On the Study of Magnetohydrodynamic Squeezing Flow of Nanofluid between Two Parallel Plates Embedded in a Porous Medium

Document Type : Original Article


1 Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

2 Works and Physical Planning Department, University of Lagos, Akoka, Lagos, Nigeria

3 Department of Mechanical Engineering, Federal University of Agriculture, Abeokuta, Nigeria


A study of magnetohydrodynamic squeezing flow of nanofluid between two parallel plates embedded in a porous medium is presented in this work. The ordinary differential equation which is transformed from the developed governing partial differential equations is solved using differential transformation method. The accuracy of the results of the approximate analytical method are established as they agree very well with the results numerical method using fourth-fifth order Runge-Kutta-Fehlberg method. Using the developed analytical solutions, the parametric studies reveal that when the velocity of the flow increases during the squeezing process, the Hartmann and squeezing numbers decrease while during the separation process, the velocity of the fluid increases with increase in Hartmann and squeezing numbers. Also, the velocity of the nanofluids further decreases as the Hartmann number increases when the plates move apart. However, it is revealed that increase in nanotube concentration leads to an increase in the velocity of the flow during the squeezing flow. The present study will be useful in various industrial, biological and engineering applications.


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[1]      Stefan J. Versuche über die scheinbare Adhäsion. Ann Der Phys Und Chemie 1875;230:316–8. doi:10.1002/andp.18752300213.
[2]      IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos Trans R Soc London 1886;177:157–234. doi:10.1098/rstl.1886.0005.
[3]      Archibald FR. Load capacity and time relations in squeeze films. Trans ASME J Lub Tech 1956;78:29–35.
[4]      Jackson JD. A study of squeezing flow. Appl Sci Res 1963;11:148–52. doi:10.1007/BF03184719.
[5]      Usha R, Sridharan R. Arbitrary squeezing of a viscous fluid between elliptic plates. Fluid Dyn Res 1996;18:35–51. doi:10.1016/0169-5983(96)00002-0.
[6]      Yang K-T. Un steady laminar boundary layer in an incompressible stagnation flow. ASME J Appl Mech 1958;80:421–7.
[7]      Kuzma DC. Fluid inertia effects in squeeze films. Appl Sci Res 1968;18:15–20. doi:10.1007/BF00382330.
[8]      Tichy JA, Winer WO. Inertial considerations in parallel circular squeeze film bearings. J Lubr Technol 1970;92:588–92.
[9]      Grimm RJ. Squeezing flows of Newtonian liquid films an analysis including fluid inertia. Appl Sci Res 1976;32:149–66. doi:10.1007/BF00383711.
[10]    Khan U, Ahmed N, Khan SIU, Bano S, Mohyud-Din ST. Unsteady squeezing flow of a Casson fluid between parallel plates. World J Model Simul 2014;10:308–19.
[11]     Birkhoff G, Hydrodynamics A. study in Logic, Fact and Similitude 1960.
[12]    Wang CY. The squeezing of a fluid between two plates. J Appl Mech 1976;43:579–83.
[13]    Wang CY, Watson LT. Squeezing of a viscous fluid between elliptic plates. Appl Sci Res 1979;35:195–207. doi:10.1007/BF00382705.
[14]    Hamdan MH, Barron RM. Analysis of the squeezing flow of dusty fluids. Appl Sci Res 1992;49:345–54. doi:10.1007/BF00419980.
[15]    Phan-Thien N. Squeezing flow of a viscoelastic solid. J Nonnewton Fluid Mech 2000;95:343–62. doi:10.1016/S0377-0257(00)00175-0.
[16]    Rashidi MM, Shahmohamadi H, Dinarvand S. Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates. Math Probl Eng 2008;2008:1–13. doi:10.1155/2008/935095.
[17]    Duwairi HM, Tashtoush B, Damseh R. On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates. Heat Mass Transf 2004. doi:10.1007/s00231-004-0525-5.
[18]    Qayyum A, Awais M, Alsaedi A, Hayat T. Unsteady squeezing flow of Jeffery fluid between two parallel disks. Chinese Phys Lett 2012;29:34701.
[19]    Mahmood M, Asghar S, Hossain MA. Squeezed flow and heat transfer over a porous surface for viscous fluid. Heat Mass Transf 2007;44:165–73. doi:10.1007/s00231-006-0218-3.
[20]    Hatami M, Jing D. Differential Transformation Method for Newtonian and non-Newtonian nanofluids flow analysis: Compared to numerical solution. Alexandria Eng J 2016;55:731–9. doi:10.1016/j.aej.2016.01.003.
[21]    Mohyud-Din ST, Zaidi ZA, Khan U, Ahmed N. On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates. Aerosp Sci Technol 2015;46:514–22. doi:10.1016/j.ast.2015.07.020.
[22]    Mohyud-Din ST,