  Convection in planetary mantles is in the so-called mixed heating mode; it is
driven by heating from below, due to a hotter core, as well as heating from
within, due to radiogenic heating and secular cooling. Thus, in order to model
the thermal evolution of terrestrial planets, we require the parameterization
of heat flux for mixed heated convection in particular. However, deriving such
a parameterization from basic principles is an elusive task. While scaling laws
for purely internal heating and purely basal heating have been successfully
determined using the idea that thermal boundary layers are marginally stable,
recent theoretical analyses have questioned the applicability of this idea to
convection in the mixed heating mode. Here, we present a scaling approach that
is rooted in the physics of convection, including the boundary layer stability
criterion. We show that, as long as interactions between thermal boundary
layers are properly accounted for, this criterion succeeds in describing
relationships between thermal boundary layer properties for mixed heated
convection. The surface heat flux of a convecting fluid is locally determined
by the properties of the upper thermal boundary layer, as opposed to globally
determined. Our foundational scaling approach can be readily extended to nearly
any complexity of convection within planetary mantles.
