Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

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

[2]  R. M. Terrill.  ON SOME EXPONENTIALLY SMALL TERMS ARISING IN FLOW THROUGH A POROUS PIPE , 1973 .

[3]  J. Majdalani,et al.  Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls , 2003 .

[4]  T. Hayat,et al.  MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel , 2006 .

[5]  T. Hayat,et al.  Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate , 2005 .

[6]  Tasawar Hayat,et al.  Transient flows of a second grade fluid , 2004 .

[7]  Morimatsu Ohki,et al.  Unsteady Flow in a Porous, Elastic, Circular Tube : Part 2. The Tube Contracting or Expanding in Radial Directions , 1982 .

[8]  J. Majdalani,et al.  Moderate‐to‐large injection and suction driven channel flows with expanding or contracting walls , 2003 .

[9]  J. Majdalani,et al.  A NOVEL INVESTIGATION OF THE OSCILLATORY FIELD OVER A TRANSPIRING SURFACE , 1998 .

[10]  C. Dawson,et al.  Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. , 2002, Journal of biomechanics.

[11]  N. M. Bujurke,et al.  Computer extended series solution for unsteady flow in a contracting or expanding pipe , 1998 .

[12]  W. K. Van Moorhem,et al.  Experimental investigation of velocity coupling in combustion instability , 1991 .

[13]  C. Wang,et al.  Pulsatile Flow in a Porous Channel , 1971 .

[14]  R. M. Terrill,et al.  On laminar flow through a uniformly porous pipe , 1969 .

[15]  W. A. Robinson.  The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls , 1976 .

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

[17]  Chunqing Lu.  On the asymptotic behavior of laminar flow through a porous pipe , 1996 .

[18]  A. S. Berman.  Laminar Flow in Channels with Porous Walls , 1953 .

[19]  Tasawar Hayat,et al.  Flow in a slowly deforming channel with weak permeability: An analytical approach , 2010 .

[20]  W. K. Van Moorhem,et al.  An Innovative Method of Investigating the Role of Turbulence in the Velocity Coupling Phenomenon , 1990 .

[21]  T. Wah.  Laminar Flow in a Uniformly Porous Channel , 1964 .

[22]  T. Hayat,et al.  On the analytic solution of the steady flow of a fourth grade fluid , 2006 .

[23]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[24]  K. S. Syed,et al.  Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel , 2009 .

[25]  J. K. Park,et al.  Velocity field of pulsatile flow in a porous tube. , 1989, Journal of biomechanics.

[26]  Hiroshi Aoki,et al.  Unsteady flows in a semi-infinite contracting or expanding pipe , 1977, Journal of Fluid Mechanics.

[27]  G. M. Shrestha,et al.  Laminar flow through parallel and uniformly porous walls of different permeability , 1965 .

[28]  Masakazu Goto,et al.  Unsteady flows in a semi-infinite expanding pipe with injection through wall , 1990 .