Secondary flow and peripheral heat flux distribution in square channels with macroscopic random roughness

We perform numerical simulations of conjugate heat transfer in square ducts for two representative rough surfaces (grit-blasted and graphite) and two fluid–solid conductivity ratios, using both DNS and RANS with the Spalart–Allmaras model. The effect of the QCR extension is also assessed, with a smooth-wall case serving as a baseline. DNS captures the altered heat-transfer distribution and secondary flows caused by roughness, whereas RANS tends to circularize velocity and temperature fields, yielding parabolic Nusselt profiles with limited sensitivity to geometric details. The QCR correction improves RANS predictions for grit-blasted roughness, where secondary flows resemble the smooth case, but degrades accuracy for the graphite surface, where eddy orientation is reversed. Despite local discrepancies, RANS agrees well with DNS in global metrics, with errors typically below 5%. For the first time, the heat-flux distribution along the duct perimeter is examined in detail, revealing that it depends not only on the roughness intensity but also on its morphological characteristics. These findings support the use of RANS for average heat-transfer prediction in rough-wall conjugate heat transfer, while underscoring the need for high-fidelity simulations to resolve the spatial complexity introduced by roughness.