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

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Abstract

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.

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References

  1. Eastman, J. A., Choi, S. U. S., Li, S., Yu, W., and Thompson, L. J. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett., 78, 718–720 (2001)

    Article  Google Scholar 

  2. Lee, S., Choi, S. U. S., Li, S., and Eastman, J. A. Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121, 280–289 (1999)

    Article  Google Scholar 

  3. Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E., and Grulke, E. A. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett., 79, 2252–2254 (2001)

    Article  Google Scholar 

  4. Xuan, Y. and Li, Q. Heat transfer enhancement of nanofluids. International Journal of Heat and Mass Transfer, 21, 58–64 (2000)

    Google Scholar 

  5. Batchelor, G. K. Sedimentation in a dilute dispersion of spheres. Journal of Fluid Mechanics, 52, 245–268 (1972)

    Article  MATH  Google Scholar 

  6. Batchelor, G. K. and Green, J. T. The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. Journal of Fluid Mechanics, 56, 375–400 (1972)

    Article  MATH  Google Scholar 

  7. Bonnecaze, R. T. and Brady, J. F. A method for determining the effective conductivity of dispersions of particles. Proc. R. Soc. Lond. A, 430, 285–313 (1990)

    Article  MATH  Google Scholar 

  8. Bonnecaze, R. T. and Brady, J. F. The effective conductivity of random suspensions of spherical particles. Proc. R. Soc. Lond. A, 432, 445–465 (1991)

    Article  Google Scholar 

  9. Davis, R. H. The effective thermal conductivity of a composite material with spherical inclusions. International Journal of Themophysics, 7, 609–620 (1986)

    Article  Google Scholar 

  10. Hamilton, R. L. and Crosser, O. K. Thermal conductivity of heterogeneous two-component systems. Industrial and Engineering Chemistry Fundamentals, 1, 187–191 (1962)

    Article  Google Scholar 

  11. Jeffrey, D. J. Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A, 335, 355–367 (1973)

    Article  Google Scholar 

  12. Lu, S. and Lin, H. Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity. Journal of Applied Physics, 79, 6761–6769 (1996)

    Article  Google Scholar 

  13. Maxwell, J. C. A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, New York, 435–441 (1891)

    Google Scholar 

  14. Congedo, P. M., Collura, S., and Congedo, P. M. Modeling and analysis of natural convection heat transfer in nanofluids. Proceedings of ASME Summer Heat Transfer Conference, 3, 569–579 (2009)

    Google Scholar 

  15. Ghasemi, B. and Aminossadati, S. M. Natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Numerical Heat Transfer, Part A: Applications, 55, 807–823 (2009)

    Article  Google Scholar 

  16. Ho, C. J., Chen, M. W., and Li, Z. W. Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity. International Journal of Heat and Mass Transfer, 51, 4506–4516 (2008)

    Article  MATH  Google Scholar 

  17. Ho, C. J., Chen, M. W., and Li, Z. W. Effect of natural convection heat transfer of nanofluid in an enclosure due to uncertainties of viscosity and thermal conductivity. Proceedings of ASME/JSME Thermal Engineering Summer Heat Transfer Conference, 1, 833–841 (2007)

    Article  Google Scholar 

  18. Hamad, M. A. A., Pop, I., and Ismail, A. I. Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate. Nonlinear Analysis: Real World Application, 12, 1338–1346 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hamad, M. A. A. and Pop, I. Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source in a nanofluid. Heat and Mass Transfer, 47, 1517–1524 (2011) DOI 10.1007/s00231-011-0816-6

    Article  Google Scholar 

  20. Hamad, M. A. A. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer, 38, 487–492 (2011)

    Article  Google Scholar 

  21. Hamad, M. A. A. and Ferdows, M. Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: a Lie group analysis. Communications in Nonlinear Science and Numerical Simulation, 17, 132–140 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Das, S. K., Choi, S. U. S., Yu, W., and Pradeep, T. Nanofluids: Science and Technology, Wiley, New Jersey (2007)

    Google Scholar 

  23. Trisaksri, V. and Wongwises, S. Critical review of heat transfer characteristics nanofluids. Renewable and Sustainable Energy Reviews, 11, 512–523 (2007)

    Article  Google Scholar 

  24. Wang, X. Q. and Mujumdar, A. S. Heat transfer characteristics of nanofluids: a review. International Journal of Thermal Sciences, 46, 1–19 (2007)

    Article  MATH  Google Scholar 

  25. Kakac, S. and Pramuanjaroenkij, A. Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52, 3187–3196 (2009)

    Article  MATH  Google Scholar 

  26. Gupta, P. S. and Gupta, A. S. Heat and mass transfer on a stretching sheet with suction or blowing. Canadian Journal of Chemical Engineering, 55, 744–746 (1977)

    Article  Google Scholar 

  27. Vajravelu, K. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Computation, 124, 281–288 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Raptis, A. and Perdikis, C. Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field. International Journal of Non-Linear Mechanics, 41, 527–529 (2006)

    Article  MATH  Google Scholar 

  29. Bataller, R. C. Similarity solutions for flow and heat transfer of a quiescent fluid over a non-linearly stretching surface. Journal of Materials Processing Technology, 203, 176–183 (2008)

    Article  Google Scholar 

  30. Prasad, K. V. and Vajravelu, K. Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. International Journal of Heat and Mass Transfer, 52, 4956–4965 (2009)

    Article  MATH  Google Scholar 

  31. Ziabakhsh, Z., Domairry, G., Bararnia, H., and Babazadeh, H. Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. Journal of the Taiwan Institute of Chemical Engineers, 41, 22–28 (2010)

    Article  Google Scholar 

  32. Akyildiz, F. T. and Siginer, D. A. Galerkin-Legendre spectral method for the velocity and thermal boundary layers over a non-linearly stretching sheet. Nonlinear Analysis: Real World Applications, 11, 735–741 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. Prasad, K. V., Vajravelu, K., and Datti, P. S. Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties. International Journal of Non-Linear Mechanics, 45, 320–330 (2010)

    Article  Google Scholar 

  34. Afzal, N. Momentum and thermal boundary layers over a two-dimensional or axisymmetric nonlinear stretching surface in a stationary fluid. International Journal of Heat and Mass Transfer, 53, 540–547 (2010)

    Article  MATH  Google Scholar 

  35. Cortell, R. Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematical and Computation, 184, 864–873 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Oztop, H. F. and Abu-Nada, E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29, 1326–1336 (2008)

    Article  Google Scholar 

  37. Aminossadati, S. M. and Ghasemi, B. Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure. European Journal of Mechanics B/Fluids, 28, 630–640 (2009)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

    M. A. A. Hamad

  2. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, 11800, Malaysia

    M. A. A. Hamad

  3. Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    M. Ferdows

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  1. M. A. A. Hamad
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  2. M. Ferdows
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Correspondence to M. A. A. Hamad.

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Hamad, M.A.A., Ferdows, M. Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet. Appl. Math. Mech.-Engl. Ed. 33, 923–930 (2012). https://doi.org/10.1007/s10483-012-1595-7

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  • DOI: https://doi.org/10.1007/s10483-012-1595-7

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