Modeling the influence of regular wall roughnesses on the heat transport

Abstract

We investigate the effect of regular wall roughness on the heat transport in thermal convection. The roughness is introduced by a set of rectangular heated/cooled obstacles located at the corresponding plates. An analytical model to estimate the Nusselt number deviations caused by the wall roughness is developed, which is based on the Prandtl-Blasius boundary layer equations and is valid for moderate Rayleigh numbers (≲ 108) and a regular wall roughness, for which the height of the obstacles and the distance between them are significantly larger than the thickness of the thermal boundary layers. The model is validated in two-dimensional simulations, for different aspect ratios of the obstacles. It is found that the model predicts the heat transport with errors ≤ 6% for all investigated cases.