406 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 84, AUGUST 2006 INTRODUCTION T he flow of fluids past spheres and circular cylinders is one of the most extensively studied problems in classical fluid mechanics. Consequently, over the years, a voluminous body of knowledge encompassing wide ranging phenomena associated with the flow over a cylinder and a sphere has emerged, albeit most of it relates to the flow of Newtonian fluids (e.g. Chhabra, 1996, 2006; Clift et al., 1978; Coutanceau and Defaye, 1991; Fornberg, 1980, 1985; Norberg, 2003; Williamson, 1996; Zdravkovich, 1997, 2003). An inspection of the available literature shows that adequate information is now available for the flow of Newtonian fluids for most conditions of interest, at least for an unconfined sphere or a cylinder. However, many materials, e.g. multiphase mixtures, high molecular weight substances, soap solutions, polymer melts and their solutions, Steady Flow of Power Law Fluids across a Circular Cylinder Ram Prakash Bharti 1 , R. P. Chhabra 1* and V. Eswaran 2 1. Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India 2. Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India etc., encountered in industrial practice display a range of rheological non-Newtonian complexities like shear-thinning, shear-thickening, yield stress, viscoelasticity, etc. (Chhabra and Richardson, 1999). A reliable knowledge of the flow and hydrodynamics forces is frequently needed to design the support structures exposed to non-Newtonian fluids in polymer processing operations, in connection with the use of thin cylinders and wires as measure- ment probes and sensors in non-Newtonian flows, and during the heating or cooling of process streams in tubular heat exchangers. In addition to the foregoing potential industrial The momentum equations describing the steady cross-flow of power law fluids past an unconfined circular cylinder have been solved numeri- cally using a semi-implicit finite volume method. The numerical results highlighting the roles of Reynolds number and power law index on the global and detailed flow characteristics have been presented over wide ranges of conditions as 5 ≤ Re ≤ 40 and 0.6 ≤ n ≤ 2. The shear-thinning behaviour (n < 1) of the fluid decreases the size of recirculation zone and also delays the separation; on the other hand, the shear-thickening fluids (n > 1) show the opposite behaviour. Furthermore, while the wake size shows non-monotonous variation with the power law index, but it does not seem to influence the values of drag coefficient. The stagnation pressure coefficient and drag coefficient also show a complex dependence on the power law index and Reynolds number. In addition, the pressure coefficient, vorticity and viscosity distributions on the surface of the cylinder have also been presented to gain further physical insights into the detailed flow kinematics. Les équations de mouvement décrivant l’écoulement transversal permanent de fluides de loi de puissance en aval d’un cylindre circulaire non confiné ont été résolues numériquement par une méthode de volumes finis semi-implicite. Des résultats numériques soulignant le rôle du nombre de Reynolds et de l’indice de loi de puissance sur les caractéristiques d’écoulement globales et détaillées sont présentés pour de vastes gammes de conditions, soit 5 ≤ Re ≤ 40 et 0,6 ≤ n ≤ 2. Le comportement rhéofluidifiant (n < 1) du fluide réduit la taille de la zone de recircu- lation et accroît également la séparation; d’autre part, les fluides rhéoépaississants (n > 1) montrent un comportement opposé. En outre, alors que la taille du sillage varie de manière non monotone avec l’indice de loi de puissance, elle ne semble pas influencer les valeurs du coefficient de traînée. Le coefficient de pression de stagnation et le coefficient de traînée montrent aussi une dépendance complexe envers l’indice de loi de puissance et le nombre de Reynolds. Les distributions des coefficients de pression, de la vorticité et de la viscosité sur la surface du cylindre sont également présentées afin de mieux comprendre les cinématiques d’écoulement détaillées. Keywords: power law fluids, circular cylinder, steady flow, drag coefficients, shear-thinning, shear-thickening * Author to whom correspondence may be addressed. E-mail address: chhabra@iitk.ac.in