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Lie group analysis of flow and heat transfer of non-Newtonian nanofluid over a stretching surface with convective boundary condition

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Abstract

The steady two-dimensional flow and heat transfer of a non-Newtonian power-law nanofluid over a stretching surface under convective boundary conditions and temperature-dependent fluid viscosity has been numerically investigated. The power-law rheology is adopted to describe non-Newtonian characteristics of the flow. Four different types of nanoparticles, namely copper (Cu), silver (Ag), alumina (Al 2 O 3) and titanium oxide (TiO 2) are considered by using sodium alginate (SA) as the base non-Newtonian fluid. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The transformed equations are solved numerically by using a shooting method with fourth-order Runge–Kutta integration scheme. The results show that the effect of viscosity on the heat transfer rate is remarkable only for relatively strong convective heating. Moreover, the skin friction coefficient and the rate of heat transfer increase with an increase in Biot number.

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Acknowledgements

The authors are very thankful to the reviewers for their encouraging comments and constructive suggestions to improve the presentation of this manuscript.

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Authors and Affiliations

  1. Helwan University, Faculty of Science, Mathematics Department, P.O. Box 11795, Cairo, Egypt

    AHMED A AFIFY & MOHAMED ABD EL-AZIZ

  2. Department of Mathematics, Deanship of Educational Services, Qassim University, P.O. Box 6595, Buraidah:, 51452, Saudi Arabia

    AHMED A AFIFY

  3. Department of Mathematics, Faculty of Science, King Khalid University, Abha, 9004, Saudi Arabia

    MOHAMED ABD EL-AZIZ

Authors
  1. AHMED A AFIFY
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  2. MOHAMED ABD EL-AZIZ
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Correspondence to AHMED A AFIFY.

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AFIFY, A.A., EL-AZIZ, M.A. Lie group analysis of flow and heat transfer of non-Newtonian nanofluid over a stretching surface with convective boundary condition. Pramana - J Phys 88, 31 (2017). https://doi.org/10.1007/s12043-016-1336-1

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  • DOI: https://doi.org/10.1007/s12043-016-1336-1

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