On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates

Mushtaq Ahmed

doi:doi:10.11648/j.ijfmts.20190503.13

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On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates

Mushtaq Ahmed

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

Received: 13 March 2019 Accepted: 26 July 2019 Published: 26 August 2019

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Abstract

This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 5, Issue 3)
DOI	10.11648/j.ijfmts.20190503.13
Page(s)	75-81
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), 2019. Published by Science Publishing Group

Keywords

Variable Viscosity Fluids, Navier-Stokes Equations with Body Force, Martin’s System, von-Mises Coordinates, Moderate Peclet Number

References

[1]	Mushtaq A., On Some Thermally Conducting Fluids: Ph.D Thesis, Department of Mathematics, University of Karachi, Pakistan, 2016.
[2]	Chandna, O. P., Oku-Ukpong E. O.; Flows for chosen vorticity functions-Exactsolutions of the Navier-Stokes Equations: International Journal of Applied Mathematics and Mathematical Sciences, 17 (1) (1994) 155-164.
[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]	Naeem, R. K.; Mushtaq A.; A class of exact solutions to the fundamental quations for plane steady ncompressible and variable viscosity fluid in the bsence 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.
[7]	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.
[8]	Mushtaq Ahmed, Waseem Ahmed Khan: A Class of New Exact Solutions of the System ofPDEfor 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.
[9]	Mushtaq Ahmed, Waseem Ahmed Khan, S. M. Shad Ahsen:A Class of Exact Solutions of Equations for Plane Steady Motion of Incompressible Fluids of Variable viscosity in presence of Body Force,:International Journal of Applied Mathematical Research, 2018, 7 (3), 77-81.www.sciencepubco.com/index.php/IJAMR, doi: 10.14419/ijamr.v7i2.12326.
[10]	Mushtaq Ahmed, 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, 2018, 4 (3) 27-33www.sciencepublishingdroup.com/j/ijfmts doi: 10.11648/j.ijfmts.20180403.11.
[11]	D. L. R. Oliver & K. J. De Witt, High Peclet number heat transfer from adroplet suspended in an electric field: Interior problem, Int. J. Heat Mass Transfer, vol. 36: 3153-3155, 1993.
[12]	B. Abramzon and C. Elata, Numerical analysis of unsteady conjugate heattransfer between a single spherical particle and surrounding flow at intermediate Reynolds and Peclet numbers, 2nd Int. Conf. on numerical methods in Thermal problems, Venice, pp. 1145-1153, 1981.
[13]	Z. G. Fenz, E. E. Michaelides, Unsteady mass transport from a sphere immersedin a porous medium at finite Peclet numbers, Int. J. Heat Mass Transfer 42:3529-3531, 1999.
[14]	Fayerweather Carl, Heat Transfer From a Droplet at Moderate Peclet Numbers with heat Generation. Ph.D. Thesis, U of Toledo, May 2007.
[15]	Martin, M. H.; The flow of a viscous fluid I: Archive for Rational Mechanics and Analysis, 1971, 41 (4), 266-286.
[16]	Daniel Zwillinger; Handbook of differential equations; Academic Press, Inc. (1989).
[17]	Mushtaq Ahmed, A Class of Exact Solutions for a Variable Viscosity Flowwith Body Force for Moderate Peclet Number Via Von-Mises Coordinates, Fluid Mechanics, 2019, 5 (1), 15-25, www.sciencepublishinggroup.com/j/fm doi: 10.11648/j.fm.20190501.13.

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APA Style

Mushtaq Ahmed. (2019). On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 75-81. https://doi.org/10.11648/j.ijfmts.20190503.13

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ACS Style

Mushtaq Ahmed. On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 75-81. doi: 10.11648/j.ijfmts.20190503.13

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AMA Style

Mushtaq Ahmed. On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. Int J Fluid Mech Therm Sci. 2019;5(3):75-81. doi: 10.11648/j.ijfmts.20190503.13

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@article{10.11648/j.ijfmts.20190503.13,
  author = {Mushtaq Ahmed},
  title = {On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {75-81},
  doi = {10.11648/j.ijfmts.20190503.13},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.13},
  abstract = {This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.},
 year = {2019}
}

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TY  - JOUR
T1  - On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates
AU  - Mushtaq Ahmed
Y1  - 2019/08/26
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.13
DO  - 10.11648/j.ijfmts.20190503.13
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  - 75
EP  - 81
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20190503.13
AB  - This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.
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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Plain Text BibTeX RIS

APA Style

Mushtaq Ahmed. (2019). On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 75-81. https://doi.org/10.11648/j.ijfmts.20190503.13

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ACS Style

Mushtaq Ahmed. On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 75-81. doi: 10.11648/j.ijfmts.20190503.13

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AMA Style

Mushtaq Ahmed. On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates. Int J Fluid Mech Therm Sci. 2019;5(3):75-81. doi: 10.11648/j.ijfmts.20190503.13

Copy | Download

@article{10.11648/j.ijfmts.20190503.13,
  author = {Mushtaq Ahmed},
  title = {On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {75-81},
  doi = {10.11648/j.ijfmts.20190503.13},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.13},
  abstract = {This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates
AU  - Mushtaq Ahmed
Y1  - 2019/08/26
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.13
DO  - 10.11648/j.ijfmts.20190503.13
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  - 75
EP  - 81
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20190503.13
AB  - This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.
VL  - 5
IS  - 3
ER  -

Copy | Download