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Different approximations to the solution of upper-convected Maxwell fluid over a porous stretching plate. (English) Zbl 1470.76111

Summary: In the present paper, we consider an incompressible magnetohydrodynamic flow of two-dimensional upper-convected Maxwell fluid over a porous stretching plate with suction and injection. The nonlinear partial differential equations are reduced to an ordinary differential equation by the similarity transformations and taking into account the boundary layer approximations. This equation is solved approximately by means of the optimal homotopy asymptotic method (OHAM). This approach is highly efficient and it controls the convergence of the approximate solutions. Different approximations to the solution are given, showing the exceptionally good agreement between the analytical and numerical solutions of the nonlinear problem. OHAM is very efficient in practice, ensuring a very rapid convergence of the solutions after only one iteration even though it does not need small or large parameters in the governing equation.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76A05 Non-Newtonian fluids
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[1] Sakiadis, B. C., Boundary layer behaviour an continuous solid surface I: boundary layer equations for two dimensional and axisymmetric flow, AIChEJ, 7, 1, 26-28 (1961) · doi:10.1002/aic.690070108
[2] Sakiadis, B. C., Boundary layer behaviour an continuous solid surface II: boundary layer on a continuous flat surface, AIChEJ, 221-225 (1961) · doi:10.1002/aic.690070211
[3] Phan-Thien, N., Plane and axi-symmetric stagnation flow of a Maxwellian fluid, Rheologica Acta, 22, 2, 127-130 (1983) · Zbl 0511.76011 · doi:10.1007/BF01332366
[4] Zheng, R.; Phan-Thien, N.; Tanner, R. I., On the flow past a sphere in a cylindrical tube: limiting Weissenberg number, Journal of Non-Newtonian Fluid Mechanics, 36, 27-49 (1990) · doi:10.1016/0377-0257(90)85002-G
[5] Sadeghy, K.; Najafi, A.-H.; Saffaripour, M., Sakiadis flow of an upper-convected Maxwell fluid, International Journal of Non-Linear Mechanics, 40, 9, 1220-1228 (2005) · Zbl 1349.76081 · doi:10.1016/j.ijnonlinmec.2005.05.006
[6] Hayat, T.; Abbas, Z.; Sajid, M., Series solution for the upper-convected Maxwell fluid over a porous stretching plate, Physics Letters A: General, Atomic and Solid State Physics, 358, 5-6, 396-403 (2006) · Zbl 1142.76511 · doi:10.1016/j.physleta.2006.04.117
[7] Hayat, T.; Sajid, M., Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid, International Journal of Engineering Science, 45, 2-8, 393-401 (2007) · Zbl 1213.76137 · doi:10.1016/j.ijengsci.2007.04.009
[8] Abbas, Z.; Hayat, T.; Sajid, M.; Asghar, S., Unsteady flow of a second grade fluid film over an unsteady stretching sheet, Mathematical and Computer Modelling, 48, 3-4, 518-526 (2008) · Zbl 1145.76317 · doi:10.1016/j.mcm.2007.09.015
[9] Abbas, Z.; Wang, Y.; Hayat, T.; Oberlack, M., Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface, Nonlinear Analysis: Real World Applications, 11, 4, 3218-3228 (2010) · Zbl 1196.35160 · doi:10.1016/j.nonrwa.2009.11.016
[10] Hayat, T.; Awais, M.; Qasim, M.; Hendi, A. A., Effects of mass transfer on the stagnation point flow of an upper-convected Maxwell (UCM) fluid, International Journal of Heat and Mass Transfer, 54, 15-16, 3777-3782 (2011) · Zbl 1308.76011 · doi:10.1016/j.ijheatmasstransfer.2011.03.003
[11] Ishak, A.; Nazar, R.; Arifin, N. M.; Pop, I., Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate, International Journal of Thermal Sciences, 47, 4, 417-422 (2008) · doi:10.1016/j.ijthermalsci.2007.03.005
[12] Sahoo, B., Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet, Applied Mathematics and Mechanics, 31, 2, 159-173 (2010) · Zbl 1397.76182 · doi:10.1007/s10483-010-0204-7
[13] Schlichting, H., Boundary Layer Theory (1964), New York, NY, USA: McGraw-Hill, New York, NY, USA
[14] Marinca, V.; Herisanu, N., Nonlinear Dynamical Systems in Engineering (2011), Heidelberg, Germany: Springer, Heidelberg, Germany · Zbl 1244.65104 · doi:10.1007/978-3-642-22735-6
[15] Marinca, V.; Herişanu, N.; Nemeş, I., Optimal homotopy asymptotic method with application to thin film flow, Central European Journal of Physics, 6, 648-653 (2008) · doi:10.2478/s11534-008-0061-x
[16] Marinca, V.; Herişanu, N.; Bota, C.; Marinca, B., An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate, Applied Mathematics Letters, 22, 2, 245-251 (2009) · Zbl 1163.76318 · doi:10.1016/j.aml.2008.03.019
[17] Marinca, V.; Herişanu, N., An optimal homotopy asymptotic approach applied to nonlinear MHD Jeffery-Hamel flow, Mathematical Problems in Engineering, 2011 (2011) · Zbl 1235.76110 · doi:10.1155/2011/169056
[18] Marinca, V.; Herişanua, N., An optimal homotopy perturbation approach to thin film flow of a fourth grade fluid, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM ’12) · doi:10.1063/1.4756674
[19] Elsgolts, L., Differential Equations and the Calculus of Variations (1973), Moscow, Russia: Mir Publishers, Moscow, Russia
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