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Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Author

Listed:
  • Constantin Fetecau

    (Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania)

  • Dumitru Vieru

    (Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, Romania)

  • Tehseen Abbas

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Rahmat Ellahi

    (Department of Mathematics & Statistics, Faculty of Basic and Applied Sciences, International Islamic University, Islamabad 44000, Pakistan
    Department of Mechanical Engineering, University of California Riverside, Riverside, CA 92521, USA)

Abstract

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Suggested Citation

  • Constantin Fetecau & Dumitru Vieru & Tehseen Abbas & Rahmat Ellahi, 2021. "Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure," Mathematics, MDPI, vol. 9(4), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:334-:d:495290
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    References listed on IDEAS

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    1. Housiadas, Kostas D. & Georgiou, Georgios C., 2018. "Analytical solution of the flow of a Newtonian fluid with pressure-dependent viscosity in a rectangular duct," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 123-128.
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