Optimal homotopy asymptotic method with application to thin film flow

• Authors: Vasile Marinca , Nicolae Herişanu , Iacob Nemeş
• Languages of publication: EN

Abstracts

EN

A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.

Keywords

EN

Optimal Homotopy Asymptotic Method (OHAM); thin film flow; fourth grade fluid

Discipline

• 47.50.-d: Non-Newtonian fluid flows
• 04.25.-g: Approximation methods; equations of motion
• 47.20.Ky: Nonlinearity, bifurcation, and symmetry breaking
• 47.15.gm: Thin film flows

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 648-653

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Vasile Marinca

• Department of Mechanics and Vibration, Politehnica University of Timişoara, Bd. Mihai Viteazu 1, 300222, Timişoara, Romania

author

Nicolae Herişanu

• Department of Mechanics and Vibration, Politehnica University of Timişoara, Bd. Mihai Viteazu 1, 300222, Timişoara, Romania

author

Iacob Nemeş

• Department of Mechanics and Vibration, Politehnica University of Timişoara, Bd. Mihai Viteazu 1, 300222, Timişoara, Romania

References

• [1] T. Hayat, M. Sajid, Phys. Lett. A 361, 316 (2007) http://dx.doi.org/10.1016/j.physleta.2006.09.060[Crossref]
• [2] A.M. Siddiqui, R. Mahmood, Q.K. Ghori, Phys. Lett. A 352, 404 (2006) http://dx.doi.org/10.1016/j.physleta.2005.12.033[Crossref]
• [3] A.M. Siddiqui, R. Mahmood, Q.K. Ghori, Int.J. Nonlinear Sci. 7, 7 (2006)
• [4] A.M. Siddiqui, M. Ahmed, Q.K. Ghori, Int. J. Nonlinear Sci. 7, 15 (2006)
• [5] P.D. Ariel, T. Hayat, S. Asghar, Int. J. Nonlinear Sci. 7, 399 (2006)
• [6] Q.K. Ghori, M. Ahmed, A.M. Siddiqui, Int. J. Nonlinear Sci. 8, 179 (2007)
• [7] H. Tari, D.D. Ganji, M. Rostamian, Int. J. Nonlinear Sci. 8, 203 (2007)
• [8] A.N. Hayfeh, Perturbation Methods (Wiley, New York, 2000)
• [9] A.N. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981)
• [10] J.D. Cole, Perturbation Methods in Applied Mathematics (Blaisdell Publishing Company, Waltham, MA, 1968)
• [11] R.E. Mickens, J. Sound Vibr. 116, 185 (1987) http://dx.doi.org/10.1016/S0022-460X(87)81330-5[Crossref]
• [12] V. Marinca, N. Herişanu, Acta Mech. 184, 231 (2006) http://dx.doi.org/10.1007/s00707-006-0336-5[Crossref]
• [13] J.H. He, Comput. Method. Appl. M. 178, 256 (1999) http://dx.doi.org/10.1016/S0045-7825(99)00018-3[Crossref]
• [14] J.H. He, Appl. Math. Comput. 156, 527 (2004) http://dx.doi.org/10.1016/j.amc.2003.08.008[Crossref]
• [15] J.H. He, Int. J. Mod. Phys. B 20, 1141 (2006) http://dx.doi.org/10.1142/S0217979206033796[Crossref]
• [16] V. Marinca, Arch. Mech. 58, 241 (2006)
• [17] S.J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999) http://dx.doi.org/10.1016/S0020-7462(98)00056-0[Crossref]
• [18] S.J. Liao, Appl. Math. Mech.-Engl. 19, 957 (1998) http://dx.doi.org/10.1007/BF02457955[Crossref]
• [19] S.J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999) http://dx.doi.org/10.1016/S0020-7462(98)00056-0[Crossref]
• [20] S.J. Liao, Int. J. Nonlinear Mech. 39, 271 (2004) http://dx.doi.org/10.1016/S0020-7462(02)00174-9[Crossref]
• [21] S.J. Liao, Appl. Math. Comput. 169, 1186 (2005) http://dx.doi.org/10.1016/j.amc.2004.10.058[Crossref]
• [22] S.J. Liao, Y. Tan, Stud. Appl. Math. 119, 297 (2007) http://dx.doi.org/10.1111/j.1467-9590.2007.00387.x[Crossref]
• [23] A. Alizadeh-Pahlavan, V. Aliakbar, F. Vakili-Farahani, K. Sadeghy, Comm. Nonlin. Sci. Num. Simul. doi:10.1016/j.cnsns.2007.09.011 [Crossref]
• [24] F.M. Allan, M.I. Syam, J. Comput. Appl. Math. 182, 362 (2005) http://dx.doi.org/10.1016/j.cam.2004.12.017[Crossref]
• [25] S. Abbasbandy, Phys. Lett. A 360, 109 (2006) http://dx.doi.org/10.1016/j.physleta.2006.07.065[Crossref]
• [26] K. Yabushita, M. Yamashita, K. Tsuboi, J. Phys. A 40, 8403 (2007) http://dx.doi.org/10.1088/1751-8113/40/29/015[Crossref]
• [27] S. Abbasbandy, Phys. Lett. A 361, 478 (2007) http://dx.doi.org/10.1016/j.physleta.2006.09.105[Crossref]
• [28] H. Xu, S.J. Liao, I. Pop, Eur. J. Mech. B-Fluid 26, 15 (2007) http://dx.doi.org/10.1016/j.euromechflu.2005.12.003[Crossref]

Identifiers

DOI

10.2478/s11534-008-0061-x