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Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation

Received: 12 December 2016     Accepted: 27 December 2016     Published: 24 April 2017
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Abstract

The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into partial differential equations by introducing a time-marching scheme. A Crank-Nicolson Newton-Richtmeyer scheme is employed to discretize the resulting equations. Initial guesses are made for the dependent variables and the solution advanced in time until temporal variations of the scalar profile are diminished and the steady-state solutions satisfy the similarity equations. A variation of the heat flux at one of the boundaries produced noticeable variations in the temperature field that can be related to the magnitude of the Prandtl number and velocity ratio parameter.

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 2)
DOI 10.11648/j.ijfmts.20170302.11
Page(s) 16-24
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Stagnation Point Flow, Heat Transfer, Prescribed Flux, Crank-Nicolson-Newton-Richtmeyer, Time Marching Scheme, Steady State, Prandtl Number, Stretching and Shrinking Sheet

References
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[3] F. Homann, “Der einfluss grosset zahigkeit bei der stromung um den Zylinder and um die kugel”, Zeitschrift fur Angewandte Mathematic und mechanic, vol. 16 pp. 153-164, 1936.
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[10] B. C. Sakiadis, “Boundary –layer behavior on continuous solid surfaces: II The boundary layer on a continuous flat surface”, AICHE J. vol. 7 pp. 221-225, 1961. Doi:10.1002/aic.690070211
[11] T. R. Mahapatra and A. S. Gupta, “Heat transfer in stagnation-point flow towards a stretching sheet”, Heat and Mass Transfer, vol. 38 pp. 517-521, 2002.
[12] P. Dulal and P. S. Hiremath, “Computational modelling of heat transfer over an unsteady stretching surface embedded in porous medium”, Mecccanica, vol. 45 pp. 415-524, 2009.
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[16] M. E. Ali and E. Magyari, “Unstaedy fluid and heat flow induced by a submerged stretching surface while its steady motion is slowing down gradually”, Int. Jnl. Heat and Mass Trans. vol. 50 pp. 188-195, 2007.
[17] A. Ishak, R. Nazar, and I. Pop, “Magnetohydrodynamics stagnation point flow towards a stretching vertical sheet”, Magneto-hydrodynamics, vol. 42 pp.17-30, 2006.
[18] H. I. Anderson, “MHD flow of viscoelastic fluid past a stretching surface”, Acta Mechanica,, vol. 95 pp. 227-230, 1992.
[19] M. I. Char, “Heat and mass transfer in a hydromagnetic flow of the viscoelstic fluid past a stretching surface”, Physics of Fluids vol. 27 pp. 1915-1917, 1994.
[20] T. R. Mahapatra and S. K. Nandy, “Momentum and heat transfer in MHD axisymmetric stagnation point flow over a shrinking sheet”, Jnl. Applied Fluid Mechanics, vol. 6 pp. 121-129, 2011.
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    Okey Oseloka Onyejekwe. (2017). Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation. International Journal of Fluid Mechanics & Thermal Sciences, 3(2), 16-24. https://doi.org/10.11648/j.ijfmts.20170302.11

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    ACS Style

    Okey Oseloka Onyejekwe. Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation. Int. J. Fluid Mech. Therm. Sci. 2017, 3(2), 16-24. doi: 10.11648/j.ijfmts.20170302.11

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    AMA Style

    Okey Oseloka Onyejekwe. Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation. Int J Fluid Mech Therm Sci. 2017;3(2):16-24. doi: 10.11648/j.ijfmts.20170302.11

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  • @article{10.11648/j.ijfmts.20170302.11,
      author = {Okey Oseloka Onyejekwe},
      title = {Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation},
      journal = {International Journal of Fluid Mechanics & Thermal Sciences},
      volume = {3},
      number = {2},
      pages = {16-24},
      doi = {10.11648/j.ijfmts.20170302.11},
      url = {https://doi.org/10.11648/j.ijfmts.20170302.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170302.11},
      abstract = {The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into partial differential equations by introducing a time-marching scheme. A Crank-Nicolson Newton-Richtmeyer scheme is employed to discretize the resulting equations. Initial guesses are made for the dependent variables and the solution advanced in time until temporal variations of the scalar profile are diminished and the steady-state solutions satisfy the similarity equations. A variation of the heat flux at one of the boundaries produced noticeable variations in the temperature field that can be related to the magnitude of the Prandtl number and velocity ratio parameter.},
     year = {2017}
    }
    

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    AU  - Okey Oseloka Onyejekwe
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    T2  - International Journal of Fluid Mechanics & Thermal Sciences
    JF  - International Journal of Fluid Mechanics & Thermal Sciences
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    AB  - The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into partial differential equations by introducing a time-marching scheme. A Crank-Nicolson Newton-Richtmeyer scheme is employed to discretize the resulting equations. Initial guesses are made for the dependent variables and the solution advanced in time until temporal variations of the scalar profile are diminished and the steady-state solutions satisfy the similarity equations. A variation of the heat flux at one of the boundaries produced noticeable variations in the temperature field that can be related to the magnitude of the Prandtl number and velocity ratio parameter.
    VL  - 3
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Author Information
  • Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa, Ethiopia

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