Abstract
The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.
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References
Mooney, M. Explicit formulas for slip and fluidity. Journal of Rheology 2(2), 210–222 (1931)
Rao, I. J. and Rajagopal, K. R. The effect of the slip condition on the flow of fluids in a channel. Acta Mech. 135(3), 113–126 (1999)
Khaled, A. R. A. and Vafai, K. The effect of slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions. Int. J. Non-Linear Mech. 39(5), 795–804 (2004)
Wang, C. Y. Flow due to a stretching boundary with partial slip-an exact solution of the Navier-Stokes equations. Chem. Eng. Sci. 57(17), 3745–3747 (2002)
Wang, C. Y. Stagnation slip flow and heat transfer on a moving plate. Chem. Eng. Sci. 61(23), 7668–7672 (2006)
Hayat, T., Masood, K., and Ayub, M. The effect of the slip condition on flows of an Oldroyd 6-constant fluid. J. Comput. Appl. Math. 202(2), 402–413 (2007)
Chaudnary, R. C., Jiha, A. K., and Hang, F. Effects of chemical reaction on MHD micropolar fluid flow past a vertical plate in slip-flow regime. Applied Mathematics and Mechanics (English Edition) 29(9), 1179–1194 (2008) DOI 10.1007/s10483-008-0907-x
Andersson, H. I. and Rousselet, M. Slip flow over a lubricated rotating disk. Int. J. Heat Fluid Flow 27(2), 329–335 (2006)
Labropulu, F. and Li, D. Stagnation-point flow of a second-grade fluid with slip. Int. J. Non-Linear Mech. 43(9), 941–947 (2008)
Zhu, J., Zheng, L. C., and Zhang, X. X. Analytic solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis. Applied Mathematics and Mechanics (English Edition) 30(4), 463–474 (2009) DOI 10.1007/s10483-009-0407-2
Mo, J. Q. Singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation. Applied Mathematics and Mechanics (English Edition) 29(8), 1105–1110 (2008) DOI 10.1007/s10483-008-0814-x
Lin, S. R. and Mo, J. Q. Nonlinear singularly perturbed problems of ultra parabolic equations. Applied Mathematics and Mechanics (English Edition) 29(10), 1377–1381 (2008) DOI 10.1007/s10483-008-1012-z
Su, X. H., Zheng, L. C., and Zhang, X. X. Analytical approximate solutions and the approximate value of skin friction coefficient for the boundary layer of power law fluids. Applied Mathematics and Mechanics (English Edition) 29(9), 1215–1220 (2008) DOI 10.1007/s10483-008-0910-4
Liang, Z. F. and Tang, X. F. Analytical solution of a fractionally damped beam by Adomian decomposition method. Applied Mathematics and Mechanics (English Edition) 28(2), 219–228 (2007) DOI 10.1007/s10483-007-0210-z
Zhang, S. Y. and Liu, Z. F. Three kinds of nonlinear dispersive waves in finite deformation elastic rods. Applied Mathematics and Mechanics (English Edition) 29(7), 909–917 (2008) DOI 10.1007/s10483-008-0709-2
Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman Hall/CRC, Boca Raton (2003)
Liao, S. J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147(2), 499–513 (2004)
Hayat, T., Abbas, Z., and Sajid, M. Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys. Lett. A 358(6), 396–403 (2006)
Xu, H. and Liao, S. J. Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. J. Non-Newtonian Fluid Mech. 129(1), 46–55 (2005)
Tan, Y., Xu, H., and Liao, S. J. Explicit series solution of travelling waves with a front of fisher equation. Chaos, Solitons & Fractals 31(26), 462–472 (2007)
Liao, S. J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications Nonlinear Science and Numerical Simulation 15(8), 2003–2016 (2009) DOI 10.1016/j.cnsns.2009.09.002
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Communicated by Zhe-wei ZHOU
Project supported by the National Natural Science Foundation of China (No. 50936003), the Open Project of State Key Laboratory for Advanced Metals and Materials and the Research Foundation of Engineering Research Institute of University of Science and Technology Beijing (No. 2009Z-02)
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Zhu, J., Zheng, Lc. & Zhang, Zg. Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet. Appl. Math. Mech.-Engl. Ed. 31, 439–448 (2010). https://doi.org/10.1007/s10483-010-0404-z
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DOI: https://doi.org/10.1007/s10483-010-0404-z