Abstract
The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f″(0) with different values of parameters are convergent.
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Fang, T., Liang, W., and Lee, C. F. A new solution branch for the Blasius equation—a shrinking sheet problem. Comput. Math. Appl. 56(12), 3088–3095 (2008)
Sajid, M. and Hayat, T. The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos, Solitons & Fractals 39(3), 1317–1323 (2009)
Hayat, T., Abbas, Z., Javed, T., and Sajid, M. Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos, Solitons & Fractals 39(4), 1615–1626 (2009)
Fang, T. and Zhang, J. Closed-form exact solutions of MHD viscous flow over a shrinking sheet. Commun. Nonlinear Sci. Numer. Simulat. 14(7), 2853–2857 (2009)
Fang, T. Boundary layer flow over a shrinking sheet with power-law velocity. Int. J. Heat Mass Tran. 51(25–26), 5838–5843 (2008)
Nadeem, S. and Awais, M. Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity. Phys. Lett. A 372(30), 4965–4972 (2008)
Hayat, T., Javed, T., and Sajid, M. Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface. Phys. Lett. A 372(18), 3264–3273 (2008)
Wang, C. Y. Stagnation flow towards a shrinking sheet. Int. J. Non-Linear Mech. 43(5), 377–382 (2008)
Hayat, T., Abbas, Z., and Ali, N. MHD flow and mass transfer of an upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Phys. Lett. A 372(26), 4698–4704 (2008)
Chaim, T. C. Hydromagnetic flow over a surface stretching with a power law velocity. Int. J. Eng. Sci. 33(3), 429–435 (1995)
Abbas, Z., Wanga, Y., Hayat, T., and Oberlack, M. Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface. Int. J. Non-Linear Mech. 43(8), 783–793 (2008)
Mohamed, R. A., Abbas, I. A., and Abo-Dahab, S. M. Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction. Commun. Nonlinear Sci. Numer. Simulat. 14(4), 1385–1395 (2009)
Hayat, T. and Ali, N. A mathematical description of peristaltic hydromagnetic flow in a tube. Appl. Math. Comput. 188(2), 1491–1502 (2007)
Attia, H. A. Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity. Int. J. Non-Linear Mech. 43(8), 707–715 (2008)
Tsai, R., Huang, K. H., and Huang, J. S. The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating. Appl. Therm. Eng. 29(10), 1921–1926 (2009)
Ghosh, A. K. and Sana, P. On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate. Acta Astronautica 64(2–3), 272–280 (2009)
Chiam, T. C. Hydromagnetic flow over a surface stretching with a power-law velocity. Int. J. Eng. Sci. 33(3), 429–435 (1995)
Liao, S. J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169(2), 1186–1194 (2005)
Abbasbandy, S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 360(1), 109–113 (2006)
Liao, S. J. and Cheung, K. F. Homotopy analysis of nonlinear progressive waves in deep water. J. Eng. Math. 45(2), 105–116 (2003)
Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton (2003)
Rashidi, M. M., Domairry, G., and Dinarvand, S. Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat. 14(3), 708–717 (2009)
Chowdhury, M. S. H., Hashim, I., and Abdulaziz, O. Comparison of homotopy analysis method and homotopy-perturbation method for purely non-linear fin-type problems. Commun. Nonlinear Sci. Numer. Simulat. 14(2), 371–378 (2009)
Bataineh, A. S., Noorani, M. S. M., and Hashim, I. On a new reliable modification of homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat. 14(2), 409–423 (2009)
Bataineh, A. S., Noorani, M. S. M., and Hashim, I. Modified homotopy analysis method for solving systems of second-order BVPs. Commun. Nonlinear Sci. Numer. Simulat. 14(2), 430–442(2009)
Bataineh, A. S., Noorani, M. S. M., and Hashim, I. Solving systems of ODEs by homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat. 13(10), 2060–2070 (2008)
Sajid, M., Ahmad, I., Hayat, T., and Ayub, M. Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet. Commun. Nonlinear Sci. Numer. Simulat. 13(10), 2193–2202 (2008)
Sajid, M. and Hayat, T. Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations. Nonlinear Analysis: Real World Applications 9(5), 2296–2301 (2008)
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Communicated by Zhe-wei ZHOU
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Nadeem, S., Hussain, A. MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method. Appl. Math. Mech.-Engl. Ed. 30, 1569–1578 (2009). https://doi.org/10.1007/s10483-009-1208-6
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DOI: https://doi.org/10.1007/s10483-009-1208-6