Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM

Mohammad Mehdi Rashidi; Navid Freidoonimehr; Ebrahim Momoniat; Behnam Rostami

doi:10.1371/journal.pone.0135004

Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM

PLoS One. 2015 Aug 12;10(8):e0135004. doi: 10.1371/journal.pone.0135004. eCollection 2015.

Authors

Mohammad Mehdi Rashidi¹, Navid Freidoonimehr², Ebrahim Momoniat³, Behnam Rostami²

Affiliations

¹ Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran; University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, Peoples Republic of China.
² Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
³ DST/NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa.

Abstract

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Models, Theoretical*

Grants and funding

EM acknowledges support from the National Research foundation of South Africa. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.