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Series solution for the upper-convected Maxwell fluid over a porous stretching plate. (English) Zbl 1142.76511

Summary: This Letter is concerned magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous stretching sheet. By means of similarity transformations, the non-linear equations governing the flow under discussion are reduced to an ordinary differential equation. With the help of homotopy analysis method (HAM), the analytical solution is obtained in the series form. Convergence of the series is explicitly discussed. The effects of various involved parameters of interest are shown on velocity and skin friction coefficient for both suction and injection.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Hayat, T.; Khan, M.; Siddiqui, A. M.; Asghar, S., Int. J. Non-Linear Mech., 39, 1621 (2004)
[2] Hayat, T.; Wang, Y.; Hutter, K., Int. J. Non-Linear Mech., 39, 1027 (2004)
[3] Rajagopal, K. R., Int. J. Non-Linear Mech., 17, 369 (1982) · Zbl 0527.76003
[4] Rajagopal, K. R., J. Non-Newtonian Fluid Mech., 15, 239 (1984) · Zbl 0568.76015
[5] Bandelli, R., Int. J. Non-Linear Mech., 30, 263 (1995)
[6] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 423 (2003)
[7] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 603 (2003)
[8] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 985 (2003)
[9] Fetecau, C.; Fetecau, C., Int. J. Engrg. Sci., 43, 781 (2005)
[10] Asghar, S.; Hayat, T.; Siddiqui, A. M., Int. J. Non-Linear Mech., 37, 75 (2002) · Zbl 1116.76310
[11] Hayat, T., Z. Angew. Math. Mech., 85, 449 (2005)
[12] Hayat, T.; Nadeem, S.; Asghar, S., Appl. Math. Comput., 151, 153 (2004)
[13] Chen, C. I.; Chen, C. K.; Yang, Y. T., Heat Mass Transfer, 40, 203 (2004)
[14] Tan, W. C.; Masuoka, T., Int. J. Non-Linear Mech., 40, 515 (2005)
[15] Tan, W. C.; Masuoka, T., Phys. Fluids, 17, 023101 (2005)
[16] Fosdick, R. L.; Rajagopal, K. R., Arch. Ration. Mech. Anal., 70, 145 (1979)
[17] Dunn, J. E.; Rajagopal, K. R., Int. J. Engrg. Sci., 33, 689 (1995)
[18] Sadeghy, K.; Sharifi, M., Int. J. Non-Linear Mech., 39, 1265 (2004)
[19] Bird, R. B.; Armstrong, R. C.; Hassager, O., Dynamics of Polymeric Liquids, Vols. I and II (1987), Wiley: Wiley New York
[20] Sadeghy, K.; Najafi, A. H.; Saffaripour, M., Int. J. Non-Linear Mech., 40, 1220 (2005)
[21] Sakiadis, B. C., Am. Inst. Chem. Engrg. J., 7, 26 (1961)
[22] Sakiadis, B. C., Am. Inst. Chem. Engrg. J., 7, 221 (1961)
[23] Cortell, R., Int. J. Non-Linear Mech., 29, 155 (1994)
[24] Cortell, R., Fluid Dynam. Res., 37, 231 (2005)
[25] Cortell, R., Appl. Math. Comput., 168, 557 (2005)
[26] Liao, S., J. Fluid Mech., 488, 189 (2003)
[27] Ariel, P. D., Int. J. Engrg. Sci., 39, 529 (2001)
[28] Liao, S. J., Beyond Perturbation: Introduction to Homotopy Analysis Method (2003), Chapman & Hall: Chapman & Hall Boca Raton
[29] Liao, S. J., Appl. Math. Comput., 147, 499 (2004)
[30] Liao, S. J., J. Fluid Mech., 385, 101 (1999)
[31] Liao, S. J.; Campo, A., J. Fluid Mech., 453, 411 (2002)
[32] Liao, S. J., J. Fluid Mech., 488, 189 (2003)
[33] Liao, S. J.; Cheung, K. F., J. Engrg. Math., 45, 105 (2003)
[34] Liao, S. J.; Pop, I., Int. J. Heat Mass Transfer., 46, 1855 (2004)
[35] Ayub, M.; Rasheed, A.; Hayat, T., Int. J. Engrg. Sci., 41, 2091 (2003)
[36] Hayat, T.; Khan, M.; Ayub, M., Int. J. Engrg. Sci., 42, 123 (2004)
[37] Hayat, T.; Khan, M.; Ayub, M., J. Math. Anal. Appl., 298, 225 (2004)
[38] Hayat, T.; Khan, M.; Asghar, S., Acta Mech., 168, 213 (2004)
[39] Yang, C.; Liao, S. J., Commun. Nonlinear Sci. Numer. Simul., 11, 83 (2006)
[40] Liao, S. J., Int. J. Heat Mass Transfer, 48/12, 2529 (2005)
[41] Liao, S. J., Commun. Nonlinear Sci. Numer. Simul., 11, 326 (2006)
[42] Cheng, J.; Liao, S. J.; Pop, I., Transport Porous Media, 61, 365 (2005)
[43] Xu, H.; Liao, S. J., J. Non-Newtonian Fluid Mech., 129, 46 (2005)
[44] Hayat, T.; Khan, M., Non-Linear Dynam., 42, 395 (2005)
[45] Wu, W.; Liao, S. J., Chaos Solutions Fractals, 26, 177 (2005)
[46] Wu, Y. Y.; Wang, C.; Liao, S. J., Chaos Solutions Fractals, 23, 1733 (2005)
[47] Hayat, T.; Khan, M.; Asghar, S., Appl. Math. Comput., 155, 417 (2004)
[48] Schlichting, H., Boundary Layer Theory (1964), McGraw-Hill: McGraw-Hill New York
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