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Received September 10, 2014
Accepted November 4, 2014
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Chemical reaction effect on double diffusive convection in porous media with magnetic and variable gravity effects
Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq 1Petroleum department, College of Engineering, University of Misan, Misan, Iraq
akilharfash@gmail.com
Korean Journal of Chemical Engineering, June 2015, 32(6), 1046-1059(14), 10.1007/s11814-014-0327-5
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Abstract
We study the problem of double diffusive convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated porous medium and subjected to a vertical magnetic field. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. Then, the accuracy of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. The strong stabilizing effect of gravity field and magnetic field is shown. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.
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References
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Ganesan P, Suganthi RK, Korean J. Chem. Eng., 30(4), 813 (2013)
Hwang IG, Korean J. Chem. Eng., 30(5), 1023 (2013)
Kim MC, Korean J. Chem. Eng., 30(4), 831 (2013)
Kim MC, Korean J. Chem. Eng., 30(6), 1207 (2013)
Kim MC, Choi CK, Int. J. Heat Mass Transf., 71, 313 (2014)
Liu Q, Shen D, Xiao R, Zhang H, Fang M, Korean J. Chem. Eng., 30(3), 613 (2013)
Lungu M, Sun J, Wang J, Zhu Z, Yang Y, Korean J. Chem. Eng., 31(7), 1148 (2014)
Nield DA, Kuznetsov AV, Transp. Porous Media, 98(3), 713 (2013)
Nield DA, Kuznetsov AV, Transp. Porous Media, 100(1), 83 (2013)
Kuznetsov AV, Nield DA, Transp. Porous Media, 100(1), 101 (2013)
Nield DA, Kuznetsov AV, Transp. Porous Media, 102(1), 1 (2014)
Kuznetsov AV, Nield DA, Transp. Porous Media, 102(1), 15 (2014)
Sharma N, Dhiman A, Kumar S, Korean J. Chem. Eng., 31(5), 754 (2014)
Shojaeian M, Shojaee SMN, Korean J. Chem. Eng., 30(4), 823 (2013)
Harfash AJ, Ricerche Mater., 63, 1 (2014)
Harfash AJ, Ann. Henri Poincare, 10.1007/s00023-013-0307-z (2014)
Harfash AJ, Anal. Math. Phys., 3, 163 (2013)
Harfash AJ, Transp. Porous Media, 103(3), 361 (2014)
Harfash AJ, Transp. Porous Media, 10.1007/s11242-014-0394-4 (2014)
Jena SK, Mahapatra SK, Sarkar A, Transp. Porous Media, 98(1), 103 (2013)
Chen B, Cunningham A, Ewing R, Peralta R, Visser E, Numerical Methods for PDEs, 10, 65 (1994)
Suchomel BJ, Chen BM, Allen MB, Transp. Porous Media, 30(1), 1 (1998)
Curran MC, Allen MB, Adv. Water Resour., 13, 70 (1990)
Ewing RE, Weekes S, Numerical methods for contaminant transport in porous media, Marcel Decker, New York, 202, 75 (1998). (1998)
Franchi F, Straughan B, Adv. Water Res., 24, 585 (2001)
Ludvigsen A, Palm E, McKibbin R, J. Geophys. Res., 97, 12315 (2001)
Gilman A, Bear J, Transp. Porous Media, 23(3), 275 (1996)
Ni J, Beckerma C, Smith TF, Effect of an electromagnetic field on natural convection in porous medium, Fundam Heat Transf Electromagn Electrost Acoust Field ASME HTD (1993). (1993)
Patil PM, Kulkarni PS, Int. J. Therm. Sci., 47, 1043 (2008)
Ibrahim FS, Elaiw AM, Bakr AA, Communications in Nonlinear Science and Numerical Simulation, 13, 1056 (2008)
Straughan B, The energy method, stability, and nonlinear convection, Springer, Series in Applied Mathematical Sciences, 91, 2nd Ed. (2004). (2004)
Harfash AJ, Int. J. Eng. Sci., 74, 91 (2014)
Harfash AJ, Transp. Porous Media, 101(2), 281 (2014)
Harfash AJ, Appl. Math. Comput., 227, 92 (2014)
Harfash AJ, Transp. Porous Media, 102(1), 43 (2014)
Harfash AJ, Acta Mechanica Sinica, 30, 144 (2014)
Harfash AJ, Int. J. Numer. Methods Fluids (2014)
Harfash AJ, J. Non-Equilib. Thermodym., 10.1515/jnet-2014-0009 (2014)
Harfash AJ, Alshara AK, J. Hydrodynamics (2014)
Harfash AJ, Hill AA, Int. J. Heat Mass Transf., 72, 609 (2014)
Galdi GP, Straughan B, Arch. Rational Mech. Anal., 89, 211 (1985)
Roberts PH, An introduction to magnetohydrodynamics, Longman, London (1967). (1967)
Fabrizio M, Morro A, Electromagnetism of continuous media, Oxford University Press, Oxford (2003). (2003)
Chandrasekhar S, Hydrodynamic and hydromagnetic stability, Dover, New York (1981). (1981)
Straughan B, Harfash AJ, Microfluid Nanofluid, 15, 109 (2013)
