Application of Homotopy Perturbation Method to Deformable Channel with Wall Suction and Injection in a Porous Medium

Abstract

This article studies the porous deformation channel flow of a viscous fluid through a porous medium. Both the analytical and numerical solutions are obtained by using homotopy perturbation and shooting methods respectively. A good agreement between analytical and numerical solutions is achieved. Furthermore, the graphical results of velocity, streamlines, normal pressure distribution and shear stress are presented for various values of emerging parameters.

A Novel Rational Harmonic Balance Approach for Periodic Solutions of Conservative Nonlinear Oscillators

“…The most commons and most widely studied methods of all approximation methods for nonlinear differential equations are perturbation methods [1,2]. Some of other techniques include variational and variational iteration methods [3][4][5][6][7][8][9][10][11][12][13][14][15], expfunction [16][17][18][19], homotopy perturbation [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], equivalent linearization [36,37], standard and modified Lindstedt-Poincaré [38][39][40][41][42][43][44], artificial parameter [45,46], parameter expanding [47,50], harmonic balance methods …”

Computation of Eigenvalues of Sturm-Liouville Problems using Homotopy Perturbation Method

“…(25) is obtained as follows, IV"w" 0 + pw" 0 (25) Using Eqn. (25) is obtained as follows, IV"w" 0 + pw" 0 (25) Using Eqn.…”

“…Also Noor and Mohyud-Din [24] used HPM for solving nonlinear higher order boundary value problems. Mahmood et al [25] applied the HPM to deformable channel with wall suction and injection in a porous medium. In relation to S-L typr problems, Coskun and Atay [26] and Atay and Coskun [27] studied column buckling problems for the columns with variable flexural stiffness and for the columns with continuous elastic restraints by using variational iteration method.…”

Analytical and numerical solution for viscous dissipation effect on the heat transfer in a deformable channel

“…Majdalani and coworkers [6][7][8] have given the solution for flow in a deformable channel but without heat transfer under various conditions. More recently Mahmood et al [9] discussed flow in a deformable channel with wall suction and injection through a porous medium. In another paper, Asghar et al [10] reconsidered the problem given in Reference [9] for symmetry and conservation laws.…”

“…More recently Mahmood et al [9] discussed flow in a deformable channel with wall suction and injection through a porous medium. In another paper, Asghar et al [10] reconsidered the problem given in Reference [9] for symmetry and conservation laws. However, none of these studies [5][6][7][8][9][10] analyzed heat transfer in a deformable channel.…”