International Journal of Fluid Mechanics & Thermal Sciences

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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

Received: 07 November 2018    Accepted: 06 December 2018    Published: 07 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.

DOI 10.11648/j.ijfmts.20180403.11
Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 4, Issue 3, September 2018)
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), 2024. 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).
Author Information
  • Department of Mathematics, University of Karachi, Karachi, Pakistan

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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://download.sciencepg.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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    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.
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