A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number

Mushtaq Ahmed

doi:doi:10.11648/j.ijfmts.20180403.11

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A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number

Mushtaq Ahmed

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 4, Issue 3)

Received: 7 November 2018 Accepted: 6 December 2018 Published: 7 January 2019

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Abstract

This is to communicate a class of new exact solutions of the equations governing the steady plane motion of fluid with constant density, constant thermal conductivity but variable viscosity and body force term to the right-hand side of Navier-Stokes equations with moderate Peclet numbers. Exact solutions are obtained for Peclet numbers between zero and infinity except 2, for given one component of the body force using successive transformation technique and a new characterization for the streamlines. A temperature distribution formula, due to heat generation, is obtained when Peclet number is 4 other wise temperature distribution is found to be constant. The exact solutions are large in number as streamlines, velocity components, viscosity function, and energy function and temperature distribution in presence of body force exists for a huge number of the moderate Peclet number.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 4, Issue 3)
DOI	10.11648/j.ijfmts.20180403.11
Page(s)	27-33
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, Moderate Peclet Number, Navier-Stokes Equations with Body Force, Incompressible Fluids

References

[1]	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. http:/www.sciencepubco.com/index.php/IJAMR. doi:10.14419/ijamr.v7i1.8836.
[2]	Mushtaq A., On Some Thermally Conducting Fluids: Ph. D Thesis, Department of Mathematics, University of Karachi, Pakistan, 2016.
[3]	B. Abramzon and C. Elata, Numerical analysis of unsteady conjugate heat transfer 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.
[4]	Z. G. Feng, E. E. Michaelides, Unsteady heat transfer from a spherical particle at finite Peclet numbers, J. Fluids Eng 118: 96-102, 1996.
[5]	Z. G. Fenz, E. E. Michaelides, Unsteady mass transport from a sphere immersed in a porous medium at finite Peclet numbers, Int. J. Heat Mass Transfer 42: 3529-3531, 1999.
[6]	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. http:/www.sciencepubco.com/index.php/IJBAS. doi:10.14419/ijbas.v4i4.5064.
[7]	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. http:/www.sciencepubco.com/index.php/IJAMR. doi:10.14419 /ijamr.v7i2.9694.
[8]	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. http:/www.sciencepubco.com/index.php/IJAMR. doi:10.14419/ijamr.v7i2.12326.
[9]	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.
[10]	Martin, M. H.; The flow of a viscous fluid I: Archive for Rational Mechanics and Analysis, 1971, 41(4), 266-286.
[11]	Daniel Zwillinger; Handbook of differential equations; Academic Press, Inc. (1989).

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APA Style

Mushtaq Ahmed. (2019). 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 & Thermal Sciences, 4(3), 27-33. https://doi.org/10.11648/j.ijfmts.20180403.11

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ACS Style

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. Int. J. Fluid Mech. Therm. Sci. 2019, 4(3), 27-33. doi: 10.11648/j.ijfmts.20180403.11

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AMA Style

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. Int J Fluid Mech Therm Sci. 2019;4(3):27-33. doi: 10.11648/j.ijfmts.20180403.11

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@article{10.11648/j.ijfmts.20180403.11,
  author = {Mushtaq Ahmed},
  title = {A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {4},
  number = {3},
  pages = {27-33},
  doi = {10.11648/j.ijfmts.20180403.11},
  url = {https://doi.org/10.11648/j.ijfmts.20180403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20180403.11},
  abstract = {This is to communicate a class of new exact solutions of the equations governing the steady plane motion of fluid with constant density, constant thermal conductivity but variable viscosity and body force term to the right-hand side of Navier-Stokes equations with moderate Peclet numbers. Exact solutions are obtained for Peclet numbers between zero and infinity except 2, for given one component of the body force using successive transformation technique and a new characterization for the streamlines. A temperature distribution formula, due to heat generation, is obtained when Peclet number is 4 other wise temperature distribution is found to be constant. The exact solutions are large in number as streamlines, velocity components, viscosity function, and energy function and temperature distribution in presence of body force exists for a huge number of the moderate Peclet number.},
 year = {2019}
}

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TY  - JOUR
T1  - A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number
AU  - Mushtaq Ahmed
Y1  - 2019/01/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20180403.11
DO  - 10.11648/j.ijfmts.20180403.11
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  - 27
EP  - 33
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20180403.11
AB  - This is to communicate a class of new exact solutions of the equations governing the steady plane motion of fluid with constant density, constant thermal conductivity but variable viscosity and body force term to the right-hand side of Navier-Stokes equations with moderate Peclet numbers. Exact solutions are obtained for Peclet numbers between zero and infinity except 2, for given one component of the body force using successive transformation technique and a new characterization for the streamlines. A temperature distribution formula, due to heat generation, is obtained when Peclet number is 4 other wise temperature distribution is found to be constant. The exact solutions are large in number as streamlines, velocity components, viscosity function, and energy function and temperature distribution in presence of body force exists for a huge number of the moderate Peclet number.
VL  - 4
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). 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 & Thermal Sciences, 4(3), 27-33. https://doi.org/10.11648/j.ijfmts.20180403.11

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ACS Style

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. Int. J. Fluid Mech. Therm. Sci. 2019, 4(3), 27-33. doi: 10.11648/j.ijfmts.20180403.11

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AMA Style

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. Int J Fluid Mech Therm Sci. 2019;4(3):27-33. doi: 10.11648/j.ijfmts.20180403.11

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@article{10.11648/j.ijfmts.20180403.11,
  author = {Mushtaq Ahmed},
  title = {A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {4},
  number = {3},
  pages = {27-33},
  doi = {10.11648/j.ijfmts.20180403.11},
  url = {https://doi.org/10.11648/j.ijfmts.20180403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20180403.11},
  abstract = {This is to communicate a class of new exact solutions of the equations governing the steady plane motion of fluid with constant density, constant thermal conductivity but variable viscosity and body force term to the right-hand side of Navier-Stokes equations with moderate Peclet numbers. Exact solutions are obtained for Peclet numbers between zero and infinity except 2, for given one component of the body force using successive transformation technique and a new characterization for the streamlines. A temperature distribution formula, due to heat generation, is obtained when Peclet number is 4 other wise temperature distribution is found to be constant. The exact solutions are large in number as streamlines, velocity components, viscosity function, and energy function and temperature distribution in presence of body force exists for a huge number of the moderate Peclet number.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Class of New Exact Solution of Equations for Motion of Variable Viscosity Fluid in Presence of Body Force with Moderate Peclet Number
AU  - Mushtaq Ahmed
Y1  - 2019/01/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20180403.11
DO  - 10.11648/j.ijfmts.20180403.11
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  - 27
EP  - 33
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20180403.11
AB  - This is to communicate a class of new exact solutions of the equations governing the steady plane motion of fluid with constant density, constant thermal conductivity but variable viscosity and body force term to the right-hand side of Navier-Stokes equations with moderate Peclet numbers. Exact solutions are obtained for Peclet numbers between zero and infinity except 2, for given one component of the body force using successive transformation technique and a new characterization for the streamlines. A temperature distribution formula, due to heat generation, is obtained when Peclet number is 4 other wise temperature distribution is found to be constant. The exact solutions are large in number as streamlines, velocity components, viscosity function, and energy function and temperature distribution in presence of body force exists for a huge number of the moderate Peclet number.
VL  - 4
IS  - 3
ER  -

Copy | Download