Chemical Engineering Science 57 (2002) 1331 – 1341 www.elsevier.com/locate/ces Laminar momentum and thermal boundary layers of power-law uids over a slender cylinder Mukta Agarwal a , R. P. Chhabra a ; ∗ , V. Eswaran b a Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India b Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India Received 30 March 2001; received in revised form 26 September 2001; accepted 3 December 2001 Abstract In this work, the momentum and thermal boundary layers for power-law uids over a thin needle have been investigated numerically under wide ranges of kinematic and physical conditions. The curvature eects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected. Extensive results on axial velocity and temperature proles elucidating the complex interplay between the shear-thinning or shear-thickening characteristics of the uid, size of the needle and the Reynolds number of ow are presented herein. The role of the two commonly used thermal boundary conditions (constant temperature and constant heat ux) has been illustrated by way of contrasting the resulting temperature proles and the values of the Nusselt number. Overall, the results presented herein encompass the following ranges of the physical and kinematic variables: 0:2 6 n 6 1:6; PrL ¡ 1000 and ReL ¡ 10 6 . ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Boundary layer; Momentum; Thermal; Power-law uids; Thin needle 1. Introduction The phenomena of momentum, heat and mass transfer in boundary layers over an immersed solid object is encoun- tered in a wide range of process engineering applications. Notwithstanding the importance of the detailed kinematics of the ow eld, it is readily recognised that reliable infor- mation on the rates of momentum, heat and mass transfer between the uid and the submerged object is frequently needed while performing process engineering and equip- ment design calculations. This information is conveniently expressed using the relevant dimensionless parameters such as the skin friction coecient, Nusselt and Sherwood num- bers as functions of the pertinent physical and kinematic variables expressed in dimensionless form as Reynolds, Prandtl and Schmidt numbers and the other system vari- ables. This functional relationship is strongly dependent on the geometry (shape and orientation) of the submerged ob- ject. Consequently, over the years, a wealth of information has accrued on dierent aspects of boundary layer ows for Newtonian uids for a range of shapes, albeit bulk of the ∗ Corresponding author. Tel.: +91-512-597393; fax: +91-512-590007. E-mail address: rpc@iitk.ac.in (R. P. Chhabra). literature is restricted to the highly idealised shapes such as a plane surface, cylinder, sphere and other axisymmetric shapes, etc. Excellent accounts of the developments in this eld (restricted to Newtonian uids) are available in classic books (Rosenhead, 1988; Schlichting & Gersten, 2000). In contrast to this, very little is known about the boundary layer ows for non-Newtonian uids which are encountered extensively in a wide variety of industrial settings including chemical, polymer, food and process industries (Chhabra & Richardson, 1999). A cursory examination of the avail- able body of information reveals that most of the bound- ary layer literature pertains to the simple power-law uid model and to the simple shapes including at plates, spheres and cylinders (Skelland, 1967; Astarita & Marrucci, 1974; Schowalter, 1978; Chhabra, 1999a; Chhabra & Richardson, 1999). The other general survey articles summarizing the key results in this area for non-Newtonian uids include that of Shenoy and Mashelkar (1982) for free convection, of Irvine Jr. and Karni (1987), of Nakayama (1988) and of Chhabra (1999b, Chap. 39) for forced convection heat and mass transfer. Similarly, the corresponding experimental re- sults and empirical correlations have been reviewed by Hart- nett and Cho (1998, Chap. 10) and by Irvine Jr. and Capo- bianchi (2000). Owing to the non-linear equation of state 0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII:S0009-2509(02)00013-1