Diffusion-thermo Effects Research Articles

Thermal-diffusion and diffusion-thermo effects on axisymmetric flow of a second grade fluid

This study investigates the thermal-diffusion and diffusion-thermo effects on the two-dimensional magnetohydrodynamics (MHD) axisymmertric flow of a second grade fluid. Mathematical analysis has been carried out in the presence of Joule heating and first order chemical reaction. Using momentum, energy and concentration laws, the governing partial differential equations have been reduced to the ordinary differential equations by suitable transformations. Series solutions are constructed by homotopy analysis method (HAM). Convergence of the derived series solutions is ensured. Plots are displayed in order to examine the influence of emerging parameters on the dimensionless components of velocity, temperature and concentration fields. Numerical computations for skin friction coefficient, Nusselt number and Sherwood number are tabulated.

UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID

This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and concentration distributions are shown for various values of the thermophysical parameters controlling the flow regime. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form.

Thermo-diffusion and diffusion-thermo effects on a three dimensional MHD mixed convection flow past an infinite vertical porous plate with thermal radiation

Thermo-diffusion and diffusion-thermo effects on a three dimensional MHD mixed convection flow past an infinite vertical porous plate with thermal radiation

Diffusion-Thermo Effects on Free Convective Heat and Mass Transfer Flow in a Vertical Channel With Symmetric Boundary Conditions

This article investigates the influence of diffusion-thermo effect on transient free convective heat and mass transfer flow in a channel bounded by two infinite vertical parallel plates. Fully developed laminar flow is considered when the boundaries are subjected to symmetric concentration and thermal input. The Dufour effect is taken into consideration. The velocity, temperature, and concentration profiles are obtained analytically using the Laplace transforms technique and used to compute the shear stress, Nusselt number, and mass flux. During the course of computation, it was found that transient solution at large time coincides with steady-state solution derived separately. Diffusion-thermo (Dufour effect) is observed to create an anomalous situation in temperature and velocity profiles for small Prandtl numbers. There is also flow reversal for a small Dufour number and negative values of the sustentation parameter (N). At steady-state, there is neither heat nor mass transfer between the fluid and the plates.

Convection from an inverted cone in a porous medium with cross-diffusion effects

In this study convection from an inverted cone in a porous medium with cross-diffusion is studied numerically. Diffusion-thermo and thermo-diffusion effects are assumed to be significant. The governing equations are transformed into nonlinear ordinary differential equations and then solved numerically using a shooting method together with a sixth order Runge–Kutta method. Verification of the accuracy and correctness of the results is achieved by solving the equations using an independent linearisation method. The effects of the Dufour and the Soret parameters are investigated. The results for the skin friction, Nusselt number and the Sherwood number are presented graphically and in tabular form.

Numerical Modelling of Non-similar Mixed Convection Heat and Species Transfer along an Inclined Solar Energy Collector Surface with Cross Diffusion Effects

An analysis is performed to study thermo-diffusion and diffusion-thermo effects on mixed convection heat and mass transfer boundary layer flow along an inclined (solar collector) plate. The resulting governing equations are transformed and then solved numerically using the local nonsimilarity method and Runge-Kutta shooting quadrature. A parametric study illustrating the influence of thermal buoyancy parameter (&#950), Prandtl number (Pr), Schmidt number (Sc), Soret number (Sr), Dufour number (Du) and concentration-to- thermal-buoyancy ratio parameter, N, on the fluid velocity, temperature and concentration profiles as well as on local skin-friction, Nusselt and Sherwood numbers is conducted. For positive inclination angle of the plate (&#947 = 70 degrees), flow velocity (f') is strongly increased i.e. accelerated, with thermal buoyancy force parameter (&#950), in particular closer to the plate surface; further into the boundary layer, &#950 has a much reduced effect. Conversely temperature (&#952) and concentration (&#968) is decreased with increasing thermal buoyancy parameter, &#950. For negative plate inclination, the flow is accelerated whereas for positive inclination it is decelerated i.e. velocity is reduced. Conversely with negative plate inclination both the temperature and concentration in the boundary layer is reduced with the opposite apparent for positive inclination. Increasing Prandtl number strongly reduces temperature in the regime whereas an increase in Schmidt number boosts temperatures with temperature overshoots near the plate surface for Sc = 3 and 5 (i.e. for Sc > 1). Concentration is reduced continuously throughout the boundary layer, however, with increasing Schmidt number. A positive increase in concentration-to-thermal-buoyancy ratio parameter, N, significantly accelerates the flow in the domain, whereas negative N causes a deceleration. A velocity overshoot is also identified for N = 20, at intermediate distance from the plate surface. Negative N (thermal and concentration buoyancy forces oppose each other) induces a slight increase in both fluid temperature and concentration, with the reverse observed for positive N (thermal and concentration buoyancy forces assisting each other). Increasing Dufour number respectively causes a rise in temperature and a decrease in concentration, whereas an increase in Soret number cools the fluid i.e. reduces temperature and enhances concentration values. In the absence of Soret and Dufour effects, positive N causes a monotonic increase in local Nusselt number, NuxRex-1/2 with &#950 Cos &#947, for N = -1 the local Nusselt number remains constant for all values of parameter, &#950 Cos &#947. Local Sherwood number, ShxRex-1/2 is boosted considerably with higher Schmidt numbers and also with positive N values. The computations in the absence of Soret and Dufour effects correlate accurately with the earlier study by Chen et al. (1980).

A theoretical and numerical study of thermosolutal convection: stability of a salinity gradient solar pond

A theoretical and numerical study of the effect of thermodiffusion on the stability of a gradient layer is presented. It intends to clarify the mechanisms of fluid dynamics and the processes which occur in a salinity gradient solar pond. A mathematical modelling is developed to describe the thermodiffusion contribution on the solar pond where thermal, radiative, and massive fluxes are coupled in the double diffusion. More realistic boundary conditions for temperature and concentration profiles are used. Our results are compared with those obtained experimentally by authors without extracting the heat flux from the storage zone. We have considered the stability analysis of the equilibrium solution. We assumed that the perturbation of quantities such as velocity, temperature, and concentration are infinitesimal. Linearized equations satisfying appropriate prescribed boundary conditions are then obtained and expanded into polynomials form. The Galerkin method along with a symbolic algebra code (Maple) are used to solve these equations. The effect of the separation coefficient y is analyzed in the positive and negative case. We have also numerically compared the critical Rayleigh numbers for the onset of convection with those obtained by the linear stability analysis for Le = 100, ?a = 0.8, and f = 0.5.

THERMAL-DIFFUSION AND DIFFUSION-THERMO EFFECTS ON NATURAL CONVECTION ALONG AN INCLINED STRETCHING SURFACE IN A POROUS MEDIUM WITH CHEMICAL REACTION

The steady natural convection along an inclined stretching surface in the presence of chemical reaction under thermal-diffusion and diffusion-thermo effects is studied. The governing equations for continuity, momentum, energy, and concentration are transformed by similarity transformation and then solved numerically using the Runge-Kutta integration with shooting scheme. Comparisons between the present data with previously published work are performed and found to be in very good agreement with each other. The obtained results show that the flow, thermal, and diffusion fields are influenced appreciably by the effects of endothermic or exothermic chemical reaction, angle of inclination, thermal radiation, magnetic field, and Soret and Dufour numbers. The physical phenomenon can be realized from the graphical profiles and in tabular form to depict special features of the solutions.

Detailed numerical simulations of intrinsically unstable two-dimensional planar lean premixed hydrogen/air flames

Lean premixed hydrogen/air flames are characterized by subunity Lewis numbers and the strong influence of thermal-diffusive instability in addition to the omnipresent hydrodynamic instability caused by thermal expansion. Such intrinsically unstable flames acquire cellular structures that modify significantly their propagation dynamics. In this paper, numerical simulations with detailed chemistry and transport are used to study premixed hydrogen/air flames at an equivalence ratio of ϕ=0.6 and p=5 atm in 2D rectangular domains with height ranging between 3 and 80 flame thicknesses and periodic boundary conditions along the lateral boundaries. The initial linear growth of perturbations superimposed on the planar front as well as the long-time nonlinear evolution are studied as a function of the periodicity height of the domain which affects the relative importance of hydrodynamic and thermodiffusive effects on the evolution of the flame front. Flame propagation in narrow domains is strongly affected by thermodiffusive effects, while in wide domains a cascade of transitions of the flame shape occurs. Further increase of the periodicity height, enhances the hydrodynamic effects, and the flame shape is dominated by the single-cusp structure predicted by the hydrodynamic theory.

Lie group analysis for thermal-diffusion and diffusion-thermo effects on free convective flow over a porous stretching surface with variable stream conditions in the presence of thermophoresis particle deposition

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with temperature-dependent fluid viscosity embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. This paper concerns with a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The impact of thermophoresis particle deposition with chemical reaction in the presence of thermal-diffusion and diffusion-thermo effects plays an important role on the temperature and concentration boundary layer. The results thus obtained are presented graphically and discussed.

Heat and Mass Transfer by MHD Stagnation-Point Flow of a Power-Law Fluid towards a Stretching Surface with Radiation, Chemical Reaction and Soret and Dufour Effects

The thermal-diffusion and diffusion-thermo effects on heat and mass transfer by magnetohydrodynamic (MHD) mixed convection stagnation-point flow of a power-law non-Newtonian fluid towards a stretching surface in the presence of a magnetic field, thermal radiation and homogenous chemical reaction effects have been studied. A suitable set of dimensionless variables is used and similar equations governing the problem are obtained. The resulting equations have the property that they reduce to various special cases previously considered in the literature. An adequate implicit tri-diagonal finite-difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. Representative results for the velocity, temperature, and concentration profiles as well as the local skin-friction coefficient, the local Nusselt number and the local Sherwood number illustrating the influence of the magnetic parameter, power-law fluid index, mixed convection parameter, concentration to thermal buoyancy ratio, thermal radiation, chemical reaction, and Dufour and Soret numbers are presented and discussed.

Separation of a Gas Mixture by Means of Optical Trapping of the Gas

Contributions of barodiffusion and thermodiffusion to separation of a methane–helium mixture are calculated with the use of a laser-induced interferential lattice with a non-resonant frequency. The process of separation is studied by the direct simulation Monte Carlo method of rarefied gas flows, which can be considered as a numerical method of the stochastic solution of the Boltzmann equation. An analysis of modeling results shows that barodiffusion arising under optical radiation owing to the influence of ponderomotive forces on the species of the gas mixture exerts a significant effect during separation of the gas mixture by means of optical trapping, in addition to the selective action of the lattice. The effect of thermodiffusion caused by heating of the mixture by the optical lattice is found to be significant only in peripheral areas of the lattice.

Effect of thermodiffusion on convective heat and mass transfer in enclosures with heat-conducting walls

The influence of Soret effect on thermogravitational convection in an enclosure with heat-conducting walls of finite thickness in the presence of local heat and mass sources is numerically analyzed. The mathematical model is formulated in dimensionless variables of streamfunction-vorticity vector. Streamlines and temperature fields representing the influence of the Rayleigh number Ra = 105, 106 and the nonstationarity factor 0 < τ < 3000 are obtained.

Thermo diffusion and chemical effects with simultaneous thermal and mass diffusion in MHD mixed convection flow with ohmic heating

Thermo diffusion and chemical effects on heat transfer in MHD mixed convection flow and masstransfer past an infinite vertical plate with Ohmic heating and viscous dissipation have beenstudied. Approximate solutions have been derived for velocity, temperature, concentration profiles,skin friction, rate of heat transfer and rate of mass transfer using perturbation technique. Theobtained results are discussed with the help of graphs to observe the effect of various parameterslike Schmidt number (Sc), Prandtl number (Pr), Magnetic parameter (M),Soret number (So) andchemical parameter (K), taking two cases viz. Case I: when Gr &gt; 0 (flow on cooled plate) and CaseII: Gr &lt; 0 (flow on heated plate). Thermal diffusion causes both the fluid velocity and temperature tofall due to the presence of the chemical effect. Velocity and temperature profiles are higher formercury than electrolytic solution. Soret effect increased the concentration of the fluid while chemicaleffect decreased.Keywords: Chemical effect; thermo diffusion; magnetic field; heat-mass transfer.DOI: 10.3329/jname.v6i2.3761

Experimental measurement of the effective diffusion and thermodiffusion coefficients for binary gas mixture in porous media

Thermodiffusion or Soret effect, corresponding to a mass flux caused by a temperature gradient applied to fluid mixture, has been taken into account in many porous media applications, particularly in chemical engineering and geophysics. In the literature, the effective macro-scale diffusion coefficients are now well established, while uncertainty remains concerning the relationship between the effective thermodiffusion coefficient and micro-scale parameters (such as pore-scale geometry). Our previous study on theoretical model of effective thermodiffusion coefficient for a pure diffusion regime confirmed that the tortuosity factor acts in the same way on both Fick diffusion coefficient and on thermodiffusion coefficient. In this study, new experimental results obtained with a two bulb apparatus are presented. The diffusion and thermodiffusion of a helium–nitrogen and helium–carbon dioxide system through cylindrical samples filed with glass spheres of different diameter are measured at the atmospheric pressure. Concentrations are determined by analyzing the gas mixture composition in the bulbs with a katharometer device. A transient-state method for coupled evaluation of thermodiffusion and Fick coefficient in two bulbs system is proposed. The obtained results are in good agreement with theoretical results from previous study and emphasize the porosity of the medium influence on both diffusion and thermodiffusion process. The tortuosity of the medium calculated using both effective diffusion and effective thermodiffusion coefficients are the same.

Impact of Thermodiffusion on Carbon Nanotube Growth by Chemical Vapor Deposition

Thermal diffusion, the process by which a multicomponent mixture develops a concentration gradient when exposed to a temperature gradient, has been studied in order to understand if its inclusion is warranted in the modeling of single-wall carbon nanotubes (SWNTs) synthesis by thermal chemical vapor deposition (CVD). A fully coupled reactor-scale model employing conservation of mass, momentum, species, and energy equations with detailed gas phase and surface reaction mechanisms has been utilized to describe the evolution of hydrogen and hydrocarbon feed streams as they undergo transport, as well as homogeneous and heterogeneous chemical reaction within a CVD reactor. Steady state velocity, temperature, and concentration fields within the reactor volume are determined, as well as concentrations of adsorbed species and SWNT growth rates. The effect of thermodiffusion in differing reactor conditions has been investigated to understand the impact on SWNT growth. Thermal diffusion can have a significant impact on SWNT growth, and the first approximation of the thermal diffusion factor, based on the Chapman–Enskog molecular theory, is sufficient for modeling thermophoretic behavior within a CVD reactor. This effect can be facilitatory or inhibitory, based on the thermal and mass flux conditions. The results of this investigation are useful in order to optimize model and reactor designs to promote optimal SWNT deposition rates.

Thermodiffusion mechanism of nonlinear absorption in nanoparticle suspensions

Results of the experimental study of the self-induced clarification (or darkening) of carbonic nanoparticle suspensions under radiation in a fiber-optic cell are presented. A model based on the thermodiffusion effect with accounting for convection is suggested.

NUMERIAL INVESTIGATION OF THERMODIFFUSION EFFECTS ON PEM FUEL CELL PERFORMANCE

An increasing amount of attention has been paid on the study of thermodiffusion effects on mass transport. This paper presents a novel mathematical model for an entire proton exchange membrane fuel cell (PEMFC) with focus placed on the modeling and assessment of the role of thermodiffusion that has been usually neglected in previous fuel cell research work. Built upon the equations of continuity, momentum, energy, species concentrations, and electric potentials in different regions of a PEMFC, a set of nonlinear partial differential equations are numerically solved using finite element methods. The simulation results demonstrate that the thermodiffusion has a noticeable impact on transport of species in an operational PEMFC.

Free convection heat and mass transfer flow in a vertical channel with the Dufour effect

The purpose of this work is to investigate analytically the free-convection and mass transfer flow in a vertical channel formed by two vertical parallel plates. Fully developed laminar flow was considered with uniform temperature and concentration on the plates. The diffusion-thermo effect was taken into consideration. The velocity, temperature, and concentration profiles were obtained analytically using the Laplace transform technique and were used to compute the shear stress, Nusselt number, and mass flux. The present analytical results were compared with those available in the literature without mass transfer and the diffusion-thermo effect and excellent agreement was observed (Singh, A. K., Gholami, H. R., and Soundalgekar, V. M. Transient free convection flow between two vertical parallel plates. J. Heat Mass Transf., 1996, 31, 329—331.). During the course of computation, it was found that the transient solution at large time coincides with the steady-state solution derived separately. The diffusion-thermo effect is observed to create an anomalous situation in temperature and velocity profiles for small Prandtl numbers. The study also revealed that the steady state of the problem is independent of the Dufour effect.

Theoretical predictions of the effective thermodiffusion coefficients in porous media

This study presents the determination of the effective Darcy-scale coefficients for heat and mass transfer in porous media including the thermodiffusion effect using a volume averaging technique. The closure problems related to the pore-scale physics and providing effective coefficients are solved over periodic unit cells representative of the porous structure. The results show that, for low Péclet numbers, the effective Soret number in porous media is the same as the one in the free fluid and that it does not depend on the solid to fluid conductivity ratio. On the opposite, in convective regimes, the effective Soret number decreases. In this case, a change of conductivity ratio will change the effective thermodiffusion coefficient as well as the effective thermal conductivity coefficient. The macroscopic model obtained by this method is validated by comparison with direct numerical simulations at the pore-scale. Then, coupling between forced convection and Soret effect for different cases is investigated.