A three-dimensional non-linear constitutive law for magnetorheological fluids, with applications

Dorfmann, A., Ogden, R.W. and Wineman, A.S. (2007) A three-dimensional non-linear constitutive law for magnetorheological fluids, with applications. International Journal of Non-Linear Mechanics, 42(2), pp. 381-390. (doi: 10.1016/j.ijnonlinmec.2007.03.002)

Abstract

In this paper we first summarize the magnetic and mechanical balance equations for magnetorheological fluids undergoing steady motion in the presence of a magnetic field. A general three-dimensional non-linear constitutive law for such a fluid is given for the case in which the magnetic induction vector is used as the independent magnetic variable. The equations are needed for the analysis of boundary-value problems involving fluids with dispersed micron-sized ferrous particles subjected to a time-independent magnetic field. For illustration, the equations are applied, in the case of an incompressible fluid, to the solution of some basic problems. We consider unidirectional flow in a region confined by two infinite parallel plates with a magnetic field applied perpendicular to the plates. Next, we examine two problems involving a circular cylindrical geometry with the fluid occupying the region between two concentric cylinders: axial flow subjected to an axial magnetic field and circumferential flow with a circumferential field. After making some simplifying assumptions on the constitutive law and choosing material parameters, numerical solutions for the velocity profiles are illustrated.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ogden, Professor Raymond
• Authors: Dorfmann, A., Ogden, R.W., and Wineman, A.S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Journal of Non-Linear Mechanics
• ISSN: 0020-7462
• Published Online: 12 March 2007