Investigation of the periodic axisymmetric flow of a viscoelastic fluid through a cylindrical tube

  • J. I. Braude V.N. Karazin Kharkov National University, 61022, Kharkov, Svobody sq., 4
  • N. M. Kizilova V.N. Karazin Kharkov National University, 61022, Kharkov, Svobody sq., 4 https://orcid.org/0000-0001-9981-7616

Abstract

A generalized Womersley model of a nonstationary axisymmetric flow of a viscous incompressible fluid through a tube of circular cross-section to periodic pressure fluctuations at the inlet of the tube is obtained due for the case of a fluid with complicated rheology. The rheological parameters of the fluid are viscosity and four relaxation coefficients for strains and stresses of the first and second order. Such rheology is proper to the non-Newtonian viscoelastic fluids with mesostructure, namely technical and biological micro/ nanofluids. It was shown that with the increase of the relaxation coefficients of the first/second order the flow rate, the average and maximum velocities decrease/increase, accordingly. Simultaneous changes in these parameters can lead to complex changes in the velocity profile, especially for higher harmonics. The studied regularities can explain the deviations of the flow parameters of different micro/nanofluids from the values predicted by the classical Womersley solution for a homogeneous Newtonian fluid, which does not take into account viscous dissipation during the rearrangement of the fluid mesostructure.

Key words: Womersley problem, viscoelastic fluids, rheological properties, mathematical modeling.

Pages of the article in the issue: 49 - 52

Language of the article: Ukrainian

References

McDonald's Blood Flow in Arteries. (2011) By Ch. Vlachopoulos, M. O'Rourke, W.W. Nichols. CRC Press. 768 p.

FRIDTJOV I. (2016) Rheology and non-Newtonian fluids. Springer. 199 p.

Complex Fluid-Flows in Microfluidics. (2017) Galindo-Rosales J.F.H. (ed.) Springer. 111 p.

HE J.-H., JI F.-Y. (2019) Two-scale mathematics and fractional calculus for thermodynamics. Thermal Sci. Vol. 23(4). p. 2131-2133.

How to Cite
Braude, J. I., & Kizilova, N. M. (1). Investigation of the periodic axisymmetric flow of a viscoelastic fluid through a cylindrical tube. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 49-52. https://doi.org/10.17721/1812-5409.2020/1-2.7
Section
Differential equations, mathematical physics and mechanics