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<=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<=Re<=1500, Gr<=5*10^7.