Laminar natural convection from a heated square cylinder immersed in power-law liquids C. Sasmal, R.P. Chhabra ⇑ Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India article info Article history: Received 14 January 2011 Received in revised form 4 April 2011 Accepted 4 April 2011 Available online 21 April 2011 Keywords: Square cylinder Natural convection Power-law fluid Grashof number Nusselt number Prandtl number abstract Laminar natural convection heat transfer from a heated long cylinder of square cross-section submerged in stagnant power-law fluids has been investigated numerically. The governing differential equations (continuity, momentum and thermal energy) have been solved over wide ranges of the pertinent dimen- sionless parameters, namely, Grashof number (10 6 Gr 6 10 5 ), Prandtl number (0:72 6 Pr 6 100) and power-law index (0:3 6 n 6 1:8) thereby covering both shear-thinning and shear-thickening type fluid behaviours. Detailed structure of the flow is studied in terms of streamline and isotherm patterns while heat transfer characteristics are analyzed in terms of the local Nusselt number distribution over the surface of the cylinder as well as its surface averaged values. Broadly, the flow remains attached to the surface up to larger values of the Grashof number in shear-thinning fluids (n < 1) than that in New- tonian media (n ¼ 1). Similarly, all else being equal, shear-thinning behaviour promotes heat transfer. Indeed, it is possible to enhance the rate of heat transfer by up to 100% under appropriate conditions, i.e., values of the Grashof number, Prandtl number and power-law index. Of course, shear-thickening fluid behaviour has an adverse influence on the rate of heat transfer. In the limiting case of the Newtonian fluid behaviour (n ¼ 1), the present predictions are in excellent agreement with the scant experimental results available in the literature. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Heat transfer from a square cylinder denotes an idealization of many industrial applications. Typical examples include design of novel heat exchanger, cooling of electronic components, thermal treatment of various food-stuffs like potato and carrot chips, beans, etc., fluidized bed drying of fibrous substances and convective drying of wood and ply boards, etc. In addition to such an over- whelming pragmatic significance, this flow configuration is also frequently employed to gain useful insights into the nature of the underlying physical processes involving momentum and heat transfer and wake phenomena, etc. Consequently, over the years, a significant body of knowledge has accrued on momentum and heat transfer characteristics in Newtonian fluids from cylinders of various cross-sections including circular, elliptical, triangular and square [1,2]. It is also appropriate to add here that not only most of such studies are limited to air and water, but more impor- tantly these pertain to either the forced or mixed convection re- gime of heat transfer [3,4]. Obviously, in most applications, free or natural convection always contributes in varying proportions to the overall rate of heat transfer, and indeed there are numerous situations in food processing applications where the only mode of heat transfer is by natural convection [5–7]. Typical examples in- clude heating of canned foods, and of other liquids confined in closed spaces. Furthermore, even in mixed convection regimes, the role of natural convection gradually increases with the decreas- ing magnitude of the imposed flow, i.e., the decreasing value of the Reynolds number. In spite of its practical and theoretical impor- tance, free convection in quiescent fluids from a long heated square cylinder has received very little attention, even in Newtonian fluids like air and water [8]. In addition to the physical properties of the medium and the size of the submerged cylinder, the rate of heat transfer is also influenced by the orientation of a square cylinder (horizontal, vertical or inclined) with respect to the direction of the gravity vector. Indeed, the corresponding values of the heat transfer coefficient can vary significantly with orientation under otherwise identical conditions. Furthermore depending upon the value of the Reynolds number (based on the characteristic velocity due to buoyancy-induced flow), the flow exhibits different flow re- gimes like laminar or turbulent, steady or unsteady, etc. This work is concerned with the prediction of heat transfer from a horizontal cylinder of square cross-section to quiescent ambient medium in the laminar flow regime. It is perhaps appropriate to add here that based on a combination of approximate analytical/numerical solu- tions complemented by experimental measurements, an adequate body of knowledge is now available enabling the prediction of the rate of heat transfer from a square cylinder in Newtonian fluids, at 0377-0257/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnnfm.2011.04.013 ⇑ Corresponding author. Tel.: +91 512 2597393; fax: +91 512 2590104. E-mail address: chhabra@iitk.ac.in (R.P. Chhabra). Journal of Non-Newtonian Fluid Mechanics 166 (2011) 811–830 Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm