Thermal evolution of telluric planets is mainly controlled by secular cooling and internal heating due to the decay of radioactive isotopes, two processes that are equivalent from the standpoint of convection dynamics. In a fluid cooled from above and volumetrically heated, convection is dominated by instabilities of the top boundary layer and the interior thermal structure is non-isentropic. Here we present innovative laboratory experiments where microwave radiation is used to generate uniform internal heat in fluids at high Prandtl number ( ) and high Rayleigh–Roberts number (ranging from to ), appropriate for planetary mantle convection. Non-invasive techniques are employed to determine both temperature and velocity fields. We successfully validate the experimental results by conducting numerical simulations in three-dimensional Cartesian geometry that reproduce the experimental conditions. Scaling laws relating key characteristics of the thermal boundary layer, namely its thickness and temperature drop, to the Rayleigh–Roberts number have been established for both rigid and free-slip boundary conditions. A robust conclusion is that for rigid boundary conditions the internal temperature is significantly higher than for free-slip boundary conditions. Our scaling laws, coupled with plausible physical parameters entering the Rayleigh–Roberts number, enable us to calculate the mantle potential temperature for the Earth and Venus, two telluric planets with different mechanical boundary conditions at their surface.

A preparation in ‘dry media’ of phenothiazine derivatives by thionation of diphenylamines using microwave-activation is presented. This method allowed the preparation of 2,4,6,8-tetra-tert-butyl-10H-phenothiazine 2e, the first 2,4,6,8-tetra-substituted derivative of this heterocycle, practically inaccessible by other thionation procedure.

Abstract A comparison of microwave-activated vs. classical organic synthesis is presented for a variety of growth-regulator compounds with a phenoxyacetic acid structure. Microwave-assisted nucleophilic substitutions are safely and conveniently carried out in an open vessel, without any solvent. Yields are very good, and reaction times are extremely short.

The thermal evolution of terrestrial planets is mainly controlled by the amount of radioactive heat sources in their mantle, and by the geometry and efficiency of solid state thermo-chemical convection within. So far, these systems have been studied using numerical methods only and cross validation by laboratory analogous experiments has not been conducted yet. To fill this gap we perform the first laboratory experiments of mantle convection driven by microwave-generated internal heating. We use a 30×30×5 cm3 experimental tank filled with 0.5 % Natrosol in water mixture (viscosity 0.6 Pa.s at 20°C). The fluid is heated from within by a microwave device that delivers a uniform volumetric heating from 10 to 70 kW/m3; the upper boundary of the fluid is kept at constant temperature, whereas the lower boundary is adiabatic. The velocity field is determined with particle image velocimetry and the temperature field is measured using thermochromic liquid crystals which enable us to charaterize the geometry of the convective regime as well as its bulk thermal evolution. Numerical simulations, conducted using Stag-3D in 3D cartesian geometry, reproduce the experimental setup (i.e., boundary conditions, box aspect ratio, temperature dependence of physical parameters, internal heating rate). The successful comparison between the experimental and numerical results validates our approach of modelling internal heating using microwaves.

Radioactive decay of unstable isotopes is one of the main heat sources in the early stages of planetary formation as well as in the mantle of terrestrial planets. Laboratory studies characterized by Rayleigh and Prandtl numbers in the range relevant for planetary bodies had remained beyond the ability of the experimental approach until the development of a new technique based on microwave heating. Using this technique, we performed a series of experiments focused on the thermal evolution of an internally heated viscous fluid cooled from above. We established a steady-state scaling law relying the internal temperature variation to the Rayleigh number and we showed that this scaling law remains valid during the transitory regime provided both internal heating and secular evolution of the temperature are taken into account. The result is a parameterized model describing the average internal temperature of the fluid as a function of time in terms of experimental conditions and fluid properties. • We generated a uniform and stable volume heat source in a large volume tank, based on absorption of microwaves guided through an innovative design of microwave circuits. • Automatic laser scanning of the tank coupled with image acquisition and processing enables us the measurement of the 3D temperature field in the convective fluid from which we extracted the volume average temperature and surface heat flux evolution in time. • We validated a transient scaling law for the time evolution of the volume average temperature in an internally-heated convective system.