Nusselt number for convection driven by tidal and radiogenic heating

The 'traditional' formulas giving the Nusselt number Nu as a function of Rayleigh number Ra cannot be used for low and moderate values of Ra. Moreover, the recent progress in 3D numerical modeling makes possible to determine the Nusselt number Nu as a function of Rayleigh number Ra for convection driven by radiogenic and tidal heating. We found that for low and moderate Ra: Nu(Ra) = ε(Ra+ξ)λ where λ depends on rheology and boundary conditions, ε depends only on the mode of heating, and ξ = ε−1/λ · Nu(Ra) makes possible to develop a parameterized theory of convection in medium size icy satellites. We also indicate some differences between convection driven by tidal and radiogenic heating and convection driven exclusively by radiogenic heating.