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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 135472, 14 pages
The One Step Optimal Homotopy Analysis Method to Circular Porous Slider
1School of Mathematical Science, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, Gomal University, Dera Ismail Khan, Pakistan
Received 4 August 2012; Revised 1 November 2012; Accepted 5 November 2012
Academic Editor: Xu Zhang
Copyright © 2012 Mohammad Ghoreishi et al. 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.
- A. S. Berman, “Laminar flow in channels with porous walls,” vol. 24, pp. 1232–1235, 1953.
- A. F. Elkouh, “Laminar flow between rotating porous disks,” Journal of the Engineering Mechanics Division, vol. 94, pp. 919–929, 1968.
- V. T. Morgan and A. Cameron, “Mechanism of lubrication in porous metal bearing,” in Proceeding Conference on Lubrication and Wear, pp. 151–175, Institution of Mechanical Engineers, London, UK, 1957.
- I. Proudman, “An example of steady laminar flow at large Reynolds number,” ASME Journal of Applied Mechanics, vol. 9, pp. 593–602, 1960.
- R. M. Terrill, “Laminar flow in a uniformly porous channel,” vol. 15, pp. 299–310, 1964.
- U. Srinivasan, “The analysis of a double-layered porous slider bearing,” Wear, vol. 42, no. 2, pp. 205–215, 1977.
- R. S. R. Gorla, “Flow and thermal characteristics of a circular porous slider bearing,” Wear, vol. 94, no. 2, pp. 157–174, 1984.
- N. Faraz, “Study of the effects of the Reynolds number on circular porous slider via variational iteration algorithm-II,” Computers and Mathematics with Applications, vol. 61, no. 8, pp. 1991–1994, 2011.
- C. Y. Wang, “Fluid dynamics of the circular porous slider,” ASME Journal of Applied Mechanics, vol. 41, no. 2, pp. 343–347, 1974.
- S.-J. Liao, Beyond Perturbation, Introduction to the Homotopy Analysis Method, vol. 2 of CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
- S.-J. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Springer and Higher Education Press, 2012.
- M. Ghoreishi, A. I. B. Md. Ismail, and A. K. Alomari, “Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3007–3015, 2011.
- M. M. Rashidi, S. A. Mohimanian pour, and S. Abbasbandy, “Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1874–1889, 2011.
- A. K. Alomari, M. S. M. Noorani, R. Nazar, and C. P. Li, “Homotopy analysis method for solving fractional Lorenz system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1864–1872, 2010.
- A. S. Bataineh, M. S. M. Noorani, and I. Hashim, “Modified homotopy analysis method for solving systems of second-order BVPs,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 430–442, 2009.
- F. Awawdeh, A. Adawi, and Z. Mustafa, “Solutions of the SIR models of epidemics using HAM,” Chaos, Solitons and Fractals, vol. 42, no. 5, pp. 3047–3052, 2009.
- N. Herisanu, V. Marinca, T. Dordea, and G. Madescu, “A new analytical approach to nonlinear vibration of an electric machine,” Proceedings of the Romanian Academy. Series A, vol. 9, no. 3, pp. 229–236, 2008.
- V. Marinca, N. Herişanu, and I. Nemeş, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, no. 3, pp. 648–653, 2008.
- V. Marinca, N. Herişanu, C. Bota, and B. Marinca, “An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate,” Applied Mathematics Letters, vol. 22, no. 2, pp. 245–251, 2009.
- V. Marinca and N. Herişanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 35, no. 6, pp. 710–715, 2008.
- S. Iqbal, M. Idrees, A. M. Siddiqui, and A. R. Ansari, “Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 2898–2909, 2010.
- Z. Niu and C. Wang, “A one-step optimal homotopy analysis method for nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2026–2036, 2010.
- S.-J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2003–2016, 2010.
- N. M. Bujurke and P. K. Achar, “Computer extended series solution of the circular porous slider,” Acta Mechanica, vol. 101, no. 1–4, pp. 81–92, 1993.
- V. Marinca and N. Herişanu, “Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method,” Journal of Sound and Vibration, vol. 329, no. 9, pp. 1450–1459, 2010.
- N. Herişanu and V. Marinca, “Accurate analytical solutions to oscillators with discontinuities and fractional-power restoring force by means of the optimal homotopy asymptotic method,” Computers & Mathematics with Applications, vol. 60, no. 6, pp. 1607–1615, 2010.