Direct numerical simulation of forced thermal convection in square ducts up to

We carry out direct numerical simulation (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case unit Prandtl number. Reynolds numbers up to $Re_\tau \approx 2000$ are considered which much higher than previous studies, and yield clear scale separation between inner- outer-layer dynamics. Close similarity behavior temperature streamwise velocity fields is confirmed as studies related plane channels pipes. Just like mean velocity, found exhibit logarithmic layers function nearest wall, however with different slope. The most important practical implication validity traditional hydraulic diameter correct reference length for reporting data, we rigorously show here. Temperature fluctuations also have similar behavior, but apparently growth their inner-scaled peak variances not observed here unlike canonical wall-bounded flows. Analysis split contributions coefficient shows that cross-stream convection associated secondary motions responsible about $5\%$ total. Finally, use DNS database highlight shortcomings linear closures flux, substantial modeling improvement may be principle obtained retaining at least three terms vector polynomial integrity basis expansion.