Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffery fluid in a rectangular duct

Abstract The purpose of this paper is to study the closed-form solutions of peristaltic flow of Jeffery fluid under the simultaneous effects of magnetohydrodynamics (MHD) and partial slip conditions in a rectangular duct. The influence of wave train propagation is also taken into account. The analysis of mathematical model consists of continuity and the momentum equations are carried out under long wavelength ( 0 → ∞ ) and low Reynolds number ( Re → 0 ) assumptions. The governing equations are first reduced to the dimensionless system of partial differential equation using the appropriate variables and afterwards exact solutions are obtained by applying the method of separation of variables. The role of pertinent parameters such as Hartmann number M , slip parameter β 1 , volumetric flow rate Q , Jeffery parameter λ 1 and the aspect ratio β against the velocity profile, pressure gradient and pressure rise is illustrated graphically. The streamlines have also been presented to discuss the trapping bolus discipline. Comparison with the existing studies is made as a limiting case of the considered problem.at the end.

[1]  N. E. Kissi,et al.  Ecoulement de fluides polymères enchevêtrés dans un capillaire. Modélisation du glissement macroscopique à la paroi , 1989 .

[2]  S. Srinivas,et al.  Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium , 2009, Appl. Math. Comput..

[3]  Kumbakonam R. Rajagopal,et al.  Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid , 1983 .

[4]  Noreen Sher Akbar,et al.  Metachronal beating of cilia under the influence of Casson fluid and magnetic field , 2015 .

[5]  Rajeev Taneja,et al.  MHD Flow with Slip Effects and Temperature-dependent Heat Source in a Viscous Incompressible Fluid Confined between a Long Vertical Wavy Wall and a Parallel Flat Wall , 2004 .

[6]  S. Srinivas,et al.  The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls , 2009, Appl. Math. Comput..

[7]  N. Nakajima,et al.  The influence of materials of construction on biconical rotor and capillary measurements of shear viscosity of rubber and its compounds and considerations of slippage , 1991 .

[8]  Y. Abd Elmaboud,et al.  Influence of induced magnetic field on peristaltic flow in an annulus , 2012 .

[9]  Rahmat Ellahi,et al.  Effects of heat transfer on peristaltic motion of Oldroyd fluid in the presence of inclined magnetic field , 2014 .

[10]  S. Hatzikiriakos,et al.  Wall slip of molten high density polyethylenes. II. Capillary rheometer studies , 1992 .

[11]  R. Mutharasan,et al.  Experimental observations of wall slip: tube and packed bed flow , 1987 .

[12]  M. Othman.  On the possibility of overstable motion of a rotating viscoelastic fluid layer heated from below under the effect of magnetic field with one relaxation time , 2004 .

[13]  Kumbakonam R. Rajagopal,et al.  A note on unsteady unidirectional flows of a non-Newtonian fluid , 1982 .

[14]  K. Rajagopal,et al.  An exact solution for the flow of a non-newtonian fluid past an infinite porous plate , 1984 .

[15]  Sohail Nadeem,et al.  Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field , 2014 .

[16]  S. Srinivas,et al.  Peristaltic transport in an asymmetric channel with heat transfer — A note , 2008 .

[17]  J. Piau,et al.  Measurement and modelling of friction in polymer melts during macroscopic slip at the wall , 1994 .

[18]  Abdelhalim Ebaid,et al.  Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel , 2008 .

[19]  S. Nadeem,et al.  Unsteady MHD flow of a non-Newtonian fluid on a porous plate , 2007 .

[20]  S Nadeem,et al.  Peristaltic flow of a Jeffrey fluid in a rectangular duct , 2010 .

[21]  I. Pop,et al.  Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions , 2014 .

[22]  W. Kwang-Hua Chu,et al.  Peristaltic transport in a slip flow , 2000 .

[23]  K. Migler,et al.  Slip transition of a polymer melt under shear stress. , 1993, Physical review letters.

[24]  G. Vinogradov,et al.  Wall slippage and elastic turbulence of polymers in the rubbery state , 1968 .

[25]  M. Kothandapani,et al.  Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel , 2008 .

[26]  C. L. Roux,et al.  Existence and Uniqueness of the Flow of Second‐Grade Fluids with Slip Boundary Conditions , 1999 .

[27]  I. Pop,et al.  Magnetohydrodynamic stagnation-point flow towards a stretching/shrinking sheet with slip effects , 2013 .

[28]  Davood Domiri Ganji,et al.  Magnetohydrodynamic free convection of Al2O3–water nanofluid considering Thermophoresis and Brownian motion effects , 2014 .

[29]  R. Ellahi.  Exact Solutions of Flows of an Oldroyd 8-Constant Fluid with Nonlinear Slip Conditions , 2010 .

[30]  Richard Haberman,et al.  Applied Partial Differential Equations with Fourier Series and Boundary Value Problems , 2012 .

[31]  R. Ellahi.  The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions , 2013 .