Int. J. of Applied Mechanics and Engineering, 2005, vol.JO, No.3, pp.463-474 ON THE STEADY FLOW OF MAGNETORHEOLOGICAL FLUIDS IN PIPES M.F. LETELIER Departamento de Ingenierfa Mecanica Universidad de Santiago de Chile Casilla 10233, Santiago, CHILE e-mail: mletelie@ lauca.us ach.cl D.A. SIGINER* Department of Mechanical Engineering, Wichita State University 1845 Fairmount, Wichita, Kansas 67260-0133, USA e-mail: dennis.siginer@wichita.edu A non-affine visco-elasto-plastic constitutive equation with yield stress is proposed to simulate the response of magnetorheological fluids to driving forces. The equation yields realistic flow patterns in the press ure gradient driven fully developed tube flow which combine the effects of viscoelasticity and yie ld stress. The interplay of yield stress and viscoelasticity results in longitudinal velocity profiles, which can be controlled by adjusting the strength of the applied magnetic field. However, for physically realistic velocity profiles to exist the material parameters of the fluid and the steady pressure gradient must satisfy certain restrictions. 1. Introduction Fluids with yield stress are used in many industrial applications. The behavior of slurries, paints, foodstuffs and other industrial products are routinely modeled using constitutive structures with yield stress of the Bingham, Herschel-Bulkley or similar type. The design of advanced devices which effectively use the phase transition properties under applied electric or magnetic fields of two new classes of fluids, electrorheological (ERF) and magnetorheological (MRF), gave rise in recent years to a new and promising field of applications. When a fluid medium is seeded with very small dielectric or iron particles, it reacts to an applied electric or magnetic field by developing non-Newtonian characteristics, most prominently a yield stress, viscosity change, and also viscoelasticity (Nakamura et al., 2004; Lee and Choi, 2002; Jolly et al., 1996; Weiss et al., 1994). Phase transition properties of these fluids can be controlled by adjusting the strength of the imposed electric or magnetic field. The controllability of the phenomena made possible the development of dampers for terrestrial and aerial vehicles (Dogruer et al., 2003; Hong et al., 2003; Choi and Kim, 2000; Lee and Wereley, 1999; 2000), haptic devices (Mavroidis et al ., 2000; Fisch et al., 2003; Mavroidis et al., 2000), seismic dampers for buildings (Oh and Onoda, 2001; Truong and Semercigil, 2001) and special composite materials (Qiu et al., 1999) among others. In all these examples fluid properties are regulated/adjusted through electric or magnetic controls, so that they assume required prescribed values at different stages of performance. Dang et al. (2000), among other researchers, have experimentally measured yield stress as a function of the strength of the magnetic fluid and iron volume. Several authors have investigated the flow of yield stress fluids through planar, circular, and annular passages (Lee and Wereley, 2000; Rov et al., 2003; Wereley, 2003; Hu and Wereley, 2003). These studies have been extended by Wang and Gordaninejad (1999) to the analysis of the behavior of ER and MR fluids which in addition to yield stress exhibit shear To whom correspondence should be addressed