Motions in the solid mantle of silicate planets are predominantly driven by internal heat sources and occur in laminar regimes that have not been systematically investigated. Using high-resolution numerical simulations conducted in three dimensions for a large range of Rayleigh–Roberts numbers ($5\times 10^{3}\leqslant Ra_{H}\leqslant 10^{9}$), we have determined the characteristics of flow in internally heated fluid layers with both rigid and free slip boundaries. Superficial planforms evolve with increasing $Ra_{H}$ from a steady-state tessellation of hexagonal cells with axial downwellings to time-dependent clusters of thin linear downwellings within large areas of nearly isothermal fluid. The transition between the two types of planforms occurs as a remarkable flow polarity reversal over a small $Ra_{H}$ range, such that downwellings go from isolated cylindrical structures encircled by upwellings to thin interconnected linear segments outlining polygonal cells. In time-dependent regimes at large values of $Ra_{H}$, linear downwellings dominate the flow field at shallow depth but split and merge at intermediate depths into nearly cylindrical plume-like structures that go through the whole layer. With increasing $Ra_{H}$, the number of plumes per unit area and their velocities increase whilst the amplitude of thermal anomalies decreases. Scaling laws for the main flow characteristics are derived for $Ra_{H}$ values in a $10^{6}$–$10^{9}$ range. For given $Ra_{H}$, plumes are significantly colder, narrower and wider apart beneath free boundaries than beneath rigid ones. From the perspective of planetary studies, these results alert to the dramatic changes of convective planform that can occur along secular cooling.

Observations of icy satellites have revealed widespread marks of cryovolcanism. Because aqueous cryomagmas are negatively buoyant, two processes are required to explain these observations: one mechanism to generate melt close enough to the surface and another one to transport this melt to the surface. Here, we investigate the generation of melting in a systematic way, using a set of 85 numerical simulations where we vary the viscosity contrast, Rayleigh number, and tidal heating rate. Applied to Europa, considering a hydrosphere composed of pure water, our simulations suggest that isolated melt pockets can be generated close to the surface ( ∼5 km) as long as the ice layer thickness ( d*) remains modest ( 15≤d*≤35 km). However, the generation of melting becomes increasingly difficult as the amount of antifreeze compounds in the subsurface ocean increases. Furthermore, the proportion of melting increases very sharply with increasing tidal heating rate. In particular, when the tidal heating rate exceeds a threshold, an asymptotic regime is reached where the surface heat flux remains constant indicating that the tidal heat generated above this threshold is only used for melting the ice shell. In that regime, we found a direct relationship between the surface heat flux and d*. Finally, we provide a new assessment of Europa's thermal state. Based on available constraints, we propose that the ice shell thickness should exceed 15 km. However, d*∼15–35 km implies a tidal power ( >2 TW) much larger than expected. An extrapolation of the trends suggested by our results indicates that a more reasonable tidal power ( ∼1 TW) would involve d*∼50–90 km.