Heat transfer in a turbulent channel flow with square bars or circular rods on one wall

Direct numerical simulations (DNS) are carried out to study the passive heat transport in a turbulent channel flow with either square bars or circular rods on one wall. Several values of the pitch ( ${\it\lambda}$ ) to height ( $k$ ) ratio and two Reynolds numbers are considered. The roughness increases the heat transfer by inducing ejections at the leading edge of the roughness elements. The amounts of heat transfer and mixing depend on the separation between the roughness elements, an increase in heat transfer accompanying an increase in drag. The ratio of non-dimensional heat flux to the non-dimensional wall shear stress is higher for circular rods than square bars irrespectively of the pitch to height ratio. The turbulent heat flux varies within the cavities and is larger near the roughness elements. Both momentum and thermal eddy diffusivities increase relative to the smooth wall. For square cavities ( ${\it\lambda}/k=2$ ) the turbulent Prandtl number is smaller than for a smooth channel near the wall. As ${\it\lambda}/k$ increases, the turbulent Prandtl number increases up to a maximum of 2.5 at the crests plane of the square bars ( ${\it\lambda}/k=7.5$ ). With increasing distance from the wall, the differences with respect to the smooth wall vanish and at three roughness heights above the crests plane, the turbulent Prandtl number is essentially the same for smooth and rough walls.