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Sorét and Dufour effects on natural convection flow past a vertical surface in a porous medium with variable viscosity. (English) Zbl 1235.76180
Summary: The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subject to variable viscosity are numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Sorét) effects. The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. The parameters of the problem are variable viscosity, buoyancy ratio, Lewis number, Prandtl number, Dufour effect, Sorét effect, and Schmidt number. The velocity, temperature, and concentration distributions are presented graphically. The Nusselt number and Sherwood number are also derived and discussed numerically.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76R10 Free convection 80A20 Heat and mass transfer, heat flow (MSC2010)
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##### References:
 [1] I. Pop. and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford, UK, 2001. [2] D. B. Ingham and I. Pop, Transport Phenomena in Porous Media III, Elsevier, Oxford, UK, 2005. [3] K. Vafai, Handbook of Porous Media, Taylor and Francis, New York, NY, USA, 2nd edition, 2005. · Zbl 1315.76005 [4] E. R. G. Eckert and R. M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill, New York, NY, USA, 1972. · Zbl 0247.76079 [5] D. R. Kassoy and A. Zebib, “Variable viscosity effects on the onset of convection in porous media,” Physics of Fluids, vol. 18, no. 12, pp. 1649-1651, 1975. · Zbl 0319.76067 · doi:10.1063/1.861083 [6] P. Cheng and W. J. Minkowycz, “Free convection about a vertical plate embedded in a porous medium with application to heat transfer from a dike,” Journal of Geophysical Research, vol. 82, no. 14, pp. 2040-2044, 1977. · doi:10.1029/JB082i014p02040 [7] A. Bejan and K. R. Khair, “Heat and mass transfer by natural convection in a porous medium,” International Journal of Heat and Mass Transfer, vol. 28, no. 5, pp. 909-918, 1985. · Zbl 0564.76085 · doi:10.1016/0017-9310(85)90272-8 [8] F. C. Lai and F. A. Kulacki, “The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium,” International Journal of Heat and Mass Transfer, vol. 33, no. 5, pp. 1028-1031, 1990. · doi:10.1016/0017-9310(90)90084-8 [9] F. C. Lai and F. A. Kulacki, “Coupled heat and mass transfer by natural convection from vertical surfaces in porous media,” International Journal of Heat and Mass Transfer, vol. 34, no. 4-5, pp. 1189-1194, 1991. · doi:10.1016/0017-9310(91)90027-C [10] E. M. A. Elbashbeshy and F. N. Ibrahim, “Steady free convection flow with variable viscosity and thermal diffusivity along a vertical plate,” Journal of Physics D, vol. 26, no. 12, pp. 2137-2143, 1993. · doi:10.1088/0022-3727/26/12/007 [11] N. G. Kafoussias and E. W. Williams, “Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity,” International Journal of Engineering Science, vol. 33, no. 9, pp. 1369-1384, 1995. · Zbl 0899.76325 · doi:10.1016/0020-7225(94)00132-4 [12] K. A. Yih, “Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and concentration in porous media: the entire regime,” International Communications in Heat and Mass Transfer, vol. 25, no. 8, pp. 1145-1158, 1998. · doi:10.1016/S0735-1933(98)00105-5 [13] R. Y. Jumah and A. S. Mujumdar, “Free convection heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical flat plate in saturated porous media,” International Communications in Heat and Mass Transfer, vol. 27, no. 4, pp. 485-494, 2000. · doi:10.1016/S0735-1933(00)00131-7 [14] M. Anghel, H. S. Takhar, and I. Pop, Dufour and Soret Effects on Free Convection Boundary Layer Over a Vertical Surface Embedded in a Porous Medium, Studia Universitatis Babes-Bolyai, 2000, Mathematica XLV: 11-22. · Zbl 1027.76050 [15] M. Kumari, “Variable viscosity effects on free and mixed convection boundary-layer flow from a horizontal surface in a saturated porous medium-variable heat flux,” Mechanics Research Communications, vol. 28, no. 3, pp. 339-348, 2001. · Zbl 0980.76535 · doi:10.1016/S0093-6413(01)00182-3 [16] A. Postelnicu, T. Grosan, and I. Pop, “The effect of variable viscosity on forced convection flow past a horizontal flat plate in a porous medium with internal heat generation,” Mechanics Research Communications, vol. 28, no. 3, pp. 331-337, 2001. · Zbl 0980.76536 · doi:10.1016/S0093-6413(01)00181-1 [17] M. A. Seddeek, “Finite element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/ absorption on a boundary layer hydro magnetic flow with heat and mass transfer over a heat surface,” Acta Mechanica, vol. 177, pp. 1-18, 2005. · Zbl 1085.76040 · doi:10.1007/s00707-005-0249-8 [18] M. A. Seddeek and A. M. Salem, “Laminar mixed convection adjacent to vertical continuously stretching sheets with variable viscosity and variable thermal diffusivity,” International Journal of Heat and Mass Transfer, vol. 41, no. 12, pp. 1048-1055, 2005. · doi:10.1007/s00231-005-0629-6 [19] M. E. Ali, “The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface,” International Journal of Thermal Sciences, vol. 45, no. 1, pp. 60-69, 2006. · doi:10.1016/j.ijthermalsci.2005.04.006 [20] M. S. Alam, M. M. Rahman, and M. A. Samad, “Numerical study of the combined free-forced convection and Mass transfer flow past a vertical porous plate in a porous medium with heat generation and thermal diffusion,” Non linear Analysis Modeling and Control, vol. 11, no. 4, pp. 331-343, 2006. · Zbl 1125.76389 [21] A. Pantokratoras, “The Falkner-skan flow with constant wall temperature and variable viscosity,” International Journal of Thermal Sciences, vol. 45, no. 4, pp. 378-389, 2006. · doi:10.1016/j.ijthermalsci.2005.06.004 [22] M. K. Partha, P. V. S. N. Murthy, and G. P. R. Sekhar, “Soret and Dufour effects in a non-Darcy porous medium,” Journal of Heat Transfer, vol. 128, no. 6, pp. 605-610, 2006. · doi:10.1115/1.2188512 [23] M. S. Alam and M. M. Rahman, “Dufour and Soret effects on mixed convection flow past a vertical porous flat plate with variable suction,” Nonlinear Analysis: Modelling and Control, vol. 11, no. 1, pp. 3-12, 2006. · Zbl 1109.76057 [24] M. A. Seddeek, A. A. Darwish, and M. S. Abdelmeguid, “Effect of chemical reaction and variable viscosity on hydro magnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, pp. 195-213, 2007. · Zbl 1106.35328 · doi:10.1016/j.cnsns.2006.02.008 [25] A. Afify, “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,” Applied Mathematical Modelling, vol. 31, pp. 1621-1634, 2007. · Zbl 1130.76075 · doi:10.1016/j.apm.2006.05.002 [26] P. A. L. Narayana and P. V. S. N. Murthy, “Soret and dufour effects on free convection heat and mass transfer in a doubly stratified darcy porous medium,” Journal of Porous Media, vol. 10, no. 6, pp. 613-623, 2007. · doi:10.1615/JPorMedia.v10.i6.70 [27] A. Postelnicu, “Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects,” Heat and Mass Transfer, vol. 43, no. 6, pp. 595-602, 2007. · doi:10.1007/s00231-006-0132-8 [28] B. B. Singh and I. M. Chandarki, “Integral treatment of coupled heat and mass transfer by natural convection from a cylinder in porous media,” International Communications in Heat and Mass Transfer, vol. 36, no. 3, pp. 269-273, 2009. · doi:10.1016/j.icheatmasstransfer.2008.11.007 [29] H. A. M. El-Arabawy, “Soret and dufour effects on natural convection flow past a vertical surface in a porous medium with variable surface temperature,” Journal of Mathematics and Statistics, vol. 5, no. 3, pp. 190-198, 2009. · Zbl 1423.80018 · doi:10.3844/jmssp.2009.190.198 [30] A. Postelnicu, “Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects,” Heat and Mass Transfer, vol. 46, no. 8-9, pp. 831-840, 2010. · doi:10.1007/s00231-010-0633-3 [31] S. S. Tak, R. Mathur, R. K. Gehlot, and A. Khan, “MHD free convection-radiation interaction along a vertical surface embedded in darcian porous medium in presence of soret and Dufour’s effects,” Thermal Science, vol. 14, no. 1, pp. 137-145, 2010. · doi:10.2298/TSCI1001137T [32] S. R. Vempati and A. B. Laxmi-Narayana-Gari, “Soret and Dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation,” Applied Mathematics and Mechanics, vol. 31, no. 12, pp. 1481-1496, 2010. · Zbl 1275.76226 · doi:10.1007/s10483-010-1378-9 [33] C. Y. Cheng, “Soret and Dufour effects on heat and mass transfer by natural convection from a vertical truncated cone in a fluid-saturated porous medium with variable wall temperature and concentration,” International Communications in Heat and Mass Transfer, vol. 37, no. 8, pp. 1031-1035, 2010. · doi:10.1016/j.icheatmasstransfer.2010.06.008 [34] J. X. Ling and A. Dybbs, “Forced convection over a flat plate submersed in a porous medium: variable viscosity case,” in Proceedings of the American Society of Mechanical Engineers, New York, NY, USA, 1987, ASME paper 87-WA/HT-23.
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