Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders M.A. Rana a, * , A.M. Siddiqui b , Rashid Qamar a a Management Information System, PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan b Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17403, USA Accepted 2 January 2007 Communicated by Prof. Ji-Huan He Abstract The hydromagnetic flow of an electrically conducting, incompressible Oldroyd 6-constant fluid between two concen- tric cylinders is investigated. The flow is generated by moving inner cylinder and/or application of the constant pressure gradient. Two non-linear boundary value problems are solved numerically. The effects of material parameters, pressure gradient, magnetic field and Hall parameter on the velocity are studied. The graphical representation of velocity reveals that characteristics for shear thinning/shear thickening behaviour of a fluid is dependent upon the rheological properties. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction Channel flows of an electrically conducting viscous fluid under the action of transverse magnetic field have been studied by many workers because of its applications in many devices such as accelerators, magnetohydrodynamic (MHD) pumps, MHD power generators, electrostatic precipitation, petroleum industry, electrostatic precipitation, purification of crude oil, aerodynamics heating and fluid droplets sprays. Various workers [1–5] have examined the channel flows of a viscous fluid under the action of a transversely applied magnetic field. These results are important for designing duct wall and cooling arrangement. Because of growing use of non-Newtonian fluids in various manufac- turing and processing industries, considerable efforts have been made towards understanding their flow. However, there is not a single governing equation which exhibits all the properties of non-Newtonian fluids and, therefore, many con- stitutive equations for non-Newtonian fluids have been proposed. Guillope and Saut [6] has established existence results for some shearing motions of viscoelastic fluids of Oldroyd type. Some exact solutions of an Oldroyd 3-constant fluid are studied in [7–10]. Baris [11] investigated the steady flow of an Oldroyd 6-constant fluid between intersecting planes using the series expansion method. Rajagopal [12,13], Erdogan [14], Siddiqui et al. [15], and Ahmed et al. [16] consid- ered non-Newtonian fluids. 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.01.143 * Corresponding author. Fax: +92 51 9290275. E-mail address: mafzalrana@yahoo.com (M.A. Rana). Chaos, Solitons and Fractals 39 (2009) 204–213 www.elsevier.com/locate/chaos