Viscous flow over a shrinking sheet with a second order slip flow model

Abstract In this paper, viscous flow over a shrinking sheet is solved analytically using a newly proposed second order slip flow model. The closed solution is an exact solution of the full governing Navier–Stokes equations. The solution has two branches in a certain range of the parameters. The effects of the two slip parameters and the mass suction parameter on the velocity distribution are presented graphically and discussed. For certain combinations of the slip parameters, the wall drag force can decrease with the increase of mass suction. These results clearly show that the second order slip flow model is necessary to predict the flow characteristics accurately.

[1]  C. Wang.  Stagnation slip flow and heat transfer on a moving plate , 2006 .

[2]  Tiegang Fang,et al.  Closed-form exact solutions of MHD viscous flow over a shrinking sheet , 2009 .

[3]  C. Wang,et al.  Viscous flow due to a shrinking sheet , 2006 .

[4]  Eugen Magyari,et al.  Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface , 1999 .

[5]  Lin Wu,et al.  A slip model for rarefied gas flows at arbitrary Knudsen number , 2008 .

[6]  Eugen Magyari,et al.  Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls , 2000 .

[7]  E. M. A. Elbashbeshy,et al.  Heat transfer over a stretching surface with variable surface heat flux , 1998 .

[8]  Tiegang Fang,et al.  Boundary layer flow over a shrinking sheet with power-law velocity , 2008 .

[9]  R. J. Goldstein,et al.  Flow and heat transfer in the boundary layer on a continuous moving surface , 1967 .

[10]  M. Ali,et al.  On thermal boundary layer on a power-law stretched surface with suction or injection , 1995 .

[11]  Wei Liang,et al.  A new solution branch for the Blasius equation - A shrinking sheet problem , 2008, Comput. Math. Appl..

[12]  S. Liao.  A new branch of solutions of boundary-layer flows over an impermeable stretched plate , 2005 .

[13]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[14]  I. Boyd,et al.  Blasius boundary layer solution with slip flow conditions , 2002 .

[15]  Shigehisa Fukui,et al.  A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems , 1990 .

[16]  Taylan Altan,et al.  Metal Forming : Fundamentals and Applications , 1983 .

[17]  Shanshan Yao,et al.  Slip MHD viscous flow over a stretching sheet - An exact solution , 2009 .

[18]  A. Yoshimura,et al.  Wall Slip Corrections for Couette and Parallel Disk Viscometers , 1988 .

[19]  C. Lee,et al.  Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases , 2006 .

[20]  Chaoyang Wang.  Exact Solutions of the Steady-State Navier-Stokes Equations , 1991 .

[21]  Z. Ji,et al.  Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer , 2009 .

[22]  Robert E. Street,et al.  Introduction to the dynamics of rarefied gases , 1967 .

[23]  Tiegang Fang,et al.  Flow between two stretchable disks—An exact solution of the Navier–Stokes equations ☆ , 2008 .

[24]  C. Wang.  Analysis of viscous flow due to a stretching sheet with surface slip and suction , 2009 .

[25]  Tasawar Hayat,et al.  On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet , 2007 .

[26]  H. Andersson.  Slip flow past a stretching surface , 2002 .

[27]  Tiegang Fang,et al.  Flow over a stretchable disk , 2007 .

[28]  Tasawar Hayat,et al.  The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet , 2009 .

[29]  Abdul Aziz,et al.  Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition , 2010 .

[30]  W. H. H. Banks,et al.  Similarity solutions of the boundary-layer equations for a stretching wall , 1983 .

[31]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[32]  E. G. Fisher,et al.  Extrusion of plastics , 1976 .

[33]  Shijun Liao,et al.  A new branch of solutions of boundary-layer flows over a permeable stretching plate , 2007 .

[34]  Tiegang Fang,et al.  A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate , 2005, Appl. Math. Lett..

[35]  Eugen Magyari,et al.  Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities , 2001 .

[36]  B. K. Dutta,et al.  Temperature field in flow over a stretching sheet with uniform heat flux , 1985 .

[37]  L. J. Grubka,et al.  Heat Transfer Characteristics of a Continuous, Stretching Surface With Variable Temperature , 1985 .

[38]  C. Wang.  Stagnation flow on a cylinder with partial slip—an exact solution of the Navier–Stokes equations , 2007 .

[39]  Cha'o-Kuang Chen,et al.  Heat transfer of a continuous, stretching surface with suction or blowing , 1988 .

[40]  Chao-Yang Wang,et al.  Flow due to a stretching boundary with partial slip—an exact solution of the Navier–Stokes equations , 2002 .

[41]  T. Hayat,et al.  MHD rotating flow of a viscous fluid over a shrinking surface , 2007 .

[42]  Imrich Klein,et al.  Engineering principles of plasticating extrusion , 1970 .

[43]  L. Crane.  Flow past a stretching plate , 1970 .

[44]  M. Gad-el-Hak.  The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture , 1999 .

[45]  G. C. Pande,et al.  Hydromagnetic Rayleigh problem for a porous wall in slip flow regime , 1996 .