Local Rayleigh and Nusselt Numbers for Cartesian convection with temperature‐dependent viscosity

We present a local treatment of the heat transport efficiency of the base‐heated cartesian convection with a temperature‐dependent viscosity, which allows us to give a clearer interpretation of Nusselt ( Nu )‐Rayleigh ( Ra ) numbers relation. The “local” Nusselt ( Nu l ) and Rayleigh ( Ra l ) numbers are defined by the local values at each boundary layer except the length scale which is the total depth. We find that Nu l ‐ Ra l relation obtained for the convection with constant viscosity and free surfaces is nearly coincident with that of the bottom boundary layer. For top boundary layer, we can treat it as a constant viscosity convection with rigid surface for large enough viscosity contrast. This interpretation can be made by choosing an appropriate temperature drop and viscosity for the definitions of Nu l and Ra l .