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Received December 29, 2014
Accepted January 23, 2015
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Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media
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, October 2015, 32(10), 1970-1985(16), 10.1007/s11814-015-0020-3
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Abstract
A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source and subjected to a vertical magnetic field and variable gravity effect. The validity of both the linear instability and global nonlinear stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good prediction on the onset of instability in the steady state throughflow. It is known that as Rc increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as Rc increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.
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References
Harfash AJ, Transp. Porous Media, 103(3), 361 (2014)
Harfash AJ, Transp. Porous Media, :10.1007/s11242-014-0394-4. (2014)
Harfash AJ, Alshara AK, Korean J. Chem. Eng., 10.1007/s11814-014-0327-5. (2015)
Nield DA, Bejan A, Convection in Porous Media, 4th Ed., Springer-Verlag, New York (2013).
Nield DA, AIChE J., 33, 1222 (1987)
Shivakumara IS, Acta Mech., 37, 151 (1999)
Shivakumara IS, Nanjundappa CE, Archives of Mechanics, 53, 1 (2001)
Khalili A, Shivakumara IS, Transp. Porous Media, 53(3), 245 (2003)
Nield DA, The stability of convective flows in porous media, In: Convective heat and mass transfer in porous media (Kakas S, et al., Eds.) 196, 79 (1990).
Rudraiah N, Shivakumara IS, Friedrich R, Int. J. Heat Mass Transf., 29, 1301 (1986)
Shivakumara IS, Further results on double diffusive magnetoconvection, In: Recent advances in fluid mechanics (Sachdev PL, Venkatachalappa M, Eds.), Gordon and Breach (1995).
Shivakumara IS, Suma SP, Acta Mech., 140, 207 (2000)
Shivakumara IS, Khalili A, Acta Mech., 152, 165 (2001)
Shivakumara IS, Sureshkumar S, J. Geophys. Eng., 4, 104 (2007)
Nield DA, Kuznetsov AV, Transp. Porous Media, 87(3), 765 (2011)
Hill AA, Rionero S, Straughan B, IMA J. Appl. Math., 72, 635 (2007)
Harfash AJ, Hill AA, Int. J. Heat Mass Transf., 72, 609 (2014)
Straughan B, The energy method, stability, and nonlinear convection, Applied Mathematical Sciences, Second Ed., 91, Springer (2004).
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, 102(1), 1 (2014)
Nield DA, Kuznetsov AV, Transp. Porous Media., 102, 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)
Straughan B, Microfluid Nanofluid, 16, 361 (2014)
Straughan B, Acta Appl. Math., 10.1007/s10440-014-9930-z. (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, J. Non-Equilib. Thermodyn., 10.1515/jnet-2014-0009. (2014)
Galdi GP, Straughan B, Arch. Rational Mech. Anal., 89, 211 (1985)
Roberts PH, An introduction to magnetohydrodynamics, Longman, London (1967).
Fabrizio M, Morro A, Electromagnetism of continuous media, Oxford University Press, Oxford (2003).
Joseph DD, Arch. Rational Mech. Anal., 35, 169 (1969)
Harfash AJ, Stability analysis for penetrative convection in a fluid layer with throughflow, Submited to European J. Mech. - B/Fluids.
Harfash AJ, Transp. Porous Media, :10.1007/s11242-014-0394-4. (2014)
Harfash AJ, Alshara AK, Korean J. Chem. Eng., 10.1007/s11814-014-0327-5. (2015)
Nield DA, Bejan A, Convection in Porous Media, 4th Ed., Springer-Verlag, New York (2013).
Nield DA, AIChE J., 33, 1222 (1987)
Shivakumara IS, Acta Mech., 37, 151 (1999)
Shivakumara IS, Nanjundappa CE, Archives of Mechanics, 53, 1 (2001)
Khalili A, Shivakumara IS, Transp. Porous Media, 53(3), 245 (2003)
Nield DA, The stability of convective flows in porous media, In: Convective heat and mass transfer in porous media (Kakas S, et al., Eds.) 196, 79 (1990).
Rudraiah N, Shivakumara IS, Friedrich R, Int. J. Heat Mass Transf., 29, 1301 (1986)
Shivakumara IS, Further results on double diffusive magnetoconvection, In: Recent advances in fluid mechanics (Sachdev PL, Venkatachalappa M, Eds.), Gordon and Breach (1995).
Shivakumara IS, Suma SP, Acta Mech., 140, 207 (2000)
Shivakumara IS, Khalili A, Acta Mech., 152, 165 (2001)
Shivakumara IS, Sureshkumar S, J. Geophys. Eng., 4, 104 (2007)
Nield DA, Kuznetsov AV, Transp. Porous Media, 87(3), 765 (2011)
Hill AA, Rionero S, Straughan B, IMA J. Appl. Math., 72, 635 (2007)
Harfash AJ, Hill AA, Int. J. Heat Mass Transf., 72, 609 (2014)
Straughan B, The energy method, stability, and nonlinear convection, Applied Mathematical Sciences, Second Ed., 91, Springer (2004).
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, 102(1), 1 (2014)
Nield DA, Kuznetsov AV, Transp. Porous Media., 102, 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)
Straughan B, Microfluid Nanofluid, 16, 361 (2014)
Straughan B, Acta Appl. Math., 10.1007/s10440-014-9930-z. (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, J. Non-Equilib. Thermodyn., 10.1515/jnet-2014-0009. (2014)
Galdi GP, Straughan B, Arch. Rational Mech. Anal., 89, 211 (1985)
Roberts PH, An introduction to magnetohydrodynamics, Longman, London (1967).
Fabrizio M, Morro A, Electromagnetism of continuous media, Oxford University Press, Oxford (2003).
Joseph DD, Arch. Rational Mech. Anal., 35, 169 (1969)
Harfash AJ, Stability analysis for penetrative convection in a fluid layer with throughflow, Submited to European J. Mech. - B/Fluids.
