A class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force

  • Authors

    • Mushtaq Ahmed University of Karachi
    • Waseem Ahmed Khan University of Karachi
    • S M. Shad Ahsen University of Blochistan
    2018-08-27
    https://doi.org/10.14419/ijamr.v7i3.12326
  • Exact Solutions in the Presence of Body Force, Exact Solutions for Incompressible Fluids, Variable Viscosity Fluids, Na-Vier-Stokes Equations with Body Force, Martin’s Coordinates.

  • Abstract

    This paper determines a class of exact solutions for plane steady motion of incompressible fluids of variable viscosity with body force term in the Navier-Stokes equations. The class consists of stream function  characterized by equation , in polar coordinates ,  where ,  and  are continuously differentiable functions, derivative of  is non-zero but double derivative of  is zero. We find exact solutions, for a suitable component of body force, considering two cases based on velocity profile. The first case fixes both the functions ,  and provides viscosity as function of temperature. Where as the second case fixes the function , leaves  arbitrary and provides viscosity and temperature for the arbitrary function . In both the cases, we can create infinite set of expressions for streamlines, viscosity function, generalized energy function and temperature distribution in the presence of body force.

     

     

  • References

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  • How to Cite

    Ahmed, M., Ahmed Khan, W., & M. Shad Ahsen, S. (2018). 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, 7(3), 77-81. https://doi.org/10.14419/ijamr.v7i3.12326

    Received date: 2018-05-01

    Accepted date: 2018-07-17

    Published date: 2018-08-27