Effective diffusion coefficient for steady two-dimensional convective flow

We use the homogenization method to obtain an expression for the effective diffusion coefficient D* for convective flows. We evaluate this expression numerically by a finite-mode truncation for two-dimensional laminar flows with arbitrary P\'eclet numbers. Our results allow us to establish the range of validity of the small- and large-P\'eclet-number asymptotic evaluations of D*. In particular, we find that for the case of rigid boundary conditions corrections to the asymptotic scaling decay only very slowly for large P\'eclet numbers and are still about 5% for P\'eclet numbers as high as 10⁶.