On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates

Mushtaq Ahmed

doi:doi:10.11648/j.ijfmts.20190503.12

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On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates

Mushtaq Ahmed

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 5, Issue 3)

Received: 13 March 2019 Accepted: 22 July 2019 Published: 10 August 2019

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Abstract

The aim of this article is to use von-Mises coordinates to find a class of new exact solutionsof the equations governing the plane steady motion with moderate Peclet number of incompressible fluid of variable viscosity in presence of body force. An equation relating a differentiable function and a stream function characterizes the class under consideration. When the differentiable function is parabolic and when it is not, in both the cases, it finds exact solutions for given one component of the body force. This discourse shows an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for moderate Peclet number in presence of body force. Moreover, for parabolic case, it obtains viscosity as a function of temperature distribution for moderate Peclet number.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 5, Issue 3)
DOI	10.11648/j.ijfmts.20190503.12
Page(s)	67-74
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

Martin’s System, Von-Mises Coordinates, Variable Viscosity, Navier-Stokes Equations with Body Force, Exact Solutions with Body Force

References

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[2]	Naeem, R. K.; Exact solutions of flow equations of an incompressible fluid of variable viscosity via one – parameter group: The Arabian Journal for Science and Engineering, 1994, 19 (1), 111-114.
[3]	Naeem, R. K.; Srfaraz, A. N.; Study of steady plane flows of an incompressible fluid of variable viscosity using Martin’s System: Journal of Applied Mechanics and Engineering, 1996, 1 (1), 397-433.
[4]	Naeem, R. K.; Steady plane flows of an incompressible fluid of variable viscosity via Hodograph transformation method: Karachi University Journal of Sciences, 2003, 3(1), 73-89.
[5]	Naeem, R. K.; On plane flows of an incompressible fluid of variable viscosity: Quarterly Science Vision, 2007, 12 (1), 125-131.
[6]	Landau L. D. and Lifshitz E. M.; Fluid Mechanics, Pergmaon Press, vol 6.
[7]	Naeem, R. K.; Mushtaq A.; A class of exact solutions to the fundamental equations for plane steady incompressible and variable viscosity fluid in the absence of body force: International Journal of Basic and Applied Sciences, 2015, 4(4), 429-465.www.sciencepubco.com/index.php/IJBAS, doi:10.14419/ijbas.v4i4.5064.
[8]	Giga, Y.; Inui, K.; Mahalov; Matasui S.; Uniform local solvability for the Navier-Stokes equations with the Coriolis force: Method and application of Analysis, 2005, 12, 381-384.
[9]	Gerbeau, J. -F.; Le Bris, C., A basic Remark on Some Navier-Stokes Equations With Body Forces: Applied Mathematics Letters, 2000, 13(1), 107-112.
[10]	Mushtaq A., On Some Thermally Conducting Fluids: Ph. D Thesis, Department of Mathematics, University of Karachi, Pakistan, 2016.
[11]	Mushtaq A.; Naeem R. K.; S. Anwer Ali; A class of new exact solutions of Navier-Stokes equations with body force for viscous incompressible fluid,: International Journal of Applied Mathematical Research, 2018, 7 (1), 22-26. www.sciencepubco.com/index.php/IJAMR, doi: 10.14419/ijamr.v7i1.8836.
[12]	Mushtaq Ahmed, Waseem Ahmed Khan: A Class of New Exact Solutions of the System of PDE for the plane motion of viscous incompressible fluids in the presence of body force,: International Journal of Applied Mathematical Research, 2018, 7 (2), 42-48. www.sciencepubco.com/index.php/IJAMR, doi: 10.14419 /ijamr.v7i2.9694.
[13]	Mushtaq Ahmed, Waseem hmed Khan, S. M. Shad Ahsen:A Class of Exact Solutions of quations for Plane Steady Motion of Incompressible Fluids of ariable viscosity in presence of ody Force,: International Journal of Applied Mathematical Research, 2018, 7 (3), 77-81. www.sciencepubco.com/index.php/IJAMR, doi: 10.14419/ijamr.v7i2.12326.
[14]	Mushtaq Ahmed, (2018), A Class of New Exact Solution of equations for Motion of Variable Viscosity Fluid In presence of Body Force with Moderate Peclet number, International Journal of Fluid Mechanics and Thermal Sciences, 4 (4) 429- www.sciencepublishingdroup.com/j/ijfms doi: 10.11648/j.ijfmts.20180401.12.
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APA Style

Mushtaq Ahmed. (2019). On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 67-74. https://doi.org/10.11648/j.ijfmts.20190503.12

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ACS Style

Mushtaq Ahmed. On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 67-74. doi: 10.11648/j.ijfmts.20190503.12

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AMA Style

Mushtaq Ahmed. On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. Int J Fluid Mech Therm Sci. 2019;5(3):67-74. doi: 10.11648/j.ijfmts.20190503.12

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@article{10.11648/j.ijfmts.20190503.12,
  author = {Mushtaq Ahmed},
  title = {On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {67-74},
  doi = {10.11648/j.ijfmts.20190503.12},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.12},
  abstract = {The aim of this article is to use von-Mises coordinates to find a class of new exact solutionsof the equations governing the plane steady motion with moderate Peclet number of incompressible fluid of variable viscosity in presence of body force. An equation relating a differentiable function and a stream function characterizes the class under consideration. When the differentiable function is parabolic and when it is not, in both the cases, it finds exact solutions for given one component of the body force. This discourse shows an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for moderate Peclet number in presence of body force. Moreover, for parabolic case, it obtains viscosity as a function of temperature distribution for moderate Peclet number.},
 year = {2019}
}

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TY  - JOUR
T1  - On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates
AU  - Mushtaq Ahmed
Y1  - 2019/08/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.12
DO  - 10.11648/j.ijfmts.20190503.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
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EP  - 74
PB  - Science Publishing Group
SN  - 2469-8113
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AB  - The aim of this article is to use von-Mises coordinates to find a class of new exact solutionsof the equations governing the plane steady motion with moderate Peclet number of incompressible fluid of variable viscosity in presence of body force. An equation relating a differentiable function and a stream function characterizes the class under consideration. When the differentiable function is parabolic and when it is not, in both the cases, it finds exact solutions for given one component of the body force. This discourse shows an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for moderate Peclet number in presence of body force. Moreover, for parabolic case, it obtains viscosity as a function of temperature distribution for moderate Peclet number.
VL  - 5
IS  - 3
ER  -

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Author Information

Mushtaq Ahmed

Department of Mathematics, University of Karachi, Karachi, Pakistan

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APA Style

Mushtaq Ahmed. (2019). On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 67-74. https://doi.org/10.11648/j.ijfmts.20190503.12

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ACS Style

Mushtaq Ahmed. On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 67-74. doi: 10.11648/j.ijfmts.20190503.12

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AMA Style

Mushtaq Ahmed. On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates. Int J Fluid Mech Therm Sci. 2019;5(3):67-74. doi: 10.11648/j.ijfmts.20190503.12

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@article{10.11648/j.ijfmts.20190503.12,
  author = {Mushtaq Ahmed},
  title = {On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {67-74},
  doi = {10.11648/j.ijfmts.20190503.12},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.12},
  abstract = {The aim of this article is to use von-Mises coordinates to find a class of new exact solutionsof the equations governing the plane steady motion with moderate Peclet number of incompressible fluid of variable viscosity in presence of body force. An equation relating a differentiable function and a stream function characterizes the class under consideration. When the differentiable function is parabolic and when it is not, in both the cases, it finds exact solutions for given one component of the body force. This discourse shows an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for moderate Peclet number in presence of body force. Moreover, for parabolic case, it obtains viscosity as a function of temperature distribution for moderate Peclet number.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Plane Motion of Incompressible Variable Viscosity Fluids with Moderate Peclet Number in Presence of Body Force Via Von-Mises Coordinates
AU  - Mushtaq Ahmed
Y1  - 2019/08/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.12
DO  - 10.11648/j.ijfmts.20190503.12
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  - 67
EP  - 74
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20190503.12
AB  - The aim of this article is to use von-Mises coordinates to find a class of new exact solutionsof the equations governing the plane steady motion with moderate Peclet number of incompressible fluid of variable viscosity in presence of body force. An equation relating a differentiable function and a stream function characterizes the class under consideration. When the differentiable function is parabolic and when it is not, in both the cases, it finds exact solutions for given one component of the body force. This discourse shows an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for moderate Peclet number in presence of body force. Moreover, for parabolic case, it obtains viscosity as a function of temperature distribution for moderate Peclet number.
VL  - 5
IS  - 3
ER  -

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