In this paper, we present the results from Direct Numerical Simulations of turbulent, incompressible flow through a square duct, with an imposed temperature difference between two opposite walls, while the other two walls are supposed to be perfectly insulated. The mean flow is sustained by an imposed, mean pressure gradient. The most interesting feature, characterizing this geometry, consists in the presence of mean secondary motions in the cross-flow plane. These motions are relatively weak, in that their maximum intensity is about 2 ÷ 3% of the mean streamwise velocity, but they have a strong effect on both the flow and temperature field patterns. In this study, we focus on weak turbulence, in that the Reynolds number, based on the bulk velocity and the hydraulic diameter, is about 4400.
Our results indicate that secondary motions do not affect significantly global parameters, like the friction factor and the Nusselt number, with respect to the plane-channel flow. It is conjectured that this circumstance could be due to a compensation effect, between the appearence of mean secondary motions, and the presence of the two boundary layers close to the vertical walls.
