Effects of variable viscosity in a third grade fluid with porous medium: An analytic solution

Abstract This study extends the analysis of ref. [Hayat T, Ellahi R, Asghar S. The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: An analytic solution, Commun Nonlinear Sci Numer Simul 2007;12:300–313] in a porous medium by employing modified Darcy’s law. Beside this Reynolds and Vogels models of temperature dependent viscosity are considered. The problem is solved using homotopy analysis method (HAM). Expressions of velocity and temperature profiles are constructed analytically and explained with the help of graphs.

[1]  T. Hayat,et al.  On analytic solution for generalized three-dimensional MHD flow over a porous stretching sheet , 2007 .

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

[3]  K. Rajagopal.  On Boundary Conditions for Fluids of the Differential Type , 1995 .

[4]  Tasawar Hayat,et al.  On the moment of a plane disk in a non-Newtonian fluid , 1999 .

[5]  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.

[6]  Kumbakonam R. Rajagopal,et al.  A note on unsteady unidirectional flows of a non-Newtonian fluid , 1982 .

[7]  T. Hayat,et al.  Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet , 2007 .

[8]  R. C. Fetecâu,et al.  Cone and plate flow of a second grade fluid , 1997 .

[9]  B. Yilbas,et al.  Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity , 2006 .

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

[11]  Tasawar Hayat,et al.  The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: An analytical solution , 2007 .

[12]  T. Hayat,et al.  Periodic unsteady flows of a non-Newtonian fluid , 1998 .

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

[14]  Kumbakonam R. Rajagopal,et al.  Start-up flows of second grade fluids in domains with one finite dimension , 1995 .

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

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

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

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

[19]  Kumbakonam R. Rajagopal,et al.  On the creeping flow of the second-order fluid , 1984 .

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

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

[22]  Wenchang Tan,et al.  STOKES FIRST PROBLEM FOR AN OLDROYD-B FLUID IN A POROUS HALF SPACE , 2005 .

[23]  Naveed Ahmed,et al.  On the MHD flow of a second grade fluid in a porous channel , 2007, Comput. Math. Appl..

[24]  Tasawar Hayat,et al.  Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet , 2007 .

[25]  T. Hayat,et al.  A note on series solution for generalized Couette flow , 2007 .

[26]  T. Hayat,et al.  Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid , 2007 .

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

[28]  Tasawar Hayat,et al.  Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid , 2007 .

[29]  P. Ariel.  Flow of viscoelastic fluids through a porous channel—I , 1993 .

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

[31]  Tasawar Hayat,et al.  Some unsteady unidirectional flows of a non-Newtonian fluid , 2000 .

[32]  T. Hayat,et al.  Wire coating analysis using MHD Oldroyd 8-constant fluid , 2007 .

[33]  Mehrdad Massoudi,et al.  Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe , 1995 .

[34]  T. Hayat,et al.  Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet , 2007 .

[35]  T. Hayat,et al.  The Influence of Hall Current on Rotating Flow of a Third Grade Fluid in a Porous Medium , 2007 .

[36]  T. Hayat,et al.  Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .

[37]  Tasawar Hayat,et al.  Note on an exact solution for the pipe flow of a third-grade fluid , 2007 .

[38]  T. Hayat,et al.  The influence of thermal radiation on MHD flow of a second grade fluid , 2007 .

[39]  Shijun Liao.  An explicit analytic solution to the Thomas-Fermi equation , 2003, Appl. Math. Comput..