Abstract
The double-diffusive natural convection past a vertical plate embedded in a fluid-saturated porous medium is considered in the boundary-layer and Boussinesq approximations. It is assumed that the Soret–Dufour cross-diffusion effects are significant. The heat and mass fluxes on the plate are prescribed as functions of the surface coordinate x. The general similarity reduction of the problem for power-law and exponential variation of the wall fluxes is given. In the case of thermosolutal symmetry, when the similar temperature and concentration fields become coincident, exact analytical as well as numerical solutions are reported and discussed in some detail. For the flows without thermosolutal symmetry, the final similarity equations have been solved numerically, by paying attention to the influence of the Soret and Dufour numbers on the departure from thermosolutal symmetry. The reported results focus on the wall temperatures and concentrations, whose reciprocals are Nusselt and Sherwood numbers, respectively.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions. Dover, New York (1972)
Afify A.: Effects of temperature-dependent viscosity with Soret and Dufour numbers on non-Darcy MHD free convective heat and mass transfer past a vertical surface embedded in a porous medium. Transp. Porous Media 66, 391–401 (2007a)
Afify A.: Effects of thermal-diffusion and diffusion-thermo on non-Darcy MHD free convective heat and mass transfer past a vertical isothermal surface embedded in a porous medium with thermal dispersion and temperature-dependent viscosity. Appl. Math. Model. 31, 1621–1634 (2007b)
Anghel M., Takhar H.S., Pop I.: Dufour and Soret effects on free convection boundary-layer over a vertical surface embedded in a porous medium. Studia Universitatis Babes-Bolyai Mathematica XLV 11(22), 11–22 (2000)
Benano-Melly L.B., Caltagirone J.P., Faissat B., Montel F., Costeseque P.: Modelling Soret coefficient measurement experiments in porous media considering thermal and solutal convection. Int. J. Heat Mass Transf. 44, 1285–1297 (2001)
Chamkha A.J., Ben-Nakhi A.: MHD mixed convection–radiation interaction along a permeable surface immersed in a porous medium in the presence of Soret and Dufour’s effects. Heat Mass Transf. 44, 845–856 (2008)
Cheng C.-Y.: Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium. Int. Commun. Heat Mass Transf. 36, 1020–1024 (2009)
Eckert E.R.G., Drake R.M.: Analysis of heat and mass transfer. McGraw-Hill, New York (1972)
Gaikwad S.N., Malashetty M.S., Rama Prasad K.L.: Linear and non-linear double diffusive convection in a fluid-saturated anisotropic porous layer with cross-diffusion effects. Transp. Porous Media 80, 537–560 (2009)
Johnson C.H., Cheng P.: Possible similarity solutions for free convection boundary-layers adjacent to flat plates in porous media. Int. J. Heat Mass Transf. 21, 709–718 (1978)
Kafoussias N.G., Williams E.W.: Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity. Int. J. Eng. Sci. 33, 1369–1384 (1995)
Lakshmi Narayana P.A., Murthy P.V.S.N.: Soret and Dufour effects in a doubly stratified Darcy porous medium. J. Porous Media 10, 613–624 (2007)
Lakshmi Narayana P.A., Murthy P.V.S.N.: Soret and Dufour effects on free convection heat and mass transfer from a horizontal flat plate in a Darcy porous medium. J. Heat Transf. Trans. ASME 130, 104504–11045045 (2008)
Li M., Tia Y., Zhai Y.: Soret and Dufour effects in strongly endothermic chemical reaction system of porous media. Trans. Nonferrous Met. Soc. China 16, 1200–1204 (2008)
Mojtabi A., Charrier-Mojtabi M.C.: Double-diffusive convection in porous media. In: Vafai, K. (ed.) Handbook of Porous Media, pp. 559–603. Marcel Dekker, New York (2000)
Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)
Partha M.K., Murth P.V.S.N., Raja Sekhar G.P.: Soret and Dufour effects in a non-Darcy porous medium. J. Heat Transf. Trans. ASME 128, 605–610 (2006)
Platten J.K., Legros J.C.: Convection in liquids. Springer, New York (1984)
Postelnicu A.: Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Int. J. Heat Mass Transf. 47, 1467–1472 (2004)
Postelnicu A.: Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat Mass Transf. 43, 595–602 (2007)
Postelnicu A.: Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects. Heat Mass Transf. 46, 831–840 (2010)
Rathish Kumar, B.V., Krishna Murthy, S.V.S.S.N.V.G.: Soret and Dufour effects on double-diffusive free convection from a corrugated vertical surface in a non-Darcy porous medium. Transp. Porous Media (2010). doi:10.1007/s11242-010-9549-0 (online)
Saghir M.Z., Jiang C.G., Chacia M., Yan Y., Khawaja M., Pan S.: Thermodiffusion in porous media. In: Ingham, D., Pop , I. (eds) Transport Phenomena in Porous Media III, Chap. 9, Pergamon, Oxford (2005)
Soret C.: Influence de la temperature sur la distribution des sels dans leurs solutions. C.R. Acad. Sci. Paris 91, 289–291 (1880)
Tsai R., Huang J.S.: Heat and mass transfer for Soret and Dufour’s effects on Hiemenz flow through porous medium onto a stretching surface. Int. J. Heat Mass Transf. 52, 2399–2406 (2009a)
Tsai R., Huang J.S.: Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes. Comp. Mat. Sci. 47, 23–30 (2009b)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Magyari, E., Postelnicu, A. Double-Diffusive Natural Convection Flows with Thermosolutal Symmetry in Porous Media in the Presence of the Soret–Dufour Effects. Transp Porous Med 88, 149–167 (2011). https://doi.org/10.1007/s11242-011-9731-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-011-9731-z