Direct numerical simulation of turbulent heat transfer in a square duct

The results from a direct numerical simulation (DNS) of turbulent, incompressible flow through a square duct, with an imposed temperature difference between the horizontal walls, are presented. The vertical walls are assumed perfectly insulated, and the Reynolds number, based on the bulk velocity and the hydraulic diameter, is about 4400. Our results indicate that secondary motions do not affect dramatically global parameters, like the friction factor and the Nusselt number, with respect to the plane‐channel flow, but the distributions of the local shear stress and heat flux at the walls are highly non‐uniform, due to the presence of these secondary motions. It is also shown that an eddy‐diffusivity approach is capable to reproduce well the turbulent heat flux. All simulations were performed by an efficient finite volume algorithm. A description of the numerical algorithm, together with an analysis of time‐accuracy, is included. The OpenMP parallel programming language was exploited to obtain a moderately‐scalable application.