Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet

doi:10.1007/s10483-012-1595-7

摘要/Abstract

摘要：

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles φ , and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.

关键词: viscous flow, similarity solution, natural boundary element method (NBEM), finite element method (FEM), couple, torsion, nanofluid, partial differential equation, nonlinearly stretching sheet, nonlinear ordinary equation

Abstract:

Key words: nanofluid, natural boundary element method (NBEM), finite element method (FEM), couple, torsion, nonlinearly stretching sheet, partial differential equation, similarity solution, nonlinear ordinary equation, viscous flow

中图分类号:

O357

M. A. A. HAMAD;M. FERDOWS. Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 923-930.

参考文献

[1] Eastman, J. A., Choi, S. U. S., Li, S., Yu,W., and Thompson, L. J. Anomalously increased effectivethermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl.Phys. Lett., 78, 718-720 (2001)
[2] Lee, S., Choi, S. U. S., Li, S., and Eastman, J. A. Measuring thermal conductivity of fluidscontaining oxide nanoparticles. Journal of Heat Transfer, 121, 280-289 (1999)
[3] Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E., and Grulke, E. A. Anomalous thermalconductivity enhancement in nanotube suspensions. Appl. Phys. Lett., 79, 2252-2254 (2001)
[4] Xuan, Y. and Li, Q. Heat transfer enhancement of nanofluids. International Journal of Heat andMass Transfer, 21, 58-64 (2000)
[5] Batchelor, G. K. Sedimentation in a dilute dispersion of spheres. Journal of Fluid Mechanics, 52,245-268 (1972)
[6] Batchelor, G. K. and Green, J. T. The hydrodynamic interaction of two small freely-movingspheres in a linear flow field. Journal of Fluid Mechanics, 56, 375-400 (1972)
[7] Bonnecaze, R. T. and Brady, J. F. A method for determining the effective conductivity of disper-sions of particles. Proc. R. Soc. Lond. A, 430, 285-313 (1990)
[8] Bonnecaze, R. T. and Brady, J. F. The effective conductivity of random suspensions of sphericalparticles. Proc. R. Soc. Lond. A, 432, 445-465 (1991)
[9] Davis, R. H. The effective thermal conductivity of a composite material with spherical inclusions.International Journal of Themophysics, 7, 609-620 (1986)
[10] Hamilton, R. L. and Crosser, O. K. Thermal conductivity of heterogeneous two-component sys-tems. Industrial and Engineering Chemistry Fundamentals, 1, 187-191 (1962)
[11] Jeffrey, D. J. Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A, 335,355-367 (1973)
[12] Lu, S. and Lin, H. Effective conductivity of composites containing aligned spheroidal inclusionsof finite conductivity. Journal of Applied Physics, 79, 6761-6769 (1996)
[13] Maxwell, J. C. A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, New York,435-441 (1891)
[14] Congedo, P. M., Collura, S., and Congedo, P. M. Modeling and analysis of natural convectionheat transfer in nanofluids. Proceedings of ASME Summer Heat Transfer Conference, 3, 569-579(2009)
[15] Ghasemi, B. and Aminossadati, S. M. Natural convection heat transfer in an inclined enclosurefilled with a water-CuO nanofluid. Numerical Heat Transfer, Part A: Applications, 55, 807-823(2009)
[16] Ho, C. J., Chen, M.W., and Li, Z.W. Numerical simulation of natural convection of nanofluid in asquare enclosure: effects due to uncertainties of viscosity and thermal conductivity. InternationalJournal of Heat and Mass Transfer, 51, 4506-4516 (2008)
[17] Ho, C. J., Chen, M. W., and Li, Z. W. Effect of natural convection heat transfer of nanofluid in anenclosure due to uncertainties of viscosity and thermal conductivity. Proceedings of ASME/JSMEThermal Engineering Summer Heat Transfer Conference, 1, 833-841 (2007)
[18] Hamad, M. A. A., Pop, I., and Ismail, A. I. Magnetic field effects on free convection flow of ananofluid past a vertical semi-infinite flat plate. Nonlinear Analysis: Real World Application, 12,1338-1346 (2011)
[19] Hamad, M. A. A. and Pop, I. Unsteady MHD free convection flow past a vertical permeable flatplate in a rotating frame of reference with constant heat source in a nanofluid. Heat and MassTransfer, 47, 1517-1524 (2011) DOI 10.1007/s00231-011-0816-6
[20] Hamad, M. A. A. Analytical solution of natural convection flow of a nanofluid over a linearlystretching sheet in the presence of magnetic field. International Communications in Heat andMass Transfer, 38, 487-492 (2011)
[21] Hamad, M. A. A. and Ferdows, M. Similarity solution of boundary layer stagnation-point flow to-wards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generationand suction/blowing: a Lie group analysis. Communications in Nonlinear Science and NumericalSimulation, 17, 132-140 (2012)
[22] Das, S. K., Choi, S. U. S., Yu, W., and Pradeep, T. Nanofluids: Science and Technology, Wiley,New Jersey (2007)
[23] Trisaksri, V. and Wongwises, S. Critical review of heat transfer characteristics nanofluids. Renew-able and Sustainable Energy Reviews, 11, 512-523 (2007)
[24] Wang, X. Q. and Mujumdar, A. S. Heat transfer characteristics of nanofluids: a review. Interna-tional Journal of Thermal Sciences, 46, 1-19 (2007)
[25] Kakac, S. and Pramuanjaroenkij, A. Review of convective heat transfer enhancement with nanoflu-ids. International Journal of Heat and Mass Transfer, 52, 3187-3196 (2009)
[26] Gupta, P. S. and Gupta, A. S. Heat and mass transfer on a stretching sheet with suction orblowing. Canadian Journal of Chemical Engineering, 55, 744-746 (1977)
[27] Vajravelu, K. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Compu-tation, 124, 281-288 (2001)
[28] Raptis, A. and Perdikis, C. Viscous flow over a non-linearly stretching sheet in the presence of achemical reaction and magnetic field. International Journal of Non-Linear Mechanics, 41, 527-529(2006)
[29] Bataller, R. C. Similarity solutions for flow and heat transfer of a quiescent fluid over a non-linearlystretching surface. Journal of Materials Processing Technology, 203, 176-183 (2008)
[30] Prasad, K. V. and Vajravelu, K. Heat transfer in the MHD flow of a power law fluid over anon-isothermal stretching sheet. International Journal of Heat and Mass Transfer, 52, 4956-4965(2009)
[31] Ziabakhsh, Z., Domairry, G., Bararnia, H., and Babazadeh, H. Analytical solution of flow anddiffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porousmedium. Journal of the Taiwan Institute of Chemical Engineers, 41, 22-28 (2010)
[32] Akyildiz, F. T. and Siginer, D. A. Galerkin-Legendre spectral method for the velocity and thermalboundary layers over a non-linearly stretching sheet. Nonlinear Analysis: Real World Applications,11, 735-741 (2010)
[33] Prasad, K. V., Vajravelu, K., and Datti, P. S. Mixed convection heat transfer over a non-linearstretching surface with variable fluid properties. International Journal of Non-Linear Mechanics,45, 320-330 (2010)
[34] Afzal, N. Momentum and thermal boundary layers over a two-dimensional or axisymmetric non-linear stretching surface in a stationary fluid. International Journal of Heat and Mass Transfer,53, 540-547 (2010)
[35] Cortell, R. Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematicaland Computation, 184, 864-873 (2007)
[36] Oztop, H. F. and Abu-Nada, E. Numerical study of natural convection in partially heated rectan-gular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29, 1326-1336 (2008)
[37] Aminossadati, S. M. and Ghasemi, B. Natural convection cooling of a localized heat source atthe bottom of a nanofluid-filled enclosure. European Journal of Mechanics B/Fluids, 28, 630-640(2009)