Eur. Phys. J. Plus (2013) 128: 133
https://doi.org/10.1140/epjp/i2013-13133-x

Regular Article

Analyzing magneto-hydrodynamic squeezing flow between two parallel disks with suction or injection by a new hybrid method based on the Tau method and the homotopy analysis method

¹ Department of Physics, Shahid Beheshti University, 19839, Tehran, Iran
² Department of Mathematics, Imam Khomeini International University, 34149-16818, Ghazvin, Iran

^* e-mail: shivanian@ikiu.ac.ir

Received: 27 March 2013
Revised: 13 May 2013
Accepted: 15 October 2013
Published online: 8 November 2013

Abstract

In this paper an algorithm based on the homotopy analysis method (HAM) is introduced to study the magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid in the presence of an applied magnetic field. The continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation via similarity transformations. In addition, by using the Tau method the problem converts to the algebraic equations to obtain the solution iteratively. The combined effect of inertia, electromagnetic forces for both suction and blowing cases is discussed. Additionally, the convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. The applicability, accuracy and efficiency of this new Tau modification of the HAM is demonstrated via the accomplished comparison.