Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet

SummaryThe problem of axisymmetric flow of a third grade fluid over a radially stretching sheet is studied. By means of similarity transformation, the governing non-linear partial differential equations are reduced to a non-linear ordinary differential equation. The ordinary differential equation is analytically solved using homotopy analysis method (HAM). The solution for the velocity is obtained. The series solution is developed and the convergence of the results is discussed. Finally, the results are discussed with various graphs.

[1]  T. Hayat,et al.  Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid , 2004 .

[2]  Shijun Liao,et al.  On the explicit, purely analytic solution of Von Kármán swirling viscous flow , 2006 .

[3]  Tasawar Hayat,et al.  Exact flow of a third grade fluid past a porous plate using homotopy analysis method , 2003 .

[4]  P. S. Datti,et al.  MHD visco-elastic fluid flow over a non-isothermal stretching sheet , 2004 .

[5]  T. Hayat,et al.  Couette and Poiseuille flows of an oldroyd 6-constant fluid with magnetic field , 2004 .

[6]  P. Ariel Axisymmetric flow of a second grade fluid past a stretching sheet , 2001 .

[7]  I. Pop,et al.  Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium , 2005 .

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

[9]  Pradeep G. Siddheshwar,et al.  Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet , 2005 .

[10]  Shijun Liao,et al.  Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate , 2005 .

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

[12]  I. Pop,et al.  Explicit analytic solution for similarity boundary layer equations , 2004 .

[13]  T. Ray Mahapatra,et al.  Stagnation-point flow of a viscoelastic fluid towards a stretching surface , 2004 .

[14]  K. Cheung,et al.  Homotopy analysis of nonlinear progressive waves in deep water , 2003 .

[15]  Kumbakonam R. Rajagopal,et al.  Thermodynamics and stability of fluids of third grade , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  Ioan Pop,et al.  Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet , 2004 .

[17]  T. Hayat,et al.  On the explicit analytic solutions of an Oldroyd 6-constant fluid , 2004 .

[18]  Shijun Liao,et al.  Analytic solutions of the temperature distribution in Blasius viscous flow problems , 2002, Journal of Fluid Mechanics.

[19]  S. Liao A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.

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

[21]  S. Liao On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet , 2003, Journal of Fluid Mechanics.

[22]  I. Liu,et al.  Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field , 2005 .

[23]  K. Sadeghy,et al.  Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate , 2004 .

[24]  Ioan Pop,et al.  On the explicit analytic solution of Cheng-Chang equation , 2003 .

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

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