Influence of slip condition on peristaltic transport of a viscoelastic fluid with fractional Burger’s model

The investigation is to explore the transportation of a viscoelastic fluid with fractional Burgers’ model by peristalsis through a channel under the influence of wall slip condition. This analysis has been carried out under the assumption of long wavelength and low Reynolds number. An approximate analytical solution of the problem is obtained by using Homotopy Analysis method (HAM). It is assumed that the cross-section of the channel varies sinusoidally along the length of channel. The expressions for axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters α and β, material constants λ1,λ2,λ3, slip parameter k and amplitude φ on the pressure difference and friction force across one wavelength are discussed numerically and with the help of illustrations.

[1]  Constantin Fetecau,et al.  Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate , 2008, Appl. Math. Comput..

[2]  S. Liao,et al.  Solving solitary waves with discontinuity by means of the homotopy analysis method , 2005 .

[3]  Constantin Fetecau,et al.  Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model , 2009 .

[4]  Tasawar Hayat,et al.  Periodic unidirectional flows of a viscoelastic fluid with the fractional Maxwell model , 2004, Appl. Math. Comput..

[5]  Tasawar Hayat,et al.  Exact peristaltic flow in tubes with an endoscope , 2006, Appl. Math. Comput..

[6]  Xu Mingyu,et al.  Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model , 2002 .

[7]  Haitao Qi,et al.  Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel , 2007 .

[8]  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 .

[9]  D Tsiklauri,et al.  Non-Newtonian effects in the peristaltic flow of a Maxwell fluid. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Weinberg,et al.  Peristaltic pumping with long wavelengths at low Reynolds number , 1968, Journal of Fluid Mechanics.

[11]  Tasawar Hayat,et al.  Slip effects on the peristaltic transport of MHD fluid with variable viscosity , 2008 .

[12]  Z An,et al.  New Ideas for Proving Convergence of Decomposition Methods , 2003 .

[13]  I. M. El-Desoky,et al.  Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid , 2006 .

[14]  Najeeb Alam Khan,et al.  Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model , 2009 .

[15]  Shaowei Wang,et al.  Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus , 2009 .

[16]  Yong Yang,et al.  Study on ride comfort of tractor with tandem suspension based on multi-body system dynamics , 2009 .

[17]  Physics Letters , 1962, Nature.

[18]  Haitao Qi,et al.  On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model , 2009 .

[19]  Tasawar Hayat,et al.  An analysis of peristaltic transport for flow of a Jeffrey fluid , 2007 .

[20]  Tasawar Hayat,et al.  Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube , 2008 .

[21]  S. Das,et al.  Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation , 2011, Int. J. Comput. Math..

[22]  Tasawar Hayat,et al.  Magnetohydrodynamic flow of an Oldroyd 6-constant fluid , 2004, Appl. Math. Comput..

[23]  S. Das,et al.  Homotopy analysis method for solving fractional hyperbolic partial differential equations , 2011, Int. J. Comput. Math..

[24]  Tan Wen-chang,et al.  A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates , 2003 .

[25]  Liao Shijun,et al.  Homotopy analysis method: A new analytic method for nonlinear problems , 1998 .

[26]  Y. Cherruault,et al.  New ideas for proving convergence of decomposition methods , 1995 .

[27]  Thomas Walker Latham.  Fluid motions in a peristaltic pump. , 1966 .

[28]  Tasawar Hayat,et al.  Hall effects on peristaltic flow of a Maxwell fluid in a porous medium , 2007 .

[29]  Tasawar Hayat,et al.  Peristaltic flow of a Maxwell fluid in a channel with compliant walls , 2009 .

[30]  X. Mingyu,et al.  Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative , 2009 .

[31]  S. Liao.  An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate , 2006 .

[32]  Haitao Qi,et al.  Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial Cylinders , 2006 .

[33]  T. Hayat,et al.  The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel , 2008 .

[34]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[35]  T. Hayat,et al.  On the MHD flow of fractional generalized Burgers’ fluid with modified Darcy’s law , 2007 .

[36]  C. Friedrich.  Relaxation and retardation functions of the Maxwell model with fractional derivatives , 1991 .

[37]  S Nadeem.  General periodic flows of fractional Oldroyd-B fluid for an edge , 2007 .

[38]  Haitao Qi,et al.  Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model , 2007 .