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Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

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  • Research Centre for Computational Mathematics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Johor 86400, Malaysia

Received date: 2011-03-23

  Revised date: 2011-12-21

  Online published: 2012-05-10

Abstract

The magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gillbased shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Cite this article

A. B. ROSMILA;R. KANDASAMY;I. MUHAIMIN . Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification[J]. Applied Mathematics and Mechanics, 2012 , 33(5) : 593 -604 . DOI: 10.1007/s10483-012-1573-9

References


[1] Choi, S. Enhancing thermal conductivity of fluids with nanoparticle. Developments and Applicationsof Non-Newtonian Flows (eds. Siginer, D. A. and Wang, H. P.), American Society ofMeehanical Engineers, San Francisco/California, 99-105 (1995)

[2] Masuda, H., Ebata, A., Teramae, K., and Hishinuma, N. Alteration of thermal conductivity andviscosity of liquid by dispersing ultra-fine particles. Netsu Bussei, 7(2), 227-233 (1993)

[3] Buongiorno, J. and Hu, W. Nanofluid coolants for advanced nuclear power plants. Proceedings ofICAPP'05, Curran Associctes, Seoul, 15-19 (2005)

[4] Buongiorno, J. Convective transport in nanofluids. ASME Journal of Heat Transfer, 128(2), 240-250 (2006)

[5] Kuznetsov, A. V. and Nield, D. A. Natural convective boundary-layer flow of a nanofluid past avertical plate. International Journal of Thermal Sciences, 49(3), 243-247 (2010)

[6] Nield, D. A. and Kuznetsov, A. V. The Cheng-Minkowycz problem for natural convectiveboundary-layer flow in a porous medium saturated by a nanofluid. International Journal of Heatand Mass Transfer, 52(9), 5792-5795 (2009)

[7] Cheng, P. and Minkowycz, W. J. Free convection about a vertical flat plate embedded in a porousmedium with application to heat transfer from a dike. Journal of Geophysics Research, 82(6),2040-2044 (1977)

[8] Birkoff, G. Mathematics for engineers. Electrical Engineering, 67(5), 1185-1188 (1948)

[9] Birkoff, G. Hydrodynamics, Princeton University Press, New Jersey (1960)

[10] Moran, M. J. and Gaggioli, R. A. Similarity analysis via group theory. AIAA Journal, 6(8),2014-2016 (1968)

[11] Moran, M. J. and Gaggioli, R. A. Reduction of the number of variables in systems of partialdifferential equations with auxiliary conditions. SIAM Journal of Applied Mathematics, 16(2),202-215 (1968)

[12] Ibrahim, F. S. and Hamad, M. A. A. Group method analysis of mixed convection boundary-layerflow of a micropolar fluid near a stagnation point on a horizontal cylinder. Acta Mechanica, 181(1),65-81 (2006)

[13] Yurusoy, M. and Pakdemirli, M. Symmetry reductions of unsteady three-dimensional boundarylayersof some non-Newtonian fluids. International Journal of Engineering Sciences, 35(2), 731-740 (1997)

[14] Yurusoy, M. and Pakdemirli, M. Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet. Mechanics Research Communications, 26(1), 171-175(1999)

[15] Yurusoy, M., Pakdemirli, M., and Noyan, O. F. Lie group analysis of creeping flow of a secondgrade fluid. International Journal of Non-Linear Mechanics, 36(8), 955-960 (2001)

[16] Hassanien, I. A. and Hamad, M. A. A. Group theoretic method for unsteady free convection flowof a micropolar fluid along a vertical plate in a thermally stratified medium. Applied MathematicalModelling, 32(6), 1099-1114 (2008)

[17] Makinde, O. D. and Aziz, A. Boundary-layer flow of a nanofluid past a stretching sheet witha convective boundary condition. International Journal of Thermal Science, 50(5), 1326-1332(2011)

[18] Oztop, H. F. and Abu-Nada, E. Numerical study of natural convection in partially heated rectangularenclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29(6),1326-1336 (2008)

[19] Akira, N. and Hitoshi, K. Similarity solutions for buoyancy induced flows over a non-isothermalcurved surface in a thermally stratified porous medium. Applied Scientific Research, 46(2), 309-314 (1989)

[20] Aminossadati, S. M. and Ghasemi, B. Natural convection cooling of a localized heat source at thebottom of a nanofluid-filled enclosure. European Journal of Mechanics B/Fluids, 28(4), 630-640(2009)

[21] Crane, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik(ZAMP), 21(4), 645-647 (1970)

[22] Vajravelu, K. Flow and heat transfer in a saturated porous medium over a stretching surface.Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 74(12), 605-614 (1994)

[23] Abel, M. S. and Veena, P. H. Visco-elastic fluid flow and heat transfer in a porous media over astretching sheet. International Journal of Non-Linear Mechanics, 33(3), 531-540 (1998)

[24] Abel, M. S., Khan, S. K., and Prasad, K. V. Momentum and heat transfer in visco-elastic fluidin a porous medium over a non-isothermal stretching sheet. International Journal of NumericalMethods and Heat Fluid Flow, 10(3), 786-801 (2000)

[25] Gill, S. A process for the step-by-step integration of differential equations in an automatic digitalcomputing machine. Proceedings of the Cambridge Philosophical Society, Cambridge UniversityPress, Cambridge, 96-108 (1951)

[26] Grubka, L. G. and Bobba, K. M. Heat characteristics of a continuous stretching surface withvariable temperature. ASME Journal of Heat Transfer, 107(2), 248-250 (1985)

[27] Ali, M. E. Heat characteristics of a continuous stretching surface. Wärme-und Stoffübertragung,29(2), 227-234 (1994)

[28] Ishak, A., Nazar, R., and Pop, I. Boundary-layer flow and heat transfer over an unsteady stretchingvertical surface. Meccanica, 44(2), 369-375 (2009)

[29] Vajravelu, K., Prasad, K. V., Lee, J. H., Lee, C. G., Pop, I., and van Gorder, R. A. Convectiveheat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface.International Journal of Thermal Sciences, 50(5), 843-851 (2011)

[30] Hamad, M. A. A., Pop, I., and Md-Ismail, A. I. Magnetic field effects on free convection flow ofa nanofluid past a vertical semi-infinite flat plate. Nonlinear Analysis: Real World Applications,12(3), 1338-1346 (2011)

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