×

zbMATH — the first resource for mathematics

On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder. (English) Zbl 1170.76307
Summary: In this Letter a totally analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder is obtained using homotopy analysis method (HAM). The series solution is developed and the recurrence relations are given explicitly. Convergence of the solution and effects of rheological parameters are discussed. The comparison of the HAM results with HPM results is made. It is found that HPM results are divergent for strong nonlinearity. The results reveal that HAM is very simple and effective and provides a simple way to control and adjust the convergence region.

MSC:
76A20 Thin fluid films
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hayat, T.; Wang, Y.; Hutter, K., Int. J. non-linear mech., 39, 1027, (2004)
[2] Rajagopal, K.R., Int. J. non-linear mech., 17, 369, (1982) · Zbl 0527.76003
[3] Rajagopal, K.R., J. non-Newtonian fluid mech., 15, 239, (1984) · Zbl 0568.76015
[4] Fetecau, C.; Fetecau, C., Int. J. non-linear mech., 38, 423, (2003)
[5] Fetecau, C.; Fetecau, C., Int. J. non-linear mech., 38, 603, (2003)
[6] Fetecau, C.; Fetecau, C., Int. J. non-linear mech., 38, 985, (2003)
[7] Fetecau, C.; Fetecau, C., Int. J. eng. sci., 43, 781, (2005)
[8] Asghar, S.; Hayat, T.; Siddiqui, A.M., Int. J. non-linear mech., 37, 75, (2002) · Zbl 1116.76310
[9] Hayat, T., Z. angew. math. mech., 85, 449, (2005)
[10] Hayat, T.; Nadeem, S.; Asghar, S., Appl. math. comput., 151, 153, (2004)
[11] Tan, W.C.; Masuoka, T., Int. J. non-linear mech., 40, 515, (2005)
[12] Cortell, R., Int. J. non-linear mech., 29, 155, (1994)
[13] Cortell, R., Appl. math. comput., 168, 557, (2005)
[14] Sadeghy, K.; Najafi, A.H.; Saffaripour, M., Int. J. non-linear mech., 40, 1220, (2005)
[15] Sadeghy, K.; Sharifi, M., Int. J. non-linear mech., 39, 1265, (2004)
[16] Cortell, R., Int. J. non-linear mech., 41, 78, (2006)
[17] Beavers, G.S.; Joseph, D.D., J. fluid mech., 69, 475, (1975)
[18] Joseph, D.D.; Beavers, G.S.; Fosdick, R.I., Arch. ration. mech. anal., 49, 321, (1973)
[19] Siddiqui, A.M.; Mahmood, R.; Ghori, Q.K., Phys. lett. A, 352, 404, (2006) · Zbl 1187.76622
[20] Liao, S.J., Beyond perturbation: introduction to homotopy analysis method, (2003), Chapman & Hall/CRC Press Boca Raton
[21] S.J. Liao, On the proposed homotopy analysis technique for nonlinear problems and its applications, Ph.D. dissertation, Shanghai Jio Tong University, 1992
[22] Liao, S.J., Appl. math. comput., 147, 499, (2004)
[23] Liao, S.J., J. fluid mech., 385, 101, (1999)
[24] Hayat, T.; Khan, M.; Ayub, M., J. math. anal. appl., 298, 225, (2004)
[25] Hayat, T.; Khan, M.; Asghar, S., Acta mech., 168, 213, (2004)
[26] Yang, C.; Liao, S.J., Commun. nonlinear sci. numer. simul., 11, 83, (2006)
[27] Liao, S.J., Int. J. heat mass transfer, 48, 2529, (2005)
[28] Liao, S.J., Commun. nonlinear sci. numer. simul., 11, 326, (2006)
[29] Liao, S.J., J. fluid mech., 488, 189, (2003)
[30] Liao, S.J.; Cheung, K.F., J. eng. math., 45, 105, (2003)
[31] Sajid, M.; Hayat, T.; Asghar, S., Phys. lett. A, 355, 18, (2006)
[32] Abbas, Z.; Sajid, M.; Hayat, T., Theor. comput. fluid dyn., 20, 229, (2006) · Zbl 1109.76065
[33] He, J.H., Commun. nonlinear sci. numer. simul., 3, 92, (1998)
[34] Fitzpatrick, P.M., Advanced calculus, (1996), PWS
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.