A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

Abstract

Abstract:The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int.

Flow and Heat Transfer of MHD Viscous Fluid Over an Unsteady Stretching Surface With Radiation Heat Flux

“…In order to solve Equations (13)-(16) by HAM (Liao, 2010;Hang et al, 2007;Dinarvand, 2009;Rashidi and Dinarvand, 2009;Dinarvand and Rashidi, 2010;Ziabakhsh and Domairry, 2009;Kumari and Nath, 2009;Wang and Pop, 2006), it is seen from the initial boundary conditions (15) and (16) that a straightforward choice as the initial approximations of f(g) is…”

“…In recent years, the homotopy analysis method has been successfully employed to solve many types of nonlinear problems in science and engineering, for example, viscous flows of non-Newtonian fluids (Ziabakhsh and Domairry, 2009;Wang and Pop, 2006) and heat transfer problems (Kumari and Nath, 2009). A more exhaustive list can be found in Liao (2003Liao ( , 2010, Hang et al (2007), Dinarvand (2009), Rashidi and Dinarvand (2009), and Dinarvand and Rashidi (2010). The aim of the present investigation is to study the flow and heat transfer of magnetohydrodynamic (MHD) viscous fluid over an unsteady horizontal stretching surface in the presence of a nonuniform magnetic field by employing the homotopy analysis technique.…”

Reliable treatments of differential transform method for two-dimensional incompressible viscous flow through slowly expanding or contracting porous walls with small-to-moderate permeability

“…Most of the scientific problems and phenomena are modeled by non-linear ordinary or partial differential equations. In recent years, many powerful methods have been developed to construct explicit analytical solution of non-linear differential equations (He, 2006;Liao, 1992;Dinarvand, 2009Dinarvand, , 2011aDinarvand, , 2010Dinarvand, , 2011b. Zhou was the first one who introduced the differential transform method (DTM) as an efficient method to apply for electrical circuits in his paper entitled "differential transformation and its application for electrical circuits" (Zhou, 1986).…”

Series Solution for Steady Three‐Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

“…In recent years, many powerful methods have been developed to construct explicit analytical solution of nonlinear differential equations. Among them, two analytical methods have drawn special attention, namely, the homotopy perturbation method HPM 6, 7 and homotopy analysis method HAM [8][9][10][11] . The essential idea in these 2 Journal of Applied Mathematics methods is to introduce a homotopy parameter, say p, which takes the value from 0 to 1.…”