Optimal homotopy asymptotic method with application to thin film flow

Abstract

Abstract:A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use. PACS

Viscous flow and heat transfer over an unsteady stretching surface

“…At this moment, the first-order approximate solution given by equation (29) depends on the parameters C 1 , C 2 , . .…”

“…The convergence of the approximate solution (29) depends upon the auxiliary convergence-control function H(η, C i ). There are many possibilities to choose the auxiliary function H(η, C i ).…”

“…If p ∈ [0, 1] denotes an embedding parameter and F is a function, then we propose to construct a homotopy [29] - [33]:…”

“…The first-order approximate solution (29) for equations (12) and (17) is obtained from equations (36) and (45):…”

“…But the use of perturbation theory in many problems is invalid for parameters beyond a certain specified range. Other procedures have been proposed such as the Adomian decomposition method [23], some linearization methods [24,25], various modified Lindstedt-Poincare methods [26], variational iteration method [27], optimal homotopy perturbation method [28] and optimal homotopy asymptotic method [29][30][31][32][33][34].…”