Fluid Flow and Heat Transfer in Power-Law Fluids Across Circular Cylinders: Analytical Study

Abstract

An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausen method is used to solve the momentum integral equation whereas the energy integral equation is solved for INTRODUCTIONMany practical situations need a knowledge of fluid flow around and heat transfer from horizontal cylinders subjected to crossflow of non-Newtonian fluids. These fluids are classified by different authors in different ways. One important classification is the purely viscous fluids (Cho [1]). These fluids are further subdivided in to shear thinning (or pseudoplastic, e. g. paints, glues, blood, and suspensions) and shear thickening (or dilatant, e. g. wet sand, sugar and borax solutions) fluids. In this study, fluid flow and heat transfer characteristics of these fluids across a circular cylinder are investigated using a power-law model. This model is based on the fact that both fluids exhibit a region of linear relationship between stress and strain rate when viewed on a log-log plot (Chhabra and Richardson [2]). This is why, pure viscous fluid are also called power-law fluids.

Effect of blockage on heat transfer from a cylinder to power law liquids

“…As noted earlier, while bulk of the information available on the momentum and heat transfer characteristics of a circular cylinder in Newtonian fluids has been thoroughly reviewed by Zdravkovich (1997Zdravkovich ( , 2003 and the recent heat transfer literature has been reviewed by Ahmad (1996) and Bharti et al (2007a), the corresponding limited information for power-law fluids has been summarized in recent studies D'Alessio and Pascal, 1996;D'Alessio and Finlay, 2004;Ferreira and Chhabra, 2004;Soares et al, 2005, Bharti et al, 2006, 2007b-d, Sivakumar et al, 2006a,b, 2007Khan et al, 2006). Suffice it to say here that reliable results on drag and heat transfer for an unconfined cylinder immersed in streaming power-law liquids encompassing the following ranges of conditions are now available: Re 40; 0.2 n 2; 0.7 P r 1000.…”

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

“…The effect on drag is particularly striking at low Reynolds number. Besides the aforementioned studies based on the numerical solution of the complete governing equations, some works have been carried out employing standard boundary layer flow approximations to obtain approximate expressions for skin friction and Nusselt number (Khan et al, 2006). A few experimental studies on flow of nonNewtonian fluids past a cylinder have also been reported (Coelho and Pinho, 2003), which elucidate the roles of visco-elastic and shear-thinning behavior on the vortex shedding characteristics.…”

Heat transfer to power-law dilatant fluids in a channel with a built-in square cylinder

“…They found the enhancement in the rate of heat transfer with the increasing degree of shear-thinning behavior; however, an opposite trend was observed in dilatant fluids for a fixed value of the blockage ratio. Aside from these studies, there have been numerous analyses based on the usual boundary layer approximation [9] and most [16]. Similarly, there are only three previous numerical studies dealing with the heat transfer from a square obstacle to power-law fluids in the steady cross-flow regime [2,3,8].…”

“…The fluid flow across cylinders (square or circular cross-section) exhibits a rich variety of flow regimes depending upon the value of the Reynolds number, power-law index and the flow domain (confined or unconfined) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Most multiphase mixtures, i.e., foams, suspensions, emulsions, etc.…”