On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates

Abstract Squeezing flow of a viscous fluid is considered. Two types of flows are discussed namely, the axisymmetric flow and two dimensional flow. Similarity transform proposed by Wang (1976) [13] has been used to reduce the Navier–Stokes equations to a highly non-linear ordinary differential equation which jointly describes both types of flows. Solution to aforementioned ordinary differential equation is obtained by using Variation of Parameters Method (VPM). VPM is free from the existence of small or large parameters and hence it can be applied to a large variety of problems as compared to the perturbation method applied by Wang (1976) [13]. Comparison among present and already existing solutions is also provided to show the efficiency of VPM. A convergence analysis is also carried out. Effects of different physical parameters on the flow field is discussed and demonstrated graphically with comprehensive discussions and explanations.

[1]  Yasir Khan,et al.  Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non- Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution , 2012 .

[2]  Sheikh Irfanullah Khan,et al.  Magneto hydrodynamic (MHD) squeezing flow of a Casson fluid between parallel disks , 2013 .

[3]  C. Wang,et al.  The Squeezing of a Fluid Between Two Plates , 1976 .

[4]  Mohammad Mehdi Rashidi,et al.  Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. , 2008 .

[5]  Muhammad Aslam Noor,et al.  Modified Variation of Parameters Method for Second-order Integro-differential Equations and Coupled Systems , 2009 .

[6]  W. A. Wolfe.  Squeeze film pressures , 1964 .

[7]  N. Phan-Thien.  Squeezing flow of a viscoelastic solid , 2000 .

[8]  T. Hayat,et al.  Application of Homotopy Perturbation Method to Deformable Channel with Wall Suction and Injection in a Porous Medium , 2008 .

[9]  M. Rady,et al.  Analytical solutions for squeeze flow with partial wall slip , 1999 .

[10]  R. Usha,et al.  Arbitrary squeezing of a viscous fluid between elliptic plates , 1996 .

[11]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[12]  G. Nath,et al.  Unsteady laminar boundary layers in a compressible stagnation flow , 1975, Journal of Fluid Mechanics.

[13]  Muhammad Aslam Noor,et al.  VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS , 2009 .

[14]  Rizwan Ul Haq,et al.  MHD flow of a Casson fluid over an exponentially shrinking sheet , 2012 .

[15]  O. Reynolds.  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 , 1886, Philosophical Transactions of the Royal Society of London.

[16]  R. Grimm.  Squeezing flows of Newtonian liquid films an analysis including fluid inertia , 1976 .

[17]  L. Watson,et al.  Squeezing of a viscous fluid between elliptic plates , 1979 .

[18]  J. Jackson.  A study of squeezing flow , 1963 .

[19]  S. Abbasbandy.  A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials , 2007 .

[20]  Muhammad Aslam Noor,et al.  Variational iteration technique for solving higher order boundary value problems , 2007, Appl. Math. Comput..

[21]  A. A. Soliman,et al.  New applications of variational iteration method , 2005 .

[22]  Saeid Abbasbandy,et al.  Numerical solution of non‐linear Klein–Gordon equations by variational iteration method , 2007 .

[23]  Dennis C. Kuzma,et al.  Fluid inertia effects in squeeze films , 1968 .

[24]  R. Barron,et al.  Analysis of the squeezing flow of dusty fluids , 1992 .

[25]  Zulfiqar Ali Zaidi,et al.  MHD squeezing flow between two infinite plates , 2014 .

[26]  Ward O. Winer,et al.  Inertial Considerations in Parallel Circular Squeeze Film Bearings , 1970 .