International Journal of Thermal Sciences 45 (2006) 433–442 www.elsevier.com/locate/ijts Predicted effects of inlet turbulent intensity on mixed convection in vertical tubes with uniform wall heat flux A. Behzadmehr a , N. Galanis b,∗ , C.T. Nguyen c a Mechanical Engineering Department, University of Sistan & Baluchestan, Iran b Génie mécanique, Université de Sherbrooke, QC, Canada J1K 2R1 c École de génie, Université de Moncton, Moncton, NB, Canada E1A 3E9 Received 4 August 2004; received in revised form 5 August 2005; accepted 5 August 2005 Available online 5 October 2005 Abstract Simultaneously developing upward mixed convection of air in vertical tubes with uniform wall heat flux was studied numerically using the three-dimensional elliptic conservation equations. The coupled hydrodynamic and thermal fields were predicted using both laminar and turbulent formulations (the latter was based on the Launder and Sharma low Reynolds number k–ε turbulence model) for Re = 1000 and three different values of the inlet turbulent intensity over a wide range of Grashof numbers (Gr  10 8 ). The turbulent formulation is more versatile since it can predict turbulent as well as laminar fully-developed flow fields. The effects of inlet turbulent intensity on the axial evolution of the hydrodynamic and thermal fields as well as on the developed velocity and temperature profiles are presented. It is also shown that the increase of the inlet turbulent intensity causes a significant decrease of the wall temperature and of the skin friction coefficient at certain Re–Gr combinations.  2005 Elsevier SAS. All rights reserved. Keywords: Mixed convection; Developing; Turbulence; Transition; Relaminarization 1. Introduction Mixed convection in ducts occurs in many industrial instal- lations such as pressurized water reactors, supercritical boilers, solar energy collectors and shell and tube heat exchangers. It is therefore being studied extensively. Jackson et al. [1] presented a comprehensive review of experimental and theoretical studies on mixed convection in vertical tubes published before 1989. Some more recent publications are referred to in the present ar- ticle. Numerical studies of mixed convection have been conducted by assuming that the flow field is laminar when Re is low or turbulent when Re is high. Thus, Wang et al. [2], Nesreddine et al. [3] and Zghal et al. [4] used the laminar equations for Re < 1500 while Cotton and Jackson [5], Satake et al. [6], Tanaka et al. [7] used the turbulent equations for Re > 2000. Nevertheless, experimental evidence compiled by Metais and * Corresponding author. E-mail address: nicolas.galanis@usherbrooke.ca (N. Galanis). Eckert [8] indicates that mixed convection can be turbulent for Reynolds numbers as low as 1000. Furthermore, a flow field which is laminar at the tube entrance may become unstable and eventually turbulent further downstream [9]. Or, as demon- strated by both numerical and experimental studies [6,7,10], a turbulent flow can become laminar under the stabilizing effect of the buoyancy force. It is therefore evident that the laminar model used for the numerical prediction of the corresponding hydrodynamic and thermal fields is of limited practical interest since it can only handle the simplest flow conditions. Scheele and Hanratty [9] studied experimentally the stability of flow in a vertical tube under mixed convection heat trans- fer by detecting temperature fluctuations in the effluent. It was found that the stability depends primarily on the shape of the ve- locity profile and only secondarily on the value of the Reynolds number. Later, Su and Chung [10] analyzed the linear stabil- ity of mixed convection flow in a vertical tube. Their results suggest that mixed convection flow in a vertical pipe can be- come unstable at low Reynolds number and Rayleigh numbers irrespective of the Prandtl number, in contrast to the isothermal case. 1290-0729/$ – see front matter  2005 Elsevier SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2005.08.004