Abstract
The problems of the oscillatory flow of a viscoelastic incompressible fluid in a flat channel are solved for a given harmonic oscillation of the fluid flow rate. The transfer function of the amplitude-phase frequency response is determined. This function is used to determine the influence of the oscillation frequency, acceleration, and relaxation properties of the liquid on the ratio of shear stress on the channel wall to the average velocity over the channel section. Changes in the amplitude and phase of the shear stress on the channel wall in an unsteady flow are also determined depending on the dimensionless oscillation frequency and the relaxation properties of the liquid. It is shown that the viscoelastic properties of the fluid, as well as its acceleration, are the limiting factors for using the quasi-stationary approach. The found formulas for determining the transfer function during the flow of a viscoelastic fluid in a non-stationary flow allow, to determine the dissipation of mechanical energy in a non-stationary flow of the medium, which are of no small importance when calculating the regulation of hydraulic and pneumatic systems.
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References
Marx, U., et al.: Homan-on-a-Chip developments: a translational cutting- edge alternative to systemic safety assessment and effecting evacuation in laboratory animals and man? ATLA 40, 235–257 (2012)
Inman, W., Domanskiy, K., Serdy, J., Ovens, B., Trimper, D., Griffith, L.G.: Dishing modeling and fabrication of a constant flow pneumatic micropump. J. Micromech. Microeng. 17, 891–899 (2007)
Akilov, Z.H.A.: Non-stationary motions of viscoelastic fluids. Tashkent: Fan (1982)
Khuzhaerov, B.K.H.: Rheological properties of mixtures. Samarkand: Sogdiana (2000)
Mirzajanzade, A.K.H., Karaev, A.K., Shirinzade, S.A.: Hydraulics in drilling and cementing oil and gas wells. M. Nedra (1977)
Gromeki, I.S.: On the theory of fluid motion in narrow cylindrical tubes, pp. 149–171 (1952)
Gromeki, I.S.: On the propagation velocity of the undulating motion of a fluid in elastic pipes.Sobr.op. - M, pp. 172–183 1952
Crandall, I.B.: Theory of vibrating systems and sounds D. Van. Nostrand Co., New York (1926)
Lambossy, P.: Oscillations foresees dun liquids incompressible et visqulux dans un tube rigide et horizontal calculi de IA force de frottement . Helv. Physiol. Acta. 25, 371–386 (1952)
Womersly, J.R.: Method for the calculation of velocity rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol, 127(3), 553–563 1955,
Richardson, E.G., Tyler, E.: The transverse Velocity gradient neat the mothe of pipes in which an alternating or continuous flow of air is established. Pros. Phys. Soc. London, v. 42 (1929)
Popov, D.N., Mokhov, I.G.: Experimental study of the profiles of local velocities in a pipe with fluctuations in the flow rate of a viscous liquid. Izv. Univ. Eng. No. 7, pp. 91–95 (1971)
Uchida, S.: The pulsating viscous flow superposed on the stead laminar motion of incompressible fluid in a circular pipe. ZAMP. 7(5). 403–422 (1956)
Ünsal, B., Ray, S., Durst, F., Ertunç, Ö.: Pulsating laminar pipe flows with sinusoidal mass flux variations. Fluid Dyn. Res. 37, 317–333 (2005)
Siegel, R., Perlmutter, M.: Heat transfer with pulsating flow in a channel, pp. 18–32
Fayzullaev, D.F., Navruzov, K.: Hydrodynamics of pulsating flows, Tashkent, Fan, p. 192 (1986)
Valueva, E.P., Purdin, M.S.: Hydrodynamics and heat transfer of pulsating laminar flow in channels. Teploenergetika, no. 9, pp. 24–33
Tsangaris, S., Vlachakis, N.W.: Exact solution of the Navier-Stokes equations for the oscillating flow in a duct of a cross-section of right-angled isosceles triangle. ZAMP, 54, 1094–1100 (2003)
Tsangaris, S., Vlachakis, N.W.: Exact solution for the pulsating finite gap Dean flow. Appl. Math. Model, 31, 1899–1906 (2007)
Jons, J.R., Walters, T.S.: Flow of elastic-viscous liquids in channels under the influence of a periodic pressure gradient. Part 1. Rheol. Acta, 6, 240–245 (1967)
Casanellas, L., Ortin, J.: Laminar oscillatory flow of Maxwell and Oldroyd-B fluids. J. Non-Newtonian Fluid. Mech. 166, 1315–1326 (2011)
Abu-El Hassan, A., El-Maghawry, E. M.: Unsteady axial viscoelastic pipe flows of anOldroyd-B fluid in // Rheology-New concepic. Appl. Methods Ed by Durairaj R. Published by In Tech. ch. 6, pp. 91–106 (2013)
Akilov, Z.A., Dzhabbarov, M.S., Khuzhayorov, B.K.: Tangential shear stress under the periodic flow of a viscoelastic fluid in a cylindrical tube. Fluid Dyn.56(2), 189–199 (2021). SSN 0015–4628,
Ding, Z, Jian, Y.: Electrokinetic oscillatory flow and energy microchannelis: a linear analysis. J. Fluid. Mech. 919, 1–31 (2021). A20. https://doi.org/10.1017/jfm. 380A20
Astarita, G., Marrucci, G.: Principles of non-Newtonian fluid mechanics. McGraw-HILL, p. 309 (1974)
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Navruzov, K., Fayziev, R.A., Mirzoev, A.A., Sharipova, S.B.k. (2023). Tangential Shear Stress in an Oscillatory Flow of a Viscoelastic Fluid in a Flat Channel. In: Koucheryavy, Y., Aziz, A. (eds) Internet of Things, Smart Spaces, and Next Generation Networks and Systems. NEW2AN 2022. Lecture Notes in Computer Science, vol 13772. Springer, Cham. https://doi.org/10.1007/978-3-031-30258-9_1
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