We study the evolution of passive scalars in both rigid and moving slab-like
domains, in both horizontally periodic and infinite contexts. The scalar is
required to satisfy Robin-type boundary conditions corresponding to Newton's
law of cooling, which lead to nontrivial equilibrium configurations. We study
the equilibration rate of the passive scalar in terms of the parameters in the
boundary condition and the equilibration rates of the background velocity field
and moving domain.Comment: 27 page