A Comparison Study of a Symmetry Solution of Magneto-Elastico-Viscous Fluid along a Semi- Infinite Plate with Homotopy Perturbation Method and4th Order Runge–Kutta Method

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

• Mohamed M. Mousa
• Aidarkhan Kaltayev

• Electrically conducting elastico-viscous fluid
• symmetry solution
• Homotopy perturbation method
• Padé approximation
• 4th order Runge–Kutta
• Maple

[1] V.M. Soundalgekar and P. Puri, On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction, J. Fluid Mech., vol. 35, pp. 561573, 1969. [2] K.R. Frater, On the solution of some boundary-value problems arising in elastic-viscous fluid mechanics, Z. Angew. Math. Phys., vol. 21, pp. 134137, 1970. [3] M.M. Helal and M.B. Abd-el-Malek, Group method analysis of magneto-elastico-viscous flow along a semi-infinite flat plate with heat transfer, J. Comput. Appl. Math., vol. 173, pp. 199210, 2005. [4] T. Cebeci and P. Bradshaw, Momentum Transfer in Boundary Layers, Hemisphere Publishing Corporation, New York, 1977. [5] J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., vol. 178, pp. 257262, 1999. [6] J.H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput., vol. 135, pp. 7379, 2003. [7] J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons and Fractals, vol. 26, pp. 695700, 2005. [8] J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, vol. 20(10), pp. 11411199, 2006. [9] M.M. Mousa and S.F. Ragab, Application of the homotopy perturbation method to linear and nonlinear schrdinger equations, Z.Naturforsch.,63a, pp. 140144, 2008. [10] J.H. He, An Elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B, vol. 22(21), pp. 34873578, 2008. [11] J.H. He, Recent development of the homotopy perturbation method, Topological Methods in Nonlinear Analysis, vol. 31, pp. 205209, 2008. [12] J.H. He, An elementary introduction to the homotopy perturbation method, Computers & Mathematics with Applications, vol. 57, pp. 410412, 2009. [13] G.A. Baker, Essentials of Pad Approximants, Academic press, New York, 1975. World Academy of Science, Engineering and Technology 55 2009504