Mixed convective heat transfer from two identical square cylinders in cross flow at Re = 100 Sandip Sarkar a , Amaresh Dalal b , G. Biswas c, * a Research and Development Division, Tata Steel, Jamshedpur 831001, India b School of Mechanical Engineering, Purdue University, West Lafayette 47907, IN, USA c Indian Institute of Technology, Kanpur 208016, India article info Article history: Received 16 March 2009 Received in revised form 27 November 2009 Accepted 4 January 2010 Keywords: Mixed convection Square cylinder Vortex shedding Aiding buoyancy Opposing buoyancy Finite element method abstract Numerical results of mixed convective heat transfer from two identical cylinders in a uniform upward flow has been demonstrated at Re = 100. The effect of aiding and opposing buoyancy is brought about by varying Richardson numbers. A stabilized SUPG based finite element technique has been used. Results are discussed for 20 cases by varying the locations of second cylinder with respect to the fixed location of the first cylinder. The effect of buoyancy on force coefficients, Strouhal number and Nusselt number is investigated. Under the same buoyancy induced field the cylinders are found to oscillate at the same fre- quency. For a particular cylinder spacing, vortex shedding is observed up to Ri = 0.25. Maximum heat transfer is found at the front face of second cylinder. It is found that hydrodynamic instabilities grow and flow shows chaotic phenomena when the system is severely influenced by thermal buoyancy. It is for the first time that such behavior for the Richardson number at this tandem configuration is being reported. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Flow and heat transfer past a square cylinder is a well investi- gated problem, and it can be considered as a prototype of the bluff body wakes because of the simplicity of the geometry and the complexity of the physical process involved. Over the past few dec- ades, considerable attention has been paid to various aspects of this flow configuration and a voluminous body of knowledge encompassing a wide range of phenomena has emerged. In a vertical flow, the velocity induced by free convection is either aligned or opposed to that of forced convection. It has been observed that in the presence of aligned free and forced convec- tion, the vortex shedding is diminished and the separation points are shifted downstream. When the free convection acts in the opposite direction, the point of separation is advanced upstream. Harlow and Fromm [1] investigated the forced convective flow past a rectangular cylinder for various Reynolds numbers. Forced convection over a row of inline cylinders placed in a channel has been studied by Kundu et al. [2]. Oosthuizen and Madan [3] studied the unsteady mixed convec- tion behind a cylinder for Re in the range between 100 and 300. Biswas et al. [4] studied unsteady mixed convection heat transfer in a horizontal channel with a built-in square obstacle. Their re- sults show that the mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers, in contrast to forced convection alone. Noto and Matsumoto [5] reported degeneration of unsteady vortices to stationary ones due to favor- able thermal buoyancy. Chang and Sa [6] studied the behavior of near-wake vortices and predicted the degeneration of purely peri- odic flows into a steady vortex pattern at a critical Grashof number of 1500. Singh et al. [7] studied the influence of favorable and ad- verse buoyancy in a vertical channel with a built-in circular cylin- der. For the Richardson number less than 0.15, the flow was characterized by broadening of the wake. The Richardson number greater than 0.15, revealed separation delay and attached twin vor- tices behind the cylinder. Sharma and Eswaran [8] studied numer- ically the heat and fluid flow across a square cylinder at Reynolds number of 100 under aiding and opposing buoyancy. They showed the influence of buoyancy on parameters characterizing the fluid flow and heat transfer. Lecordier et al. [9] studied suppression of vortex shedding due to the change in viscosity and density of the fluid with temperature. Shi et al. [10] computed effect of dynamic viscosity and density variations with heating. The authors con- cluded that both effects have significant influence on vortex shed- ding frequency and the heat transfer characteristics. The flow past tube bundles is a logical extension of cylinders in tandem and transverse arrangements. Bhattacharyya et al. [11] re- ported the vortex shedding in shear flow past tandem square cylin- ders in the vicinity of a plane wall up to a Reynolds number of 200. 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.02.053 * Corresponding author. Present address: Central Mechanical Engineering Research Institute (CSIR), Durgapur 713209, India. Tel.: +91 343 2546749; fax: +91 343 2546745. E-mail address: gtm@iitk.ac.in (G. Biswas). International Journal of Heat and Mass Transfer 53 (2010) 2628–2642 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt