Soret effect on the shock responses of generalized diffusion-thermoelasticity

The in-service environment in most generalized diffusion-thermoelasticity problems is nonisothermal. It is known that Soret effect, i.e., temperature-gradient driven diffusion phenomenon, should be considered in nonuniform temperature field. This provides us a motivation to construct a new model of generalized diffusion-thermoelasticity with Soret effect and investigate the transient shock responses. The governing equations with Soret parameter are obtained in the context of generalized diffusion-thermoelasticity theory. To solve the problem, Laplace transformation techniques are used. For numerical evaluation, a problem of transient response for a slim strip with one end subjecting to thermal and chemical disturbances is studied. Numerical results are obtained and illustrated graphically. Parametric studies are performed to evaluate the influences of Soret parameter on the responses. The results show that Soret effect has significant effects on chemical potential, displacement, stress and concentration.     

A novel membrane transport model for polymer electrolyte fuel cell simulations

This work presents the development of a 1D model describing water and charge transport through the polymer electrolyte membrane (PEM) in the fuel cell. The considered driving forces are electrical potential, concentration and pressure gradients. The membrane properties such as water diffusion and electro-osmotic coefficients, water sorption and ionic conductivity are treated as temperature dependent functions. The dependencies of diffusion and electro-osmotic coefficients on the membrane water concentration are described by linear functions. The membrane conductivity is computed in the framework of the percolation theory under consideration that the conducting phase in the PEM is formed by a hydrated functional groups and absorbed water. This developed membrane model was implemented in the CFD code AVL FIRE using 1D/3D coupling. The simulated polarization curves at various humidification of the cathode are found in good agreement with the experiments thus confirming the validity of the model.     

Modeling of gas transport through a tubular solid oxide fuel cell and the porous anode layer

A design model is a necessary tool to understand the gas transport phenomena that occurs in a tubular solid oxide fuel cell (SOFC). This paper describes a computational model, which studies the gas flow through an anode-supported tubular SOFC and the subsequent diffusion of gas through its porous anode. The model is a numerical solution for the gas flow through a plug flow reactor with a diffusion layer, which includes the activation, ohmic, and concentration polarizations. Gas diffusion is modeled using the dusty-gas equations which include Knudsen diffusion. Mercury intrusion porosimetry (MIP) is used to experimentally determine micro-structural parameters such as porosity, tortuosity and effective diffusion coefficients, which are used in the diffusion equations for the porous anode layer. It was found that diffusion in the anode plays a key role in the performance of a tubular SOFC. The concentration gradient of hydrogen and water results in a lower concentration of hydrogen and a higher concentration of water at the reactive triple phase boundary (TPB) than in the fuel stream which both lead to a lower cell voltage. The gas diffusion determines the limiting current density of the cell where a higher concentration drop of hydrogen results in a lower limiting current density. The model validates well with experimental data and is used to improve micro-tubular solid oxide fuel cell designs.     

Effects of Soret diffusion on the exergy losses in hydrogen laminar premixed flames

The analysis of the exergy loss is an effective tool for evaluating second-law irreversibility in laminar flames. However, despite numerous studies underlining the importance of taking into account thermal diffusion in laminar flame studies, especially in hydrogen/air flames, this phenomenon is usually neglected in the exergy analysis of these flames. Therefore, this work investigates the effect of Soret diffusion on the exergy loss in laminar premixed flames for hydrogen/air mixtures using a detailed reaction mechanism and the multicomponent transport model. The study starts from conditions in which the importance of the Soret effect is well established in the scientific literature. It is found that, while the exergy losses directly due to the Soret effect are negligible, the Soret effect can appreciably affect the other exergy loss contributions and hence the total exergy loss. Hence, the Soret effect, unlike what has usually been assumed, is not negligible in flame calculations at least when this effect is known to affect laminar flame speed.     

A 3D transient nonlinear modelling of coupled heat,mass and deformation fields in anisotropic material

This paper deals with the numerical solution of a three-dimensional problem of non-isothermal moisture transfer in the anisotropic structure of wood and corresponding wood deformations in convective drying.The simulation is based on the unsteady-state nonlinear diffusion of moisture and heat with respect to the orthotropic nature of wood. The moisture gradient and the temperature gradient are set as driving forces for mass and heat transfer. The model respects the dependence of material coefficients on temperature and moisture, the Soret effect, the Duffour effect and the anisotropic nature of wood. A matrix form of the multiphysics model for FEM solver was derived and numerical simulations were performed.     

Soret‐Dufour effects in electroosmotic biorheological flow of Jeffrey fluid

The Soret and Dufour cross‐diffusion on the electrokinetic flow of Jeffrey fluid augmented with peristalsis have been presented. The fundamental equations are employed to predict the mass distribution in the two‐dimensional asymmetric electroosmotic channel. Reliable approximations such as low Peclet, low Reynolds, and large wavelength are utilized. The analytical solutions of the concentration, temperature, velocity, and stream function are obtained. To predict the effects of prominent parameters such as fluid parameter, electroosmotic parameter, Brinkman, Soret, and Schmidt number graphs are plotted. The phenomenon of trapping is also discussed to observe the behavior on streamlines. It is observed that the electroosmotic parameter enhances the temperature profile. With the increase in Jeffrey fluid parameter, the Nusselt number is decreased. Furthermore, the concentration is decreased with the elevation in Soret and Schmidt numbers. The current study can help reduce the conversion stages necessary for the integration of the low voltage output in an electrokinetic biomass process.     

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21076     

Modelling water intrusion and oxygen diffusion in a reconstructed microporous layer of PEM fuel cells

The hydrophobic microporous layer (MPL) in PEM fuel cell improves water management but reduces oxygen transport. We investigate these conflict impacts using nanotomography and pore-scale modelling. The binary image of a MPL is acquired using FIB/SEM tomography. The water produced at the cathode is assumed to condense in the catalyst layer (CL), and then builds up a pressure before moving into the MPL. Water distribution in the MPL is calculated from its pore geometry, and oxygen transport through it is simulated using pore-scale models considering both bulk and Knudsen diffusions. The simulated oxygen concentration and flux at all voxels are volumetrically averaged to calculate the effective diffusion coefficients. For water flow, we found that when the MPL is too hydrophobic, water is unable to move through it and must find alternative exits. For oxygen diffusion, we found that the interaction of the bulk and Knudsen diffusions at pore scale creates an extra resistance after the volumetric average, and that the conventional dusty model substantially overestimates the effective diffusion coefficient.     

Soret and Dufour effects between two rectangular plane walls with heat source/sink

This study addresses the thermo‐diffusion and the diffusion‐thermo phenomena in a semi‐infinite absorbent channel whose walls are contracting/expanding, with heat source/sink effects. The governing partial differential equations with suitable boundary conditions are transformed to a system of dimensionless ordinary differential equations. An analytic solution of the problem has been found using a technique called homotopy analysis method (HAM). HAM gives consistently valid answers to the problem over an extensive variety of parameters and also provides better accuracy. To validate the analytical results, a comparison has been presented with a numerical solution calculated by using the parallel shooting method. The effects of dimensionless parameters, that is, deformation parameter, Reynolds number, Soret and Dufour numbers, and heat source/sink parameter on the expressions of velocity, temperature, and concentration profiles are analyzed graphically to understand the physics of the deformable channel. It has been noted that the velocity across the channel is higher for the expanding channel, as compared to that for the contracting channel. Also the Soret and Dufour number increases the temperature of the fluid, and decreases the concentration. The temperature profile has an increasing behavior in the case of heat source, and a decreasing behavior in the case of heat sink.     

A mechanistic study of Soret diffusion in hydrogen–air flames

The separate and combined effects of Soret diffusion of the hydrogen molecule (H₂) and radical (H) on the structure and propagation speed of the freely-propagating planar premixed flames, and the strain-induced extinction response of premixed and nonpremixed counterflow flames, were computationally studied for hydrogen–air mixtures using a detailed reaction mechanism and transport properties. Results show that, except for the conservative freely-propagating planar flame, Soret diffusion of H₂ increases the fuel concentration entering the flame structure and as such modifies the mixture stoichiometry and flame temperature, which could lead to substantial increase (decrease) of the flame speed for the lean (rich) mixtures respectively. On the other hand, Soret diffusion of H actively modifies its concentration and distribution in the reaction zone, which in turn affects the individual reaction rates. In particular, the reaction rates of the symmetric, twin, counterflow premixed flames, especially at near-extinction states, can be increased for lean flames but decreased for rich flames, whose active reaction regions are respectively located at, and away from, the stagnation surface. However, such a difference is eliminated for the single counterflow flame stabilized by an opposing cold nitrogen stream, as the active reaction zone up to the state of extinction is always located away from the stagnation surface. Finally, the reaction rate is increased in general for diffusion flames because the bell-shaped temperature distribution localizes the H concentration to the reaction region which has the maximum temperature.     

Determination of methanol diffusion and electroosmotic drag coefficients in proton-exchange-membranes for DMFC

Methanol diffusion and electroosmotic drag coefficients for different polymer–electrolyte-membranes have been investigated. It is essential to understand the transport phenomena of water and methanol transport in perfluoro sulfonic acid (PSA) membranes under different methanol concentrations and current densities in order to optimize cell performance and operation. The dependence of the methanol diffusion coefficient as well as the electroosmotic drag coefficient on methanol concentration and current density were observed. The results are discussed in comparison to measured values obtained by other scientific groups.     

Cross–diffusion effects on mixed convection from an exponentially stretching surface in non–Darcy porous medium

The Soret and Dufour effects on mixed convection flow and heat and mass transfers from an exponentially stretching surface in a quiescent fluid–saturated non–Darcy porous medium is studied. Stretching velocity, wall temperature, and wall concentration are assumed to have specific exponential function forms. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using an implicit finite difference scheme known as the Keller–box method. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. The influence of buoyancy, Soret and Dufour numbers, and Darcy and non–Darcy parameters on the convective transport in the boundary layer region is analyzed. Also, the numerical values of the skin friction, heat, and mass transfer coefficients for different values of governing parameters are also tabulated. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21032     

Free convection and mass transfer flow of non-newtonian fluid with thermal diffusion effect

An analytical study is performed to examine the thermal diffusion characteristics of free convection and mass transfer flow in a non-Newtonian fluid (Walters, 1962: liquid B') past a uniformly accelerated infinite vertical plate in the presence of thermal diffusion. The expression for the velocity field is obtained by the Laplace transform technique. The influence of the Soret number (a thermal diffusion parameter) on the velocity field is extensively discussed with the help of graphs.     

Characteristics of water transport through the membrane in direct methanol fuel cells operating with neat methanol

The water required for the methanol oxidation reaction in a direct methanol fuel cell (DMFC) operating with neat methanol can be supplied by diffusion from the cathode to the anode through the membrane. In this work, we present a method that allows the water transport rate through the membrane to be in-situ determined. With this method, the effects of the design parameters of the membrane electrode assembly (MEA) and operating conditions on the water transport through the membrane are investigated. The experimental data show that the water flux by diffusion from the cathode to the anode is higher than the opposite flow flux of water due to electro-osmotic drag (EOD) at a given current density, resulting in a net water transport from the cathode to the anode. The results also show that thinning the anode gas diffusion layer (GDL) and the membrane as well as thickening the cathode GDL can enhance the water transport flux from the cathode to the anode. However, a too thin anode GDL or a too thick cathode GDL will lower the cell performance due to the increases in the water concentration loss at the anode catalyst layer (CL) and the oxygen concentration loss at the cathode CL, respectively.     

Aspects of parabolic motion of MHD fluid flow past a vertical porous plate with cross-diffusion effects

In the presence of Soret and Dufour effects, a numerical analysis is performed for an unstable magnetohydrodynamics convective flow of parabolic motion with variable temperature and concentration. The finite-difference method is used to solve the set of nondimensional governing equations with boundary conditions numerically. Graphs are used to investigate the effect of various physical characteristics on flow quantities. Variations in skin friction, Nusselt number, and Sherwood number are also examined using tables for physical curiosity. This study is unique in that it takes into account changeable temperature as well as concentration with Soret and Dufour effects. The magnetic parameter, Prandtl number, heat source, radiation parameter, Schmidt number, and chemical reaction parameter show a significant increase in skin friction, whereas the Grashof number, modified Grashof number, permeability parameter, radiation absorption parameter, Dufour number, and Soret number show the opposite trend. As the Soret number rises, the concentration rises as well, whereas the opposite is true for the Schmidt number and the chemical reaction parameter. The current study is highly supported by previously published data that have been verified.     

Double‐Diffusive Convective Transport in a Nanofluid‐Saturated Porous Layer with Cross Diffusion and Variation of Viscosity and Conductivity

The onset of double‐diffusive nanofluid convection in a fluid‐saturated horizontal porous layer is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. The Darcy model has been used for the porous medium, while the nanofluid incorporates the effects of Brownian motion along with thermophoresis. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In addition, the thermal energy equation includes regular diffusion and cross diffusion terms. The linear stability analysis is based on the normal mode technique, while for nonlinear analysis, minimal representation of the truncated Fourier series representation involving only two terms has been used. It is found that for the stationary mode the Soret parameter, Dufour parameter, viscosity ratio, and conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret parameter, Dufour parameter, and viscosity ratio have a stabilizing effect while the solutal Rayleigh number and conductivity ratio destabilize the system. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of the Dufour parameter and solutal Rayleigh number. The Soret parameter enhances the solute concentration Nusselt number while it retards the thermal Nusselt number and concentration Nusselt number. The viscosity ratio and conductivity ratio enhances the heat and mass transports. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large, all three transient Nusselt values approach a steady value. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 628–652, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21102     

MHD mass transfer flow past an inclined plate with variable temperature and plate velocity embedded in a porous medium

An exact solution of unsteady MHD free convective mass transfer flow past an infinite inclined plate embedded in a saturated porous medium with variable plate velocity, temperature, and mass diffusion has been presented. An attempt has been made to analyze the Soret effect and the influence of the angle of inclination on the flow and transport properties, in the presence of thermal radiation, heat source, and chemical reaction. The equations governing the flow, heat, and mass transfer are solved by employing the Laplace transform technique, in closed form. The variations in fluid velocity, temperature, and concentration profiles are shown graphically whereas the numerical values of shear stress, the rate of heat transfer, and the rate of mass transfer from the plate to the fluid are presented in tabular form for various values of the flow parameters. The results show that the flow is accelerated due to the Soret effect while the angle of inclination sustains a retarding effect on fluid velocity. Further it is observed that the viscous drag at the plate and the mass diffusion from the plate to the fluid decrease under the influence of thermal diffusion.     

Extended Graetz problem accompanied by Dufour and Soret effects

Simultaneous heat and mass transfer between parallel plates are analyzed taking into account the Soret and Dufour effects. Both heat and mass transport are examined considering conduction in the axial and transverse directions plus longitudinal advection. The equations differ from the classical heat and mass transfer ones in considering the effect of the temperature gradient upon the mass flux, and conversely the effect of the concentration gradient upon heat flux, in accordance with the dictates of thermodynamics of irreversible processes. The special problems solved evaluate the effect of an imposed temperature difference between the confining walls upon the solute concentration distribution of a multisolute which diffuses against the concentration gradient forced by the prevailing temperature gradient. Details and numerical results are presented only for binary solutions.The asymptotic concentration difference, for a specified temperature difference, depends on the Soret and Dufour coefficients. The approach to the asymptotes is determined by the complete solution of the governing equations.     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a downward-pointing vertical cone in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local Nusselt number tends to decrease as the Dufour parameter is increased. The effect of the Dufour parameter on the local Nusselt number becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number.