The effects of irregular roughness with different surface power spectrums on the heat transfer of natural convection in enclosures

The effects of different irregular roughness on natural convection in a cavity having an aspect ratio of 4 are investigated numerically considering the compressibility of the working fluid for a Rayleigh number (Ra) of 1 × 10⁶. Because of the common existence in nature, the self-affine fractal surface with Gaussian height distribution has been chosen as the type of irregular roughness. According to the power spectral densities, four different irregular roughness have been generated based on the 4 different roll-off wavenumbers. The existence of roughness peaks will amplify the local Nusselt number (Nu), as the roll-off wavenumber of roughness elements increases, this augment will increase as well. In contrast, the rough valleys will decrease the local Nu. For the average Nu over an entire rough surface, the increase of roll-off wavenumber causes the decrease of average Nu. Further, the contributions from different roughness regions to the average Nu have been investigated and the results show that the partial average Nu over the roughness top region is affected slightly by the change of roughness roll-off wavenumber, but this effect is much more appreciable on the partial average Nu over the roughness bottom region.