Parametric models of planets used to study their thermal evolution are generally based on scaling laws for purely thermal convection. However, planetary mantles may be chemically highly differentiated due to partial melting, which may form thick layers of depleted and dehydrated melting residue (e.g. continental roots). This results in inhomogeneity of density, which affects the driving force of convection, and viscosity (through the water content), which directly influences the dynamics of the system. This work investigates the applicability of scaling laws developed for purely thermally convecting systems to chemically differentiated systems representative of planetary mantles. The effects of depletion related buoyancy and melting related dehydration, and particularly the stratified convection patterns which may result from these, are considered. Two different strategies are applied to this end. First, a large number of numerical thermochemical convection experiments are performed, of which the dynamics and heat flow characteristics are studied. Secondly, theoretical approximations are developed from existing scaling laws to describe the heat flow of chemically stratified systems with separately convecting layers. These are tested using numerical simulations. The results show that the presence of a chemical stratification in the mantle may significantly alter heat flow patterns relative to a purely thermally convecting system by either influencing the thickness of the thermal boundary layer or dividing the convecting part of the system in vertically separate cells. This is consistent with recent petrological findings. Although the chemical stratification may be inherently instable against remixing, the present results suggest that the timescales of remixing may be much larger than those of thermal equilibration. Therefore, it is important to consider chemical stratification in thermal evolution models. For present-day Earth conditions and realistic rheological parameters, the results predict that the lower parts of continental roots may be convecting separately from the underlying mantle. The thick depleted layer which has been speculated to underly the martian crust may also have exhibited convection in the lower parts. When convection takes place in the depleted zone, mantle heat flow values are predicted to increase by a factor of 2-5 relative to non-convecting depleted zones. If this process acts for significant periods of time during planetary evolution, it will strongly influence the planet's thermal evolution.
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