Analysis of MHD Jeffery Hamel Flow with Suction/Injection by Homotopy Analysis Method

Salim  Hamrelaine; Fateh  Mebarek-Oudina; Mohamed Rafik  Sari

Authors

Salim Hamrelaine Department of Technology, University of 20 août 1955-Skikda, Algeria
Fateh Mebarek-Oudina Department of Physics, Faculty of Sciences, University of 20 août 1955-Skikda, Algeria
Mohamed Rafik Sari Mechanical department, University Badji Mokhtar Annaba, Algeria

Keywords:

Jeffery Hamel flow, MHD, onlinear differential equations, Homotopy Analysis Method (HAM), suction/ injection

Abstract

This article treats analytically, the magnetohydrodynamic flow through non-parallel porous walls or between two solid porous plates intersecting at an angle, that can be interpreted as a combination between the classical Jeffery Hamel flow added of one injection/suction. The governing equations of the problem are converted from traditional Navier-Stokes equations of fluid mechanics accompanied by those of Maxwell's electromagnetism to ordinary nonlinear differential equations for modeling. A semi-analytic solution is developed by using Homotopy Analysis Method (HAM) whereas the numerical solution is presented by Runge-Kutta scheme. A comparative study between the analytical and numerical solutions is made. The results confirm clearly that the two methods coincide closely for different angles (?), Reynolds numbers (Re), injection parameter (S) and Hartmann number (Ha).