DNS of conjugate heat transfer in presence of rough surfaces

Often in the numerical simulations of turbulent heat transfer in a channel, the temperature is assigned as boundary condition at the wall. This condition is rather different from that in real experiments, where solid walls are thick and a constant temperature is imposed at the exterior of the walls. In the present work, rough channel flows with a Prandtl number PrF=ν/αF=1 have been simulated transporting thermal fields in presence of walls with two different thermal diffusivities αSi. In one case, the thermal diffusivity corresponds to that of a material with conductivity 10 times greater than copper. In the other, the thermal diffusivity is that of glass. The upper wall of the channel is smooth and 0.5h thick (h being the half height of the channel). The lower wall is made of a rough layer of height k=0.2h superimposed to a uniform layer 0.3h thick. Several simulations were performed varying the roughness elements. Above the crests plane the total stress has a linear behaviour as in a smooth channel. By normalising the total stress with the stress at the smooth wall, it has been found that the surface made by three-dimensional staggered cubes leads to a drag 2.3 times greater than that of smooth walls. On the other hand, for triangular longitudinal bars the drag reduces. The heat transfer is reduced for low conducting walls, however the influence of the shape of the roughness is similar to that for high conducting walls. This has been observed through flow visualizations and joint pdf between velocity and temperature fields.