This work is concerned with the influence of uniform suction or injection on unsteady incompressible Couette flow for the Eyring-Powell model. The resulting unsteady problem for horizontal velocity field is solved by means of homotopy analysis method (HAM). The characteristics of the horizontal velocity field and wall shear stress are analyzed and dis cussed. Pade approximants and Taylor polynomials are also found for velocity profile and are used to make the maxi mum error as small as possible. The graphs of the error for the Pade approximation and Taylor approximation are drawn and discussed. Convergence of the series solution is also discussed with the help of h -curve and interval of conver gence is also found.
T. Hayat, M. Khan, A. M. Siddiqui and S. Asghar, “Transient Flows of a Second Grade Fluid,” International Journal of Non-Linear Mechanics, Vol. 39, No. 10, 2004, pp. 1621-1633. http://dx.doi.org/10.1016/j.ijnonlinmec.2002.12.001
T. Hayat, Z. Abbas and M. Sajid, “Heat and Mass Transfer Analysis on the Flow of a Second Grade Fluid in the Presence of Chemical Reaction,” Physics Letters A, Vol. 372, No. 14, 2008, pp. 2004-2408. http://dx.doi.org/10.1016/j.physleta.2007.10.102
T. Hayat, R. Ellahi and F. M. Mahomed, “Exact Solution of a Thin Film Flow of an Oldroyd 6-Constant Fluid over a Moving Belt,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 1, 2009, pp. 133-139. http://dx.doi.org/10.1016/j.cnsns.2007.08.001
T. Hayat, R. Ellahi and F. M. Mahomed, “Exact Solutions for Thin Film Flow of a Third Grade Fluid Down an Inclined Plane,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1336-1341. http://dx.doi.org/10.1016/j.chaos.2008.03.006
T. Hayat, T. Javed and Z. Abbas, “MHD Flow of a Micropolar Fluid near a Stagnation Point towards a NonLinear Stretching Surface,” Nonlinear Analysis: Real World Applications, Vol. 10, No. 3, 2009, pp. 1514-1526. http://dx.doi.org/10.1016/j.nonrwa.2008.01.019
S. Asghar, M. Khan and T. Hayat, “Magnetohydrodynamic Transient Flows of a Non-Newtonian Fluid,” International Journal of Non-Linear Mechanics, Vol. 40, No. 5, 2005, pp. 589-601. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.07.011
M. Khan, Z. Abbas and T. Hayat, “Analytic Solution for Flow of Sisko Fluid through a Porous Medium,” Transport in Porous Media, Vol. 71, No. 1, 2008, pp. 23-37 http://dx.doi.org/10.1007/s11242-007-9109-4
M. Khan, S. Hyder Ali, T. Hayat and C. Fetecau, “MHD Flows of a Second Grade Fluid between Two Side Walls Perpendicular to a Plate through a Porous Medium,” International Journal of Non-Linear Mechanics, Vol. 43, No. 4, 2008, pp. 302-319. http://dx.doi.org/10.1016/j.ijnonlinmec.2007.12.016
R. Cortell, “A Note on Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 41, No. 1, 2006, pp. 78-85. http://dx.doi.org/10.1016/j.ijnonlinmec.2005.04.008
R. Cortell, “MHD Flow and Mass Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species,” Chemical Engineering and Processing: Process Intensification, Vol. 46, No. 8, 2007, pp. 721-728. http://dx.doi.org/10.1016/j.cep.2006.09.008
M. Ayub, H. Zaman, M. Sajid and T. Hayat, “Analytical Solution of Stagnation-Point Flow of a Viscoelastic Fluid towards a Stretching Surface,” Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 9, 2008, pp.1822-1835. http://dx.doi.org/10.1016/j.cnsns.2007.04.021
M. Ayub, H. Zaman and M. Ahmad, “Series Solution of Hydromagnetic Flow and Heat Transfer with Hall Effect in a Second Grade Fluid over a Stretching Sheet,” Central European Journal of Physics, Vol. 8, No. 1, 2010, pp. 135-149. http://dx.doi.org/10.2478/s11534-009-0110-0
M. Ayub and H. Zaman, “Analytical Solution of Orthogonal Flow Impinging on a Wall with Suction or Blowing,” Journal of Basic and Applied Sciences, Vol. 6, No. 2, 2010, pp. 93-97.
P. D. Ariel, T. Hayat and S. Asghar, “The Flow of an Elastico-Viscous Fluid Past a Stretching Sheet with Partial Slip,” Acta Mechanica, Vol. 187, No. 1-4, 2006, pp. 29-35. http://dx.doi.org/10.1007/s00707-006-0370-3
K. R. Rajagopal, “A Note on Unsteady Unidirectional Flows of a Non-Newtonian Fluid,” International Journal of Non-Linear Mechanics, Vol. 17, No. 5-6, 1982, pp. 369-373. http://dx.doi.org/10.1016/0020-7462(82)90006-3
K. R. Rajagopal, “On the Creeping Flow of the Second-Order Fluid,” International Journal of Non-Linear Mechanics, Vol. 15, No. 2, 1984, pp. 239-246. http://dx.doi.org/10.1016/0377-0257(84)80008-7
K. R. Rajagopal and T. Y. Na, “On Stoke’s Problem for a Non-Newtonian Fluid,” Acta Mechanica, Vol. 48, No. 3-4, 1983, pp. 233-239. http://dx.doi.org/10.1007/BF01170422
M. E. Erdogan, “Plane Surface Suddenly Set in Motion in a Non-Newtonian Fluid,” Acta Mechanica, Vol. 108, No. 1-4, 1995, pp. 179-187. http://dx.doi.org/10.1007/BF01177337
A. M. Siddiqui and P. N. Kaloni, “Certain Inverse Solutions of a Non-Newtonian Fluid,” International Journal of Non-Linear Mechanics, Vol. 21, No. 6, 1986, pp. 459-473. http://dx.doi.org/10.1016/0020-7462(86)90042-9
C. Fetecau, “Cone and Plate Flow of a Second Grade,” Acta Mechanica, Vol. 122, No. 1-4, 1977, pp. 225-230.
T. Fang, “A Note on the Incompressible Couette Flow with Porous Walls,” International Communications in Heat and Mass Transfer, Vol. 31, No. 1, 2004, pp. 31-41. http://dx.doi.org/10.1016/S0735-1933(03)00199-4
A. R. A. Khaled and K. Vafai, “The Effect of the Slip Condition on Stokes and Couette Flows due to an Oscillating Wall: Exact Solutions,” International Journal of Non-Linear Mechanics, Vol. 39, No. 5, 2004, pp. 795-809. http://dx.doi.org/10.1016/S0020-7462(03)00043-X
S. Asghar, T. Hayat and P. D. Ariel, “Unsteady Couette Flows in a Second Grade Fluid with Variable Material Properties,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 1, 2009, pp. 154-159. http://dx.doi.org/10.1016/j.cnsns.2007.07.016
T. Hayat, E. Momoniat and F. M. Mahomed, “Axial Couette Flow of an Electrically Conducting Fluid in an Annulus,” International Journal of Modern Physics B, Vol. 22, No. 15, 2008, pp. 2489-2500. http://dx.doi.org/10.1142/S0217979208039587
T. Hayat and A. H. Kara, “Couette Flow of a Third-Grade Fluid with Variable Magnetic Field,” Mathematical and Computer Modelling, Vol. 43, No. 1-2, 2006, pp. 132-137
G. S. Seth, Md. S. Ansari and R. Nandkeolyar, “Effects of Rotation and Magnetic Field on Unsteady Couette Flow in a Porous Channel,” Journal of Applied Fluid Mechanics, Vol. 4, No. 2, 2011, pp. 95-103.
R. Bhaskara and N. D. Bathaiah, “Halll Effects on MHD Couette Flow through a Porous Straight Channel,” Defense Science Journal, Vol. 32, No. 4, 1982, pp. 313-326.
S. Das, S. L. Maji, M. Guria and R. N. Jana, “Unsteady MHD Couette Flow in a Rotating System,” Mathematical and Computer Modelling, Vol. 50, No. 7-8, 2009, pp. 1211-1217. http://dx.doi.org/10.1016/j.mcm.2009.05.036
R. Ganapathy, “A Note on Oscillatory Couette Flow in a Rotating System,” ASME Journal of Applied Mechanics, Vol. 61, No. 1, 1994, pp. 208-209. http://dx.doi.org/10.1115/1.2901403
M. Guria, R. N. Jana and S. K. Ghosh, “Unsteady Couette Flow in A Rotating System,” International Journal of Non-Linear Mechanics, Vol. 41, No. 6-7, 2006, pp. 838-843. http://dx.doi.org/10.1016/j.ijnonlinmec.2006.04.010
M. Guria, S. Das, R. N. Jana and S. K. Ghosh, “Oscillatory Couette Flow in the Presence of an Inclined Magnetic Field,” Meccanica, Vol. 44, No. 5, 2009, pp. 555-564. http://dx.doi.org/10.1007/s11012-009-9195-1
K. D. Singh, M. G. Gorla and H. Raj, “A Periodic Solution of Oscillatory Couette Flow through Porous Medium in Rotating System,” Indian Journal of Pure and Applied Mathematics, Vol. 36, 2005, pp. 151-159.
R. E. Powell and H. Eyring, “Mechanism for the Relaxation Theory of Viscosity,” Nature, Vol. 154, No. 55, 1944, pp. 427-428.
N. T. M. Eldabe, A. A. Hassan and M. A. A. Mohamed, “Effects of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates,” Zeitschrift für Naturforschung, Vol. 58, No. 2, 2003, pp. 204-210.
J. Zueco and O. A. Beg, “Network Numerical Simulation Applied to Pulsatile Non-Newtonian Flow through a Channel with Couple Stress and Wall Mass Flux Effects,” International Journal of Applied Mathematics and Mechanics, Vol. 5, 2009, pp. 1-16.
K. V. Prasad, P. S. Datti and B. T. Raju, “Momentum and Heat Transfer of a Non-Newtonian Eyring-Powell Fluid over a Non-Isothermal Stretching Sheet,” International Journal of Mathematical Archive, Vol. 4, No. 1, 2013, pp. 230-241.
M. Patel and M. G. Timol, “Numerical Treatment of MHD Powell-Eyring Fluid Flow Using the Method of Satisfaction of Asymptotic Boundary Conditions,” International Journal of Computer Science, Vol. 1, No. 2, 2011, pp. 71-78.
V. Sirohi, M. G. Timol and N. I. Kalathia, “Numerical Treatment of Powell-Eyring Fluid Flow past a 90? Wedge,” Reg Journal of Heat and Mass Transfer, Vol. 6, No. 3, 1984, pp. 219-223.
T. Javed, N. Ali, Z. Abbas and M. Sajid, “Flow of an Eyring-Powell Non-Newtonian Fluid over a Stretching Sheet,” Chemical Engineering Communications, Vol. 200, 2013, pp. 327-336. http://dx.doi.org/10.1080/00986445.2012.703151
S. Noreen and M. Qasim, “Peristaltic Flow of MHD Eyring-Powell Fluid in a Channel,” The European Physical Journal Plus, Vol. 128, No. 8, 2013, pp. 91-103. http://dx.doi.org/10.1140/epjp/i2013-13091-3
S. J. Liao, “Notes on the Homotopy Analysis Method: Some Definitions and Theorems,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, 2009, pp. 983-997
S. J. Liao, J. Su and A. T. Chwang, “Series Solution for a Nonlinear Model of Combined Convective and Radiative Cooling of a Spherical Body,” International Journal of Heat and Mass Transfer, Vol. 49, No. 15-16, 2006, pp. 2437-2445 http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.01.030
S. J. Liao, “An Analytic Solution of Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate,” Communications in Nonlinear Science and Numerical Simulation, Vol. 11, No. 3, 2006, pp. 326-339.
S. J. Liao, “On the Homotopy Analysis Method for Nonlinear Problems,” Applied Mathematics and Computation, Vol. 147, No. 2, 2004, pp. 499-513.
S. J. Liao, “An Analytic Approximate Technique for Free Oscillations of Positively Damped Systems with Algebraically Decaying Amplitude,” International Journal of Non-Linear Mechanics, Vol. 38, No. 8, 2003, pp. 1173-1183. http://dx.doi.org/10.1016/S0020-7462(02)00062-8
S. J. Liao and A. Campo, “Analytic Solutions of the Temperature Distribution in Blasius Viscous Flow Problems,” Journal of Fluid Mechanics, Vol. 453, 2002, pp. 411-425. http://dx.doi.org/10.1017/S0022112001007169
S. J. Liao, “An Analytic Approximation of the Drag Coefficient for the Viscous Flow past a Sphere,” International Journal of Non-Linear Mechanics, Vol. 37, No. 1, 2002, pp. 1-18. http://dx.doi.org/10.1016/S0020-7462(00)00092-5
S. J. Liao, “An Explicit, Totally Analytic Approximate Solution for Blasius’ Viscous Flow Problems,” International Journal of Non-Linear Mechanics, Vol. 34, No. 4, 1999, pp. 759-778. http://dx.doi.org/10.1016/S0020-7462(98)00056-0
S. J. Liao, “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problem,” Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.
S. Abbasbandy, T. Hayat, R. Ellahi and S. Asghar, “Numerical Results of Flow in a Third Grade Fluid between Two Porous Walls,” Zeitschrift Fur Naturforschung A, Vol. 64a, 2009, pp. 59-64.
S. Abbasbandy and F. S. Zakaria, “Soliton Solution for the Fifth-Order Kdv Equation with the Homotopy Analysis Method,” Nonlinear Dynamics, Vol. 51, No. 1-2, 2008, pp. 83-87. http://dx.doi.org/10.1007/s11071-006-9193-y
S. Abbasbandy, “Approximate Solution of the Nonlinear Model of Diffusion and Reaction Catalysts by Means of the Homotopy Analysis Method,” Chemical Engineering Journal, Vol. 136, No. 2-3, 2008, pp. 144-150. http://dx.doi.org/10.1016/j.cej.2007.03.022
S. Abbasbandy, “The Application of Homotopy Analysis Method to Solve a Generalized Hirota-Satsuma Coupled KdV Equation,” Physics Letters A, Vol. 361, No. 6, 2007, pp. 478-483. http://dx.doi.org/10.1016/j.physleta.2006.09.105
S. Abbasbandy, “Homotopy Analysis Method for Heat Radiation Equations,” International Communications in Heat and Mass Transfer, Vol. 34, No. 3, 2007, pp. 380-387. http://dx.doi.org/10.1016/j.icheatmasstransfer.2006.12.001
S. Abbasbandy, “The Application of Homotopy Analysis Method to Nonlinear Equations Arising in Heat Transfer,” Physics Letters A, Vol. 360, No. 1, 2006, pp. 109-113. http://dx.doi.org/10.1016/j.physleta.2006.07.065
H. Zaman and M. Ayub, “Series Solution of Unsteady Free Convection Flow with Mass Transfer along an Accelerated Vertical Porous Plate with Suction,” Central European Journal of Physics, Vol. 8, No. 6, 2010, pp. 931-939. http://dx.doi.org/10.2478/s11534-010-0007-y
H. Zaman, T. Hayat, M. Ayub and R. S. R. Gorla, “Series Solution for Heat Transfer from a Continuous Surface in a Parallel Free Stream of Viscoelastic Fluid,” Numerical Methods for Partial Differential Equations, Vol. 27, No. 6, 2011, pp. 1511-1524. http://dx.doi.org/10.1002/num.20593
T. Hayat, H. Zaman and M. Ayub, “Analytic Solution of Hydromagnetic Flow with Hall Effect over a Surface Stretching with a Power Law Velocity,” Numerical Methods for Partial Differential Equations, Vol. 27, No. 4, 2010, pp. 937-959. http://dx.doi.org/10.1002/num.20562
J. H. Mathews and K. D. Fink, “Numerical Methods Using MATLAB,” Printice-Hall Inc., Upper Saddle River, 2004.
F. Labropulu and O. P. Chandna, “Oblique Flow Impinging on a Wall with Suction or Blowing,” Acta Mechanica, Vol. 115, No. 1-4, 1996, pp. 15-25. http://dx.doi.org/10.1007/BF01187425
F. Ahmad and W. H. Albarakati, “An Approximate Analytic Solution of the Blasius Problem,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, 2008, pp. 1021-1024.