A Novel Numerical Technique for Two‐Dimensional Laminar Flow between Two Moving Porous Walls

Abstract

We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series was compared with numerical approximations and with earlier results where the homotopy analysis and homotopy perturbation methods were used. We show that both the spectral-homotopy analysis method and successive linearisation method are computationally efficient and accurate in finding solutions of nonlinear boundary value problems.

An improved spectral homotopy analysis method for solving boundary layer problems

“…These methods include the Adomian decomposition method [15][16][17], differential transform method [18], variational iteration method [19], homotopy analysis method (HAM) [20][21][22][23], and the spectral-homotopy analysis (SHAM) (see Motsa et al [24,25]) which sought to remove some of the perceived limitations of the HAM. More recently, successive linearization method [26][27][28], has been used successfully to solve nonlinear equations that govern the flow of fluids in bounded domains.…”

Cross-Diffusion, Viscous Dissipation and Radiation Effects on an Exponentially Stretching Surface in Porous Media

“…The system of equations (12)- (14) together with the boundary conditions (15) were solved using a successive linearisation method (SLM) (see [22,32]). The SLM is based on the assumption that the unknown functions f (η), θ(η) and φ(η) can be expanded as…”

“…Starting from the initial guesses, the subsequent solutions F i , Θ i and Φ i (i ≥ 1) are obtained by successively solving the linearised form of the equations which are obtained by substituting equation (22) in the governing equations. The linearised equations to be solved are…”

“…The successive linearisation method (SLM) which has been used in a limited number of studies (see [3,5,[20][21][22]32]) is used to solve the governing coupled non-linear system of equations. Recent studies such as [4,22,23] have suggested that the successive linearisation method is accurate and converges rapidly to the numerical results when compared to other semi-analytical methods such as the Adomian decomposition method, the variational iteration method and the homotopy perturbation method. The SLM method can be used in place of traditional numerical methods such as finite differences, Runge-Kutta shooting methods, finite elements in solving non-linear boundary value problems.…”

Nonlinear Convective Transport Along an Inclined Plate in Non-Darcy Porous Medium Saturated by a Micropolar Fluid With Convective Boundary Condition

“…(20) - (23) and Eqs. (25) - (28) along with the boundary conditions (24) and (29) are evaluated using one of the non-perturbation method named as Successive Linearization Method(for more details see, Makukula et al, 2010;Awad et al, 2011;Khidir et al, 2015 ). Using the successive linearization technique, the nonlinear boundary layer equations will reduce to a system of linear differential equations.…”