Exact flow of a third grade fluid past a porous plate using homotopy analysis method

The flow of a third grade fluid past a porous plate is considered. An exact analytical solution of the governing non-linear differential equation is constructed using homotopy analysis method. It is observed that the relevant perturbation solution corresponds to a special case of the presented solution.

[1]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

[2]  Shijun Liao,et al.  A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method , 1992 .

[3]  Siddhartha Sen,et al.  Topology and geometry for physicists , 1983 .

[4]  S. Liao.  An approximate solution technique not depending on small parameters: A special example , 1995 .

[5]  Plane steady flows of a third grade fluid , 1987 .

[6]  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.

[7]  K. Rajagopal,et al.  Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders , 1999 .

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

[9]  S. Liao,et al.  Application of Homotopy Analysis Method in Nonlinear Oscillations , 1998 .

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

[11]  S. Liao.  An explicit, totally analytic approximate solution for Blasius’ viscous flow problems , 1999 .

[12]  M. Erdoğan,et al.  Plane surface suddenly set in motion in a non-Newtonian fluid , 1995 .

[13]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .

[14]  S. Liao.  An analytic approximation of the drag coefficient for the viscous flow past a sphere , 2002 .

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

[16]  S. Liao.  APPLICATION OF PROCESS ANALYSIS METHOD TO THE SOLUTION OF 2-D NONLINEAR PROGRESSIVE GRAVITY WAVES , 1992 .

[17]  S. Liao.  An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude , 2003 .

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

[19]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[20]  MHD rotating flow of a third-grade fluid on an oscillating porous plate , 2001 .

[21]  Georges Papy.  Topologie als Grundlage des Analysis-Unterrichts , 1968 .

[22]  Shijun Liao,et al.  Higher‐order streamfunction‐vorticity formulation of 2D steady‐state Navier‐Stokes equations , 1992 .

[23]  M. De.  Handbuch der Physik , 1957 .

[24]  S. Liao.  A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics , 1997 .

[25]  S. Liao.  AN EXPLICIT TOTALLY ANALYTIC APPROXIMATION OF BLASIUS VISCOUS FLOW PROBLEMS , 1999 .

[26]  A. Dold.  Lectures on Algebraic Topology , 1972 .

[27]  Kumbakonam R. Rajagopal,et al.  On Stokes' problem for a non-Newtonian fluid , 1983 .