Effective surface modeling for momentum and heat transfer over rough surfaces: Application to a natural convection problem

In this paper, we propose efficient and suitable effective surface models for steady laminar flows with heat transfer over rough surfaces. These models are developed in the frame of a domain decomposition method and consist in replacing the rough boundaries by effective smooth surfaces on which effective boundary conditions or wall laws are prescribed. The associated effective properties, namely the effective friction and heat transfer coefficients, are determined by the resolution of local closure problems over a representative pattern of the roughnesses. The impact of the flow parameters on these effective coefficients is analyzed, which allows to obtain useful estimates in some specific cases. Finally, two-dimensional numerical experiments are performed for a natural convection problem in a stamp shaped cavity to assess the validity of the proposed effective surface models. Throughout these tests, we also study numerically the impact of the position of the effective surface on momentum and heat transfers.