A novel approach to approximate unsteady squeezing flow through porous medium | [Journal of Prime Research in Mathematics • 2016]

Author(s):

1. MUBASHIR QAYYUM: Department of Mathematics, National University of Computer and Emerg- ing Sciences - FAST Peshawar, Pakistan

2. HAMID KHAN: Department of Mathematics, National University of Computer and Emerg- ing Sciences - FAST Peshawar, Pakistan

3. M.T. RAHIM: Department of Mathematics, National University of Computer and Emerg- ing Sciences - FAST Peshawar, Pakistan

Abstract:

In this article, a new alteration of the Homotopy Perturba- tion Method (HPM) is proposed to approximate the solution of unsteady axisymmetric flow of Newtonian fluid. The flow is squeezed between two circular plates and passes through a porous medium channel. The alter- ation extends the Homotopy Perturbation with a Laplace transform, which is referred to as the Laplace Transform Homotopy Perturbation Method (LTHPM) in this manuscript. A single fourth order non-linear ordinary differential equation is obtained using similarity transformations. The re- sulting boundary value problem is then solved through LTHPM, HPM and fourth order Implicit Runge Kutta Method (IRK4). Convergence of the proposed scheme is checked by finding absolute residual errors of various order solutions. Also, the validity is confirmed by comparing numerical and analytical (LTHPM) solutions. The comparison of obtained residual errors shows that LTHPM is an effective scheme that can be applied to various initial and boundary value problems in science and engineering.

Page(s): 91-109

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 12, Issue: 1, Year: 2016

Keywords:

34K28 , AMS SUBJECT , Squeezing Flow , Porous Media , Laplace Transform Homotopy Perturbation Method , Primary 34K10 , 76S99

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