Int. J. of Appl. Math and Mech. 9 (16): 1-21, 2013. ELEMENT-FREE GALERKIN METHOD (EFGM) COMPUTATION OF TRANSIENT MICROPOLAR MAGNETIC SQUEEZE BIOFILM O. Anwar Bég 1 , R. Bhargava 2 , S. Singh 2 , and H. Maregere 3 1 Gort Engovation Research- Propulsion, Nanofluids and Biophysics, Southmere Avenue, Bradford, BD7 3NU, England, UK 2 Mathematics Department, Indian Institute of Technology-Roorkee, India. 3 Sulzer Pumps (UK) Ltd., Manor Mill Lane, Leeds, LS11 8BR, England, UK Email: gortoab@gmail.com Received 16 July 2012; accepted 29 July 2013 ABSTRACT In this article we examine numerically the unsteady squeezing hydrodynamics of an electrically-conducting micropolar lubricant between two parallel plates in the presence of a uniform strength magnetic field. The governing partial differential equations are transformed into non-dimensional, nonlinear coupled ordinary differential equations for translational and angular momentum (micro-inertia). These equations are solved numerically using the Element Free Galerkin Method (EFGM). Excellent accuracy is achieved. The influence of magnetic field parameter (Ha), micropolar spin gradient viscosity parameter (), Eringen vortex viscosity parameter (R) and unsteadiness parameter (S) on linear and angular velocity (micro- rotation) are presented graphically. The excellent potential of EFGM in bio-lubrication flows is highlighted. Keywords: Hydromagnetic, Computational bio-tribology, Squeeze films, smart biomechanics, Conducting micropolar lubricant, Unsteadiness, Element free Galerkin method 1 INTRODUCTION Numerical analyses of squeeze film flows in bio-tribology and other lubrications systems provide an important parallel to experimental studies. In the past several decades many techniques have been employed to simulate a diverse array of such flows for both Newtonian and non-Newtonian lubricants. Wu (Wu 1986) used a finite element penalty scheme for studying elastohydrodynamic contact mechanics. Ran et al. (Ran et al. 2009) employed the homotopy analysis method to analyze the squeeze film of a Newtonian fluid between parallel plates. Ahmadian et al. (Ahmadian et al. 2006) employed a finite element code to analyze the squeeze film damping behavior of electrostatical actuated micro-structures. Feng and Jiang (Feng and Jiang 2011) used a molecular dynamics numerical model to simulate the squeeze- film damping effect on the performance of nano-resonators in the free molecular regime. Based on a Lennard-Jones potential for intermolecular interactions, they computed the variation in the quality factor (Q-factor) of the nano-resonator with some characteristic parameters for squeeze-film damping. Hashimoto (Hashimoto 1994) used an integral numerical approach to analyze viscoelastic squeeze film characteristics subjected to fluid inertia effects for parallel circular type squeeze films. He employed a nonlinear Maxwell-