- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2012 (2012), Article ID 634925, 11 pages
A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method
1Department of Mechanical Engineering, University of California Riverside, Bourns Hall, A373, Riverside, CA 92521, USA
2Department of Mathematics & Statistics, FBAS, IIU, H-10, Islamabad 44000, Pakistan
Received 14 December 2011; Accepted 27 January 2012
Academic Editor: Teoman Özer
Copyright © 2012 R. Ellahi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- W. Tan and T. Masuoka, “Stability analysis of a Maxwell fluid in a porous medium heated from below,” Physics Letters A, vol. 360, no. 3, pp. 454–460, 2007.
- T. Hayat and F. M. Mahomed, “Note on an exact solution for the pipe flow of a third-grade fluid,” Acta Mechanica, vol. 190, no. 1–4, pp. 233–236, 2007.
- W. Tan and T. Masuoka, “Stokes' first problem for a second grade fluid in a porous half-space with heated boundary,” International Journal of Non-Linear Mechanics, vol. 40, no. 4, pp. 515–522, 2005.
- M. Y. Malik, A. Hussain, and S. Nadeem, “Flow of a Jeffery-six constant fluid between coaxial cylinders with heat transfer analysis,” Communications in Theoretical Physics, vol. 56, no. 2, pp. 345–351, 2011.
- M. Y. Malik, A. Hussain, S. Nadeem, and T. Hayat, “Flow of a third grade fluid between coaxial cylinders with variable viscosity,” Zeitschrift fur Naturforschung A, vol. 64, no. 9-10, pp. 588–596, 2009.
- M. Hameed and S. Nadeem, “Unsteady MHD flow of a non-Newtonian fluid on a porous plate,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 724–733, 2007.
- R. Ellahi, Steady and Unsteady Flow for Newtonian and Non-Newtonian Fluids: Basics, Concepts and Methods, VDM, Saarbrücken, Germany, 2009.
- R. Ellahi and S. Afzal, “Effects of variable viscosity in a third grade fluid with porous medium: an analytic solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2056–2072, 2009.
- M. Massoudi and I. Christie, “Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe,” International Journal of Non-Linear Mechanics, vol. 30, no. 5, pp. 687–699, 1995.
- T. Hayat, R. Ellahi, and S. Asghar, “The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: an analytical solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 3, pp. 300–313, 2007.
- S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis, Shanghai Jiao Tong University, Shanghai, China, 1992.
- S. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, vol. 2, Chapman & Hall, Boca Raton, Fla, USA, 2004.
- S. Abbasbandy, “The application of homotopy analysis method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 360, no. 1, pp. 109–113, 2006.
- R. Ellahi, “Effects of the slip boundary condition on non-Newtonian flows in a channel,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1377–1384, 2009.
- T. Hayat, R. Ellahi, P. D. Ariel, and S. Asghar, “Homotopy solution for the channel flow of a third grade fluid,” Nonlinear Dynamics, vol. 45, no. 1-2, pp. 55–64, 2006.
- R. A. Van Gorder and K. Vajravelu, “On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 12, pp. 4078–4089, 2009.
- 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, pp. 1173–1183, 2003.