Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re = 1000, Re = 1500 and Gr less than or equal to 10(8) using a low Reynolds number k-epsilon. model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar-turbulent transition and relaminarization of the flow. They also distinguish the Re-Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000 less than or equal to Re,< 1500, Gr ≤ 5 x 10(7). (C) 2003 Elsevier Ltd. All rights reserved.