An Analytical Approximation For Boundary Layer Flow Convection Heat And Mass Transfer Over A Flat Plate

Volume 5, Issue 4, pp 241--257

Publication Date: 2012-12-30


Hossein Aminikhah - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
Ali Jamalian - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.


In this article, Laplace transform and new homotopy perturbation methods are adopted to study the problem of forced convection over a horizontal flat plate analytically. The problem is a system of nonlinear ordinary differential equations which arises in boundary layer flow. The solutions approximated by the proposed method are shown to be precise as compared to the corresponding results obtained by numerical method. A high accuracy of new method is evident.


Laplace transform, New homotopy perturbation method, Blasius equation.


[1] H. Blasius The Boundary Layers in Fluid with Little Friction (in German) Zeitschrift fur Mathematik und Physik, 56 (1) 908 1-37; English translation available as NACATM 1256, February 1950.
[2] J.H. He, Homotopy perturbation technique, Comput Meth Appl Mech Eng,178, (1999) 257-262.
[3] J.H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int J Non-linear Mech, 35, (2000) 37-43.
[4] J.H. He, New interpretation of homotopy perturbation method, Int J Mod Phys B, 20, (2006) 2561-8.
[5] J.H. He, Recent development of homotopy perturbation method, Topol. Meth Nonlinear Anal,31, (2008) 205-9.
[6] J.H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl Math Comput,151, (2004) 287-92.
[7] J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Soliton Fract,26, (2005) 695-700.
[8] J.H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Soliton Fract,26, (2005) 827- 33.
[9] A. Rajabi, D.D. Ganji, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys Lett A,360, (2007) 570-3.
[10] D.D. Ganji, A. Sadighi, Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J Comput Appl Math, 207, (2007) 24- 34.
[11] D.D. Ganji, The application of Hes homotopy perturbation method to nonlinear equations arising in heat transfer, Phys Lett A, 355, (2006) 337-41.
[12] G.A. Afrouzi, D. D. Ganji, H. Hosseinzadeh, R.A. Talarposhti, Fourth order Volterra integro differential equations using modifed homotopy-perturbation method, The Journal of Mathematics and Computer Science, 3 (2011) 179-191.
[13]Mohamed I. A. Othman, A. M. S. Mahdy and R. M. Farouk, Numerical Solution of 12th Order Boundary Value Problems by Using Homotopy Perturbation Method, The Journal of Mathematics and Computer Science, 1 (2010) 14-27.
[15] S. Abbasbandy, A numerical solution of Blasius equation by Adomians decomposition method and comparison with homotopy perturbation method, Chaos Soliton Fract,31, (2007) 257-60.
[16] J. Biazar, H. Ghazvini, Exact solutions for nonlinear Schrodinger equations by He's homo-topy perturbation method, Phys Lett A, 366, (2007) 79-84.
[17] S. Abbasbandy, Numerical solutions of the integral equations: homotopy perturbation and Adomians decomposition method, Appl Math Comput,173, (2006) 493-500.
[18] JH. He, Homotopy perturbation method for solving boundary value problems, Phys Lett A,350, (2006) 87-8.
[19] Q. Wang, Homotopy perturbation method for fractional KdV-Burgers equation, Chaos Soliton Fract,35, (2008) 843-850.
[20] E. Yusufoglu, Homotopy perturbation method for solving a nonlinear system of second order boundary value problems,Int J Nonlinear Sci Numer Simul, 8, (2007) 353-8.
[21] Y. Khan, N. Faraz, A. Yildirim and Q. Wu, A Series Solution of the Long Porous Slider, Tribology Transactions,54, 2, (2011) 187-191.
[22] M. Esmaeilpour, D.D. Ganji, Application of He’s homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate, Physics Letters A 372, (2007) 33–38.
[23] L. Howarth, On the Solution of the Laminar Boundary-Layer Equations, Proceedings of the Royal Society of London, A 164 (1983) 547-579.
[24] H. Aminikhah, Analytical Approximation to the Solution of Nonlinear Blasius’ Viscous Flow Equation by LTNHPM, ISRN Mathematical Analysis vol. 2012, Article ID 957473, 10 pages, 2012. doi:10.5402/2012/957473.
[25] H. Aminikhah, M. Hemmatnezhad, An efficient method for quadratic Riccati differential equation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 835–839.
[26] H. Aminikhah, A. Jamalian, A new efficient method for solving the nonlinear Fokker–Planck equation, Scientia Iranica, In Press, Available online 3 July 2012.
[27] H. Aminikhah, F. Mehrdoust, A. Jamalian, A New Efficient Method for Nonlinear Fisher-Type Equations, Journal of Applied Mathematics, vol. 2012, Article ID 586454, 18 pages, 2012. doi:10.1155/2012/586454.
[28] R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot, Transport Phenomena, John Wiley& Sons (ASIA) Pte Ltd, 627.


XML export