Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K. Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder. (English) Zbl 1187.76622 Phys. Lett., A 352, No. 4-5, 404-410 (2006). Summary: The present Letter applies the homotopy perturbation method and the traditional perturbation method to obtain analytic approximations of the nonlinear equations modeling thin film flow of a fourth grade fluid falling on the outer surface of an infinitely long vertical cylinder. Expressions for the velocity, volume flux and average velocity are obtained. Comparison of the results obtained by the two methods reveal that homotopy perturbation method is more effective and easy to use. Cited in 85 Documents MSC: 76A20 Thin fluid films Keywords:thin film flow; fourth grade fluid; perturbation method; homotopy perturbation method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Nayfeh, A. H., Perturbation Methods (1973), Wiley: Wiley New York · Zbl 0375.35005 [2] Nayfeh, A. H., Introduction to Perturbation Techniques (1979), Wiley: Wiley New York [3] Rand, R. H.; Armbruster, D., Perturbation Methods, Bifurcation Theory and Computer Algebra (1987), Springer: Springer Berlin · Zbl 0651.34001 [4] He, J. H., Comput. Methods Appl. Mech. Eng., 178, 257 (1999) · Zbl 0956.70017 [5] He, J. H., Appl. Math. Comput., 135, 73 (2003) [6] He, J. H., Int. J. Nonlinear Mech., 35, 37 (2000) · Zbl 1068.74618 [7] He, J. H., Phys. Lett. A, 350, 87 (2006) [8] He, J. H., Int. J. Nonlinear Sci. Numer. Simulat., 6, 2, 207 (2005) · Zbl 1401.65085 [9] He, J. H., Chaos Solitons Fractals, 26, 3, 827 (2005) · Zbl 1093.34520 [10] He, J. H., Appl. Math. Comput., 156, 3, 591 (2004) · Zbl 1061.65040 [11] He, J. H., Chaos Solitons Fractals, 26, 3, 695 (2005) · Zbl 1072.35502 [12] He, J. H., Appl. Math. Comput., 151, 1, 287 (2004) · Zbl 1039.65052 [13] S. Abbasbandy, Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2005.08.178; S. Abbasbandy, Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2005.08.178 · Zbl 1142.65417 [14] L. Cveticanin, Homotopy perturbation method for pure nonlinear differential equation, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2005.08.180; L. Cveticanin, Homotopy perturbation method for pure nonlinear differential equation, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2005.08.180 · Zbl 1142.65418 [15] El-Shahed, M., Int. J. Nonlinear Sci. Numer. Simulat., 6, 2, 163 (2005) · Zbl 1401.65150 [16] Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K., Int. J. Nonlinear Sci. Numer. Simulat., 7, 1, 7 (2006) [17] Siddiqui, A. M.; Ahmed, M.; Ghori, Q. K., Int. J. Nonlinear Sci. Numer. Simulat., 7, 1, 15 (2006) · Zbl 1401.76018 [18] Nuttall, H., Int. J. Eng. Sci., 4, 249 (1966) [19] He, J. H., Int. J. Nonlinear Sci. Numer. Simulat., 4, 3, 313 (2003) [20] Liu, H. M., Chaos Solitons Fractals, 23, 2, 573 (2005) · Zbl 1135.76597 [21] Kapitza, P. L., Zh. Eksp. Teor. Fiz., 18, 3 (1949) [22] Yih, C. S., Phys. Fluids, 6, 321 (1963) · Zbl 0116.19102 [23] Krishna, M. V.G.; Lin, S. P., Phys. Fluids, 20, 1039 (1977) · Zbl 0381.76040 [24] Andersson, H. I.; Dahi, E. N., J. Phys. D: Appl. Phys., 32, 1557 (1999) [25] Cheng, P.-J.; Lai, H.-Y.; Chen, C.-K., J. Phys. D: Appl. Phys., 33, 1674 (2000) [26] Truesdell, C.; Noll, W., The Non-Linear Field Theories of Mechanics (1992), Springer: Springer Berlin · Zbl 0779.73004 [27] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics (1989), Pergamon: Pergamon New York · Zbl 0146.22405 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.