetic field and Joule heating effects are assumed present. Dimensionless variables are used to transform related expressions into ordinary differential system (ODEs). To gain convergent series solutions the homotopy analysis method (HAM) is utilized and solutions convergence discussed. Graphical results illustrating influences of melting parameter, Prandtl number, bio-convection Lewis number, radiation parameter, Dufour number, Soret number, Peclet number, Brownian motion parameter and various other emerging variables are presented. Here microorganism field is observed to be a decreasing function of bio-convection Lewis number. Velocity is an increasing function of melting parameter. Higher Dufour number result in temperature reduction while higher Soret number reduce concentration. Main results of current analysis are listed in conclusion section.

Study of MHD Mixed Convention Flow and Heat Transfer Through Porous Media

In this present paper, the effects of chemical reaction on two-dimensional mixed convection flow and heat transfer of an electrically conducting micropolar fluid in a porous medium between two parallel plates with Soret and Dufour have been considered. The reduced flow field equations are solved using the quasilinearization method. The effects of various parameters such as Hartmann number, inverse Darcy's parameter, Schmidt number, Prandtl number, chemical reaction rate, Soret and Dufour numbers on the velocity components, microrotation, temperature distribution, and concentration are studied in detail and presented in the form of graphs. The flow through porous boundaries has many applications in science and technology such as water waves over a shallow beach, mechanics of the cochlea in the human ear, aerodynamic heating, flow of blood in the arteries, and petroleum industry. Several authors have studied theoretically the laminar flow in porous channels. Berman [1] considered the viscous fluid and analyzed the flow characteristics when it passed through the porous walls. Later the same problem for different permeability was studied by Terril and Shrestha [2]. The theory of micropolar fluids was introduced by Eringen [3] which are considered as an extension of generalized viscous fluids with microstructure. Examples for micropolar fluids include lubricants, colloidal suspensions, porous rocks, aerogels, polymer blends, and microemulsions. The same Berman problem with micropolar fluid was discussed by Sastry and Rama Mohan Rao [4]. The flow and heat transfer of micropolar fluid between two porous parallel plates was analyzed by Ojjela and Naresh Kumar [5]. Srinivasacharya et al. [6] obtained an analytical solution for the unsteady Stokes flow of micropolar fluid between two parallel plates. The effect of buoyancy parameter on flow and heat transfer of micropolar fluid between two vertical parallel plates was investigated by Maiti [7].