Increase In Soret Number Research Articles

Soret-Dufour effects on MHD rotating flow of a viscoelastic fluid

Purpose – The purpose of this paper is to study the heat and mass transfer with Soret-Dufour effects for the magnetohydrodynamic three-dimensional flow of second grade fluid in the rotating frame of reference. Design/methodology/approach – Series solution is obtained by homotopy analysis method. Findings – Increase in Soret number, Schmidt number and Dufour number, the heat transfer increases and mass transfer decreases. Effects of Prandtl and Eckert numbers are qualitatively similar as they assist the temperature profile and reduce the concentration of species. Increase in the length of the channel versus height increases the temperature profile but decreases the concentration field. Increase in the second grade fluid parameter causes reduction in both the temperature and concentration fields. The heat flux values at the lower plate are smaller than the values at the upper plate, whereas the situation is opposite in the case of mass transfer. Originality/value – These findings will be useful for the fluid flow in porous channel.

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy—Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy—Rayleigh number increases with increasing value of the solutal Darcy—Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy—Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.

Thermo-diffusion and diffusion-thermo effects on MHD free convection flow past a vertical porous plate embedded in a non-Darcian porous medium

An analysis is presented for the steady free convection heat and mass transfer past a vertical porous plate in a non-Darcy porous medium subjected to uniform magnetic field with Soret (thermo-diffusion) and Dufour (diffusion-thermo) effects included. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting non-linear system of partial differential equations are solved using the efficient Keller-box implicit numerical finite difference method. Increasing magnetohydrodynamic body force parameter ( M) is found to decelerate the flow. Increasing Soret number and simultaneously decreasing Dufour number enhances the local heat transfer rate (local Nusselt number) at the plate surface with the opposite effect sustained for the mass transfer rate (local Sherwood number). Increasing Forchheimer inertial drag parameter ( Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Applications of the model arise in metallurgical materials processing, chemical engineering flow control, geothermal hydromagnetics, etc.

Effects of Hall Current and Mass Transfer on the Unsteady Magnetohydrodynamic Flow in a Porous Channel

The combined effects of Hall current and mass transfer on the unsteady magnetohydrodynamic (MHD) flow of a viscous fluid passing through a porous channel have been investigated. The flow in the fluid has been induced due to external pressure gradient. The closed form analytical solutions have been obtained for the velocity, temperature and concentration fields. The analytical expressions for non-dimensional Skin-friction, Nusselt number and Sherwood number have been computed. The influence of various embedded flow parameters have been analyzed through graphs. The solutions obtained show that the influence of Hall parameter and mass transfer phenomenon give some interesting results. It is found that the Hall parameter have an increasing effect on the fluid velocity and approaches to the steady state as the time parameter is increased. The fluid concentration is increased for larger values of Peclet and Schmidt numbers whereas decreased with increase in Soret number and time parameter.

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).

Modified Differential Transform Method (DTM) Simulation of Hydromagnetic Multi-Physical Flow Phenomena from a Rotating Disk

A similarity solution for the steady hydromagnetic convective heat and mass transfer with slip flow from a spinning disk with viscous dissipation and Ohmic heating yields a system of non-linear, coupled, ordinary differential equations. These equations are analytically solved by applying a newly developed method namely the DTM-Pade technique which is a combination of the Differential Transform Method (DTM) and the Pade approximation. A full analytical solution is presented, as a benchmark for alternative numerical solutions. DTM-Pade is implemented without requiring linearization, discretization, or perturbation, and holds significant potential for solving strongly nonlinear differential equations which arise frequently in fluid dynamics. The regime studied is shown to be controlled by the slip parameter (γ), magnetohydrodynamic body force parameter (M), Eckert (viscous heating) number (Ec), Schmidt number (Sc), Soret number (Sr), Dufour number (Du) and Prandtl number (Pr). The influence of selected parameters on the evolution of dimensionless velocity, temperature and concentration distributions is studied graphically. Increasing magnetic field (M) is found to significantly inhibit the radial (f) and tangential (g) velocities, but to accentuate the axial velocity field (h); furthermore temperature (θ) and concentration (φ) are both enhanced with increasing M. Increasing Soret number (Sr) acts to boost the dimensionless concentration (φ). Temperatures are significantly elevated in the boundary layer regime with a rise in Eckert number (Ec). Excellent correlation between the DTM-Pade technique and numerical (shooting) solutions is achieved. The model has important applications in industrial energy systems, process mechanical engineering, electromagnetic materials processing and electro-conductive chemical transport processes.

10.2478/s11814-009-0158-y

The Dufour and Soret effects on the unsteady laminar free convective flow with mass transfer flow past a semi-infinite isothermal vertical cylinder were studied numerically. The governing partial differential equations were converted into a non-dimensional form and solved numerically by applying a Crank-Nicolson type of implicit finite-difference method with a tri-diagonal matrix manipulation and an iterative procedure. For the hydrogen-air mixture, which is a non-chemical reacting fluid, the profiles of the unsteady dimensionless velocity, temperature and concentration are shown graphically for the different values of thermal and mass Grashof numbers, thermal diffusion parameters (Soret numbers) and diffusion-thermo parameters (Dufour numbers). Finally, the simulated values of the average skin-friction coefficient, the average Nusselt number and the average Sherwood number are presented. The numerical results reveal that for an increasing Soret number or decreasing Dufour number, the time to reach the temporal maximum and the steady-state decreases for the flow variables. As the Soret number increases or the Dufour number decreases, both the skin friction and the Sherwood number increase, whereas the Nusselt number decreases.

Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects

An analysis is presented for the steady free convection heat and mass transfer from a spherical body in a micropolar fluid with Soret/Dufour effects included. The governing boundary layer equations are transformed into a non-dimensional form and the resulting non-linear system of partial differential equations are solved using the efficient Keller-box implicit numerical finite difference method. Excellent correlation of the present numerical solutions is achieved for the case of free convection micropolar flow neglecting Sort/Dufour effects, with the earlier study by Nazar et al. (2002) [12]. With increasing Soret number, the local Nusselt number is boosted considerably, with the converse response with an increase in Dufour number. Increasing micropolar vortex viscosity parameter ( K) decelerates the flow near the sphere surface but serves to accelerate the flow further from the sphere wall. With increasing K, reverse spin is induced of the micro-elements near the sphere surface. Temperature is strongly boosted throughout the boundary layer regime with increasing K with a similar response computed for the species concentration Buoyancy-assistance ( N > 0) accelerates the flow whereas buoyancy-opposition ( N < 0) retards flow. Reverse spin of micro-elements (i.e. negative micro-rotation) is reduced near the sphere surface with buoyancy-opposition but exacerbated with buoyancy-assistance. Buoyancy-assistance serves to depress both temperature and concentration values through the boundary layer regime with the reverse effect sustained with buoyancy-opposition. An increase in Schmidt number acts to strongly inhibit the flow and also to stifle micro-rotation of the micro-elements. Conversely both temperatures and concentration values are accentuated with increasing Schmidt number. The study has important applications in buoyancy-driven, chemical engineering flow regimes.

A numerical study of the Dufour and Soret effects on unsteady natural convection flow past an isothermal vertical cylinder

The Dufour and Soret effects on the unsteady laminar free convective flow with mass transfer flow past a semi-infinite isothermal vertical cylinder were studied numerically. The governing partial differential equations were converted into a non-dimensional form and solved numerically by applying a Crank-Nicolson type of implicit finite-difference method with a tri-diagonal matrix manipulation and an iterative procedure. For the hydrogen-air mixture, which is a non-chemical reacting fluid, the profiles of the unsteady dimensionless velocity, temperature and concentration are shown graphically for the different values of thermal and mass Grashof numbers, thermal diffusion parameters (Soret numbers) and diffusion-thermo parameters (Dufour numbers). Finally, the simulated values of the average skin-friction coefficient, the average Nusselt number and the average Sherwood number are presented. The numerical results reveal that for an increasing Soret number or decreasing Dufour number, the time to reach the temporal maximum and the steady-state decreases for the flow variables. As the Soret number increases or the Dufour number decreases, both the skin friction and the Sherwood number increase, whereas the Nusselt number decreases.

Soret effect on propagation of thermoconvective waves in a binary mixture

Effects of thermal diffusion (Soret effect) on the propagation of thermoconvective waves (TCW) in a layer of binary mixture are investigated. It is shown that undamped propagation of TCW is possible in a layer heated from below provided the Soret number is large and positive. A novel result of the analysis is that for a layer heated from below, TCW which are strongly damped in the absence of thermal diffusion may propagate almost undamped in the low frequency limit in the presence of thermal diffusion for some negative value of Soret number. It is further shown that for a layer heated from above such that the solute concentration increases vertically upward, weakly damped propagation of TCW in the low frequency limit is inhibited with increase in Soret number.