Transient Taylor–Dean flow in a composite annulus with porous walls partially filled with porous material
Tóm tắt
The sole aim of this article is to examine the relative contribution of suction/injection parameter on Taylor–Dean flow in a composite annular gap partially filled with porous material. In the present setup, the Newtonian fluid flow is induced by the circumferential motion of both cylinders and pressure gradient imposed in the Azimuthal direction. The mathematical model governing the flow is rendered dimensionless using appropriate dimensionless quantities transformed using the Laplace transform technique. Using suitable Ansatz, the equation is reduced to the Bessel differential equations and solved. The solution of converted to the time domain using a well-known numerical scheme known as the Riemann-sum approximation. The variation of the Newtonian fluid for different flow parameters is presented graphically. The solution method is validated by obtaining the steady-state solution and also using the implicit finite different approach (IFD); comparison of the methods is depicted in tabular form (see Tables 1, 2). It is deduced generally that the Newtonian fluid is higher when injection at the outer cylinder except when Da is small also higher interfacial velocity can be achieved by taking positive value of
Từ khóa
Tài liệu tham khảo
Dean, W.R.: Fluid motion in a curved channel. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 121, 402–420 (1928)
Gupta, R.K., Gupta, K.: Steady flow of an elasticoviscous fluid in porous coaxial circular cylinder. Indian J. Pure Appl. Math. 27(4), 423–434 (1996)
Tsangaris, S.: Oscillatory flow of an incompressible viscous-fluid in a straight annular pipe. J. Mech. Theor. Appl. 3(3), 467 (1984)
Goldstein, S.: Modern Developments in Fluid Dynamics, pp. 315–316. Clarendon Press (1938)
Bhatnagar, R.K.: Flow of an oldroyd fluid in a circular pipe with time-dependent pressure gradient. Appl. Sci. Res. 30(4), 241–267 (1975). https://doi.org/10.1007/BF00386693
Uchida, S.: The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe. J. Appl. Math. 7, 403–422 (1956)
Richardson, E.G., Tyler, E.: The transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Phys. Soc. 42(1), 1–15 (1929)
Dryden, H.L., Murnaghan, F.D., Bateman, H.: Hydrodynamics. Dover Publ. Inc. (1956)
Gupta, S., Poulikakos, D., Kurtcuoglu, V.: Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid. Phys. Fluids 20(9), 1–12 (2008)
Tsangaris, S., Kondaxakis, D., Vlachakis, N.W.: Exact solution of the Navier–Stokes equations for the pulsating dean flow in a channel with porous walls. Int. J. Eng. Sci. 44(20), 1498–1509 (2006). https://doi.org/10.1016/j.ijengsci.2006.08.010
Tsangaris, S., Vlachakis, N.W.: Exact solution for the pulsating finite gap dean flow. Appl. Math. Model. 31(9), 1899–1906 (2007). https://doi.org/10.1016/j.apm.2006.06.011
Jha, B.K., Yahaya, J.D.: Transient Dean flow in an annulus: a semi-analytical approach. J. Taibah Univ. Sci. 13(1), 169–176 (2019). https://doi.org/10.1080/16583655.2018.1549529
Jha, B.K., Yahaya, J.D.: Transient Dean flow in a channel with suction/injection: a semi-analytical approach. J. Process Mech. Eng. 233(5), 1–9 (2019)
Yen, J.T., Chang, C.C.: Magnetohydrodynamic channel flow under time-dependent pressure gradient. Phys. Fluids. 4(11), 1355–1360 (1961). https://doi.org/10.1063/1.1706224
Nandi, S.: Unsteady hydromagnetic flow in a porous annulus with time-dependent pressure gradient. Pure. Appl. Geophys. 79, 33–40 (1970)
McGinty, S., McKee, S., McDermott, R.: Analytic solutions of Newtonian and non-Newtonian pipe flows subject to a general time-dependent pressure gradient. J. Non-Newtonian Fluid Mech. 162, 54–77 (2009)
Mendiburu, A.A., Carrocci, L.R., Carvalho, J.A.: Analytical solutions for transient one-dimensional Couette flow considering constant and time-dependent pressure gradients. Engenharia Térmica (Therm. Eng.). 8, 92–98 (2009)
Jha, B.K., Gambo, D.: Combined effects of suction/injection and exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a semi-analytical approach. Int. J. Geomath. 11, 28 (2020). https://doi.org/10.1007/s13137-020-00164-w
Jha, B.K., Gambo, D.: Role of exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a Riemann-sum approximation approach. Arab. J. Basic Appl. Sci. 28(1), 1–10 (2021). https://doi.org/10.1080/25765299.2020.1861754
Jha, B.K., Yusuf, T.S.: Transient pressure-driven flow in an annulus partially filled with porous material: Azimuthal pressure gradient. Math. Model. Eng. Probl. 5(3), 260–267 (2018)
Azad, M.A.K., Andallah, L.S.: Explicit exponential finite difference scheme for 1D Navier–Stokes equation with time-dependent pressure gradient. J. Bangladesh Math. Soc. 36, 79–90 (2016)
Sayed-Ahmed, M.E., Attia, H.A., Ewis, K.M.: Time-dependent pressure gradient effect on unsteady MHD Couette flow and heat transfer of a Casson fluid. Engineering 3, 38–49 (2010)
Tsimpoukis, A., Valougeorgis, D.: Rarefied isothermal gas flow in a long circular tube due to oscillating pressure gradient. Microfluidics Nanofluidics 22(1), 5 (2017). https://doi.org/10.1007/s10404-017-2024-2
Khali, S., Nebbali, R., Bouhadef, K.: Effect of a porous layer on Newtonian and power-law fluids flow between rotating cylinders using lattice Boltzmann method. J. Braz. Soc. Mech. Sci. Eng. (2017). https://doi.org/10.1007/s40430-017-0809-6
Waters, S.L., Pedley, T.J.: Oscillatory flow in a tube of time-dependent curvature. Part 1. Perturbation to flow in a stationary curved tube. J. Fluid Mech. 383, 327–352 (1999)
Khadrawi, A.F., Al-Nimr, M.A.: Unsteady natural convection fluid flow in a vertical microchannel under the effect of the Dual-Phase-Lag heat conduction model. Int. J. Thermophys. 28, 1387–1400 (2007)
Jha, B.K., Apere, C.A.: Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus. AIP Adv. 1, 042121-1-042121–15 (2011)
Tzou, D.Y.: Macro to Micro Scale Heat Transfer: The Lagging Behavior. Taylor and Francis (1997)