Mixed convection from a heated semi-circular cylinder to power-law fluids in the steady flow regime Avinash Chandra, R.P. Chhabra ⇑ Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India article info Article history: Received 21 March 2011 Received in revised form 11 August 2011 Accepted 18 August 2011 Available online 7 October 2011 Keywords: Mixed convection Semi-circular cylinder Power-law fluids Richardson number Drag coefficient Reynolds number Prandtl number Nusselt number abstract Steady mixed convection heat transfer from a heated semi-circular cylinder immersed in power-law flu- ids is considered here with its curved surface facing upstream. The imposed flow and the buoyancy act in the same direction thereby resulting in the so-called aiding-buoyancy configuration. The momentum and thermal energy equations have been solved numerically over the following ranges of conditions: 0 6 Ri 6 2, 0:2 6 n 6 1:8, 1 6 Re 6 30 and 1 6 Pr 6 100. The combined effects of the forced and free con- vection on the flow and thermal fields are visualized in terms of the streamline and isotherm contours. Further insights are provided in terms of the distribution of pressure coefficient and local Nusselt number along the cylinder surface. Finally, the overall macroscopic characteristics are reported in terms of the individual and total drag coefficients and the average Nusselt number as functions of the pertinent dimensionless parameters. The influence of the power-law index is strongly modulated by the value of the Reynolds number. Broadly, drag coefficient shows a monotonic increase as the value of the Richard- son number or Reynolds number increases. At low Reynolds numbers, such as Re = 1, the local value of the Nusselt number is found to be maximum at corners and for high values of the Reynolds number, it shifts towards the front stagnation point. The average Nusselt number increases with an increase in the value of the Reynolds number, Prandtl number and Richardson number. Broadly, shear-thinning vis- cosity facilitates heat transfer whereas shear-thickening has an adverse effect on it. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Heat transfer in the mixed convection regime from variously shaped bodies immersed in moving fluids constitutes an important field of study from both theoretical and pragmatic considerations. Typical examples include tubular, pin-type and novel design of heat exchangers. For instance, flow and heat transfer past 2-D ob- jects of various shapes such as semi-circular cylinder, triangular, trapezoidal, etc. are encountered in compact heat exchangers. Additional examples are found in cooling of electronic components and in thermal treatment of foodstuffs. From a theoretical stand- point, the momentum and thermal energy equations are coupled via the body force term. Under these conditions, the velocity and temperature fields interact in an intricate manner. Thus, for in- stance, depending upon the shape and orientation of the bluff body with respect to the direction of the external flow and of gravity, the type of flow (laminar or turbulent), the onset of flow separation and of the laminar vortex shedding flow regime are strongly influ- enced by the value of the relevant governing parameters. On the other hand, in most practical situations, natural convection is always present and it contributes to the overall rate of the heat transfer in varying proportions. In an application, the relative importance of the free and forced convection is judged by the value of the Richardson number, Ri, which is given by the ratio of the Grashof number (Gr) to the Reynolds number squared (Re 2 ), i.e., Ri = Gr/Re 2 . In physical terms, the Richardson number denotes the relative strengths of the buoyancy-induced and externally imposed flow. Thus, vanishingly small values, Ri ? 0, denote the pure forced convection regime whereas Ri ? 1 corresponds to the free convec- tion regime. The value of Ri = 1 indicates the fact that the exter- nally imposed velocity is comparable to that induced by the buoyancy effects. The need to estimate the rate of heat transfer be- tween a heated object and a flowing fluid therefore often arises in process engineering calculations. For a given shape and orientation of the object, this information is conveniently expressed in terms of the Nusselt number (Nu) as a function of the Reynolds number, Grashof number and Prandtl number or a combination thereof such as the Richardson number (Ri). Hence, over the years, a volu- minous body of knowledge has accrued on mixed convection from circular, square cross-section cylinders immersed in Newtonian fluids [1–8]. Consequently, based on a combination of analytical, numerical and experimental results, it is now possible to estimate the value of the Nusselt number under most conditions of practical 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.09.004 ⇑ Corresponding author. Tel.: +91 512 2597393; fax: +91 512 2590104. E-mail address: chhabra@iitk.ac.in (R.P. Chhabra). International Journal of Heat and Mass Transfer 55 (2012) 214–234 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt