What is dufour effect

The Soret effect, for instance, has been utilized for isotope separation, and in mixtures between gases with very light molecular weight H 2 , He. For medium molecular weight N 2 , air , the Dufour effect was found to be of a considerable magnitude such that it cannot be neglected Eckert and Drake [ 4 ]. Kassoy and Zebib [ 5 ] studied the effect of variable viscosity on the onset of convection in porous medium.

Cheng and Minkowycz [ 6 ] studied the effect of free convection about a vertical plate embedded in a porous medium with application to heat transfer from a dike. Bejan and Khair [ 7 ] studied the buoyancy-induced heat and mass transfer from a vertical plate embedded in a saturated porous medium. Lai and Kulacki [ 8 ] studied the coupled heat and mass transfer by natural convection from vertical surface in a porous medium.

The same authors [ 9 ] also studied the effect of variable viscosity on convection heat transfer along a vertical surface in a saturated porous medium. Elbashbeshy and Ibrahim [ 10 ] investigated the effect of steady free convection flow with variable viscosity and thermal diffusivity along a vertical plate.

Kafoussias and Williams [ 11 ] studied the thermal-diffusion and diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary layer flow, over a vertical plate, with temperature-dependent viscosity. Yih [ 12 ] analyzed the coupled heat and mass transfer in mixed convection about a wedge for variable wall temperature and concentration.

Jumah and Mujumdar [ 13 ] studied the coupled heat and mass transfer for non-Newtonian fluids. Anghel et al. Kumari [ 15 ] analyzed the effect of variable viscosity on free and mixed convection boundary layer flow from a horizontal surface in a saturated porous medium.

Postelnicu et al. Seddeek [ 17 ], Seddeek and Salem [ 18 ] studied the effects of chemical reaction, variable viscosity, and thermal diffusivity on mixed convection heat and mass transfer through porous media.

Ali [ 19 ] studied the effect of variable viscosity on mixed convection along a vertical plate. Alam et al. Pantokratoras [ 21 ] analyzed the effect of variable viscosity with constant wall temperature.

Partha et al. Alam and Rahman [ 23 ] studied the Dufour and Soret effects on mixed convective flow past a vertical porous plate with variable suction. Seddeek et al. Another contribution to the theme of Dufour and Soret effects can be found in the paper by Afify [ 25 ], where there is a non-Darcy free convection past a vertical surface with temperature viscosity.

Narayana and Murthy [ 26 ] studied the Soret and Dufour effects in a doubly stratified Darcy porous medium. Singh and Chandarki [ 28 ] used integral treatment to obtain the expressions for Nusselt number and Sherwood number. El-Arabawy [ 29 ] studied the Soret and Dufour effects in a vertical plate with variable surface temperature. Postelnicu [ 30 ] analyzed the effect of Soret and Dufour on heat and mass transfer at a stagnation point. Tak et al. Recently, Cheng [ 33 ] studied the Soret and Dufour on heat and mass transfer on a vertical truncated cone with variable wall temperature and concentration.

The aim of this paper is to study the effect of Soret and Dufour on heat and mass transfer by natural convection from a vertical plate with variable viscosity. Consider a vertical surface embedded in a saturated porous medium. The properties of the fluid and porous medium are isotropic, and the viscosity of the fluid is assumed to be an inverse linear function of temperature. In this case, the effect of variable viscosity can be neglected.

Equations 3. The value of Prandtl number Pr is taken equal to 0. The values of the Dufour number and Soret number are taken in such a way that their product is constant according to their definition provided that the mean temperature is kept constant as well. Figure 1 shows that as Dufour number increases, the velocity decreases slightly for decrease in Soret number. From Figure 2 , it is evident that as Dufour number increases, the temperature increases for decrease in Soret number.

Figure 3 shows that as Dufour number increases, the concentration decreases for decrease in Soret number. From Figures 12 and 13 , it is evident that as the Prandtl number increases, the velocity and temperature increase. Figure 14 shows that as the prandtl number increases, the concentrations decrease. The Dufour and Soret effect on free convective heat and mass transfer flow past a semi-infinite vertical plate under the influence of variable viscosity has been studied.

For the stable branches, the quantities , , and decrease by increasing the permeability of the porous medium. Similar behaviors were reported in previous studies [ 5 , 36 ]. Note that the variations versus of the flow intensity corresponding to the unstable branches are remarkably strong in specific ranges of the latter parameter.

However, the effect of on and corresponding to the unstable branches is clearly much less important. For the combinations 0. For these regions 2 and 3 can be computed analytically by solving the following equation:. For the combinations , 0. Note that the bifurcation around is supercritical for regions 2 and 3 and subcritical for regions 4, 5, and 6 results not reported here.

For regions 4, 5, and 6, can be computed analytically by solving the following equation: with. For the combination , a singularity is registered in the curve of at the critical Darcy number , as can be seen in Figure 9 b. For the latter combination, the term that represents the inverse of the Nusselt number is zero for , leading to an infinite value for.

This means that, for , the Dufour heat flux induced by the concentration gradient compensates the ordinary heat flux induced by the temperature gradient. Such a compensation is not observed for the mass transfer as and.

For the particular combination , induced by the unstable branch in its existence range is higher than that induced by the stable branch see behavior in the vicinity of. Note that and induced by the stable branches are larger than those corresponding to unstable branches for all the combinations considered in Figures 9 a — 9 b. Combined effects of Soret and Dufour parameters on thermosolutal convection in shallow horizontal Brinkman porous enclosures with stress-free upper surfaces is evaluated analytically and numerically.

The analytical results obtained using the parallel flow assumption are validated numerically by solving the full governing equations.

The thresholds marking the onset of stationary and finite amplitude convection are determined analytically according to the control parameters. The analytical study shows that the plane can be divided into up to six regions corresponding to different parallel flow regimes.

The number, the location, and the extent of these regions are strongly controlled by Dufour and Soret numbers. Depending on the value of the Soret number, the Dufour effect may affect considerably the fluid flow and heat and mass transfer characteristics. By analyzing the effect of on , , and for various , we observe the existence of critical nodes small ranges of for which these quantities are quasi-independent of. These nodes did not correspond to the same range of for , , and.

This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Sergey A. Received 12 Nov Revised 18 Jan Accepted 24 Jan Published 31 Mar Abstract In this paper, thermo-diffusion Soret effect and diffusion-thermo Dufour effect effects on double-diffusive natural convection induced in a horizontal Brinkman porous layer with a stress-free upper boundary are investigated.

Introduction Natural convection involving binary mixtures in the porous and fluid media is still a relevant field of investigation since it occurs in wide ranges of applications in many engineering problems and natural fields such as geophysics, oil reservoirs, storage of nuclear wastes, operation of solar ponds, chemical reactors, migration of mixtures in fibrous insulation, and metal manufacturing processes.

Mathematical Formulation of the Problem The domain under study, sketched in Figure 1 , is a two-dimensional horizontal porous cavity saturated with a binary mixture.

Figure 1. Mesh Analytical results. Table 1. Effect of the grid size for , , , , and. Figure 2. Delimitation of the regions corresponding to different behaviors for.

Figure 3. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. Temperature a and concentration b profiles along y at midwidth of the cavity for , , , and. Figure 9. References I. Huppert and J.

Rehberg and G. Mamou and P. Amahmid, M. Hasnaoui, M. Mamou, and P. Hussain, H. Jamal, and N. Sharma, P. Kumar Bharti, and R. Shah, I. Animasaun, R. Ibraheem, H. Babatunde, N. Sandeep, and I. Blanco, P. Polyakov, M. Bou-Ali, and S. Van Vaerenbergh and J. Yacine, A. Mojtabi, R. Bennacer, and A. Rtibi, M. Hasnaoui, and A.

Elhajjar, A. Mojtabi, P. Bourich, M. Hasnaoui, A. Amahmid, and M. Mamou, and A. Amahmid, A. Raji et al. Ojjela, A. Raju, and N. Zhao, L. Zheng, X. Zhang, and F. Wang, M. Yang, Y. He, and Y. Ren and C. Balla and K. Al-Mudhaf, A. Rashad, S. Ahmed, A. Chamkha, and S. Cormack, L. Leal, and J. Part 2. Abstract: The present article examines Soret and Dufour effects on the three-dimensional mixed convective flow of an Oldroyd-B nanoliquid.

Besides, concentration and thermal buoyancy impacts are inspected. The velocity slip, convective and zero nanoparticle mass flux boundary condition at the surface are taken into account.

Nonlinear system of equations which are highly coupled is solved via optimal homotopy algorithm. The influence of pertinent parameters on velocity, temperature, and concentration are analyzed graphically.

The impact of Dufour number is quite substantial on temperature whereas Soret number increases the concentration. To see the legitimacy of the present work, the present results are compared with the results available in the literature and noted an excellent agreement for the limiting cases. Sivasankaran, Oluwole Daniel Makinde. The governing time-dependent partial differential equations are transformed into non-linear ordinarydifferential equations using similarity transformations.

These equations subject to the appropriate boundary conditions are solved analytically by homotopy analysis method HAM and numerically by Runge-Kutta fourth order method and shooting technique. The numerical solution is compared with analytical solution. The influence of the different parameters on velocity, temperature and concentration profiles are discussed in graphical as well as in tabular form.

Abstract: The combined effects diffusion-thermo, chemical reaction, buoyancy forces, radiative heat flux, velocity slip and magnetic field on an unsteady hydromagnetic mixed convective flow of an electrically conducting fluid with heat and mass transfer over an inclined vertical porous plate embedded in a porous medium is studied. The imposed thermal boundary conditions include prescribed uniform plate surface temperature PST and prescribed heat flux PHF.

The governing equations are solved analytically with the help of two term perturbation technique. The influence of various thermophysical parameters on the fluid velocity, temperature and species concentration are presented graphically while numerical values of skin friction, Nusselt and Sherwood numbers are presented in tabular form for different values and discussed. A special case of our results show excellent agreement with the earlier results in the literature.

Authors: Machireddy Gnaneswara Reddy, B. Prasanna Kumara, Oluwole Daniel Makinde. Abstract: The hydromagnetic peristaltic motion of Carreau and Casson nanofluids flow in an irregular channel in the presence of diffusion thermo Soret and thermo diffusion Dufour impacts has been examined. The effect of thermal radiation is incorporated in the energy equation and velocity slip included in the boundary conditions. The dimensionless governing equations for the flow, fluid temperature and nanoparticle concentration are acquired for the suppositions of low Reynolds number and large wavelength.

Resulting flow problem has been solved numerically. Outcome of emerging sundry variables on these three flow profiles are graphically analyzed. Axial velocity enhances near the walls of the irregular channel to the mounting values of Hartmann number where as the velocity declines in the central part of the irregular channel.

Temperature magnifies considerably with the boosting values of Dufour number. Impact of Soret number decays concentration. Also, a comparative study is made for the numerical results of axial velocity with the existing reports.