International Journal of Thermal Sciences 45 (2006) 1008–1020 www.elsevier.com/locate/ijts Fluid flow and convective heat transfer in a rotating helical square duct Yitung Chen a,∗ , Huajun Chen a,b , Benzhao Zhang b , Hsuan-Tsung Hsieh a a Department of Mechanical Engineering, University of Nevada, Las Vegas, NV89154, USA b Department of mechanics, Zhejiang University, Hangzhou, 310027, PR China Received 27 December 2004; received in revised form 1 November 2005; accepted 13 January 2006 Available online 28 February 2006 Abstract A numerical study is performed to examine the characteristics of fluid flow and convective heat transfer in a helical square duct rotating at a constant angular velocity about the center of curvature. Due to the combined effects of rotation (the Coriolis force), torsion and curvature (the centrifugal force), the flow behaviors become very complicated. A wide range of parameters is covered in this work. The variations of flow structure and temperature distribution with the force ratio F (the ratio of the Coriolis force to the centrifugal force) and the torsion are examined in details. The effects of rotation and torsion on the friction factor and Nusselt number are also studied at length. And also multiple solutions for a rotating toroidal square duct have been obtained. Certain hitherto unknown flow patterns are found. The present work shows both the nature of flow behaviors and the characteristics of heat transfer in a rotating helical square duct.  2006 Elsevier SAS. All rights reserved. Keywords: Secondary flow; Heat transfer; Rotating duct; Helical duct 1. Introduction The flow of a fluid through a non-straight pipe system cre- ates a secondary flow taking place in a plane perpendicular to the main flow. Although the magnitude of the secondary flow is much smaller than the main flow, it has been verified that the secondary flow can enhance the heat transfer significantly in cooled ducts. Additionally, a higher secondary flow produces a higher flow resistance, which results in the main flow requir- ing more power to sustain the axial flux as compared to flows in a straight pipe/duct without secondary flow. On the other hand, secondary flows lead to vibrations and noises. Because secondary flow is one of the most important aspects of flow dynamics in non-straight pipe systems, knowledge and under- standing of flow physics are important in engineering designs and operations. Because of the importance of secondary flow in engineering applications, the characteristics of the complex hydrodynamic phenomenon have been the subject of many studies. Secondary flows in stationary curved ducts (with or without finite pitches) * Corresponding author. Tel.: +(702)895 1202; fax: +(702)895 3936. E-mail address: uuchen@nscee.edu (Y. Chen). related to engineering applications for different cross-sections have been investigated theoretically, numerically and experi- mentally. Berger et al. [1], Nandakumar and Masliyah [2], Ito [3] and Berger [4] have reviewed fluid flow and heat transfer in curved ducts. To enhance the rate of heat and mass transfer, the helical ducts with a finite pitch have been used extensively in various industrial applications. Useful characteristics include high rates of heat and mass transfer, enhanced cross-sectional mixing, low axial dispersion and an extended laminar flow. Previous work by Germano [5], Tuttle [6], Liu and Masliyah [7], Zabielski and Mestel [8] on helical ducts were mainly focused on sta- tionary ducts with a circular cross sections. Only a few studies took helical square ducts into account. Chen and Jan [9] stud- ied the torsion effect on fully developed laminar flow in helical square ducts with the Galerkin finite-element method and found that the Dean instability can be avoided due to the torsion. On the other hand Boliander [10,11] obtained the opposite con- clusion when he studied the helical square ducts with a finite volume method and detected two unconditionally stable solu- tion branches. Thomson et al. [12] examined the convective heat transfer in helical ducts with a rectangular cross section in 1290-0729/$ – see front matter  2006 Elsevier SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2006.01.006