Journal of Prime Research in Mathematics

# A novel approach to approximate unsteady squeezing flow through porous medium

Mubashir Qayyum
Department of Mathematics, National University of Computer and Emerging Sciences – FAST Peshawar, Pakistan.
Hamid Khan
Department of Mathematics, National University of Computer and Emerging Sciences – FAST Peshawar, Pakistan.
M.T. Rahim
Department of Mathematics, National University of Computer and Emerging Sciences – FAST Peshawar, Pakistan.

$$^{1}$$Corresponding Author: mubashir.qayyum@nu.edu.pk

### Abstract

In this article, a new alteration of the Homotopy Perturbation 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 alteration 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 resulting 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

#### Keywords:

Squeezing Flow, Porous Media, Laplace Transform Homotopy Perturbation Method.