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

Okey Oseloka Onyejekwe

doi:doi:10.11648/j.ijfmts.20170302.11

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

Okey Oseloka Onyejekwe

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 2)

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), 2024. 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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[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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APA Style

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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TY  - JOUR
T1  - Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation
AU  - Okey Oseloka Onyejekwe
Y1  - 2017/04/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170302.11
DO  - 10.11648/j.ijfmts.20170302.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 16
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PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170302.11
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
IS  - 2
ER  -

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Author Information

Okey Oseloka Onyejekwe

Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa, Ethiopia

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APA Style

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation
AU  - Okey Oseloka Onyejekwe
Y1  - 2017/04/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170302.11
DO  - 10.11648/j.ijfmts.20170302.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 16
EP  - 24
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170302.11
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
IS  - 2
ER  -

Copy | Download