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

doi:10.1007/s10483-012-1573-9

Abstract

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.

Key words: nanofluid, magnetic field, Lie symmetry group transformation, porous medium, thermal stratification

2010 MSC Number:

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. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 593-604.

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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)