Coupling radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm: A general theoretical framework for linear situations.

It was recently shown that radiation, conduction and convection can be combined within a single Monte Carlo algorithm and that such an algorithm immediately benefits from state-of-the-art computer-graphics advances when dealing with complex geometries. The theoretical foundations that make this coupling possible are fully exposed for the first time, supporting the intuitive pictures of continuous thermal paths that run through the different physics at work. First, the theoretical frameworks of propagators and Green's functions are used to demonstrate that a coupled model involving different physical phenomena can be probabilized. Second, they are extended and made operational using the Feynman-Kac theory and stochastic processes. Finally, the theoretical framework is supported by a new proposal for an approximation of coupled Brownian trajectories compatible with the algorithmic design required by ray-tracing acceleration techniques in highly refined geometry.

Thermal conductivity measurement of insulating materials up to 1000 °C with a needle probe.

The hot wire method is one of the few methods that can be applied to measure the thermal conductivity of materials at 1000 °C and above. However, in the case of granular or electrically conductive materials, the heating wire and thermocouple must be insulated from the material by placing them in a sheath (or a needle). In this case, it is shown that the method of using the slope of the curve T = f[ln(t)] could lead to estimation errors of up to 30% for some materials. A complete quadrupolar model of the system needle/material is developed, and a sensitivity analysis of the probe temperature to the different parameters allowed for the selection of a reduced model, enabling a precise estimation of the thermal conductivity. Measurements carried out between 600 and 1000 °C on a material of known thermal conductivity led to deviations of less than 3%. The method is finally applied up to 1000 °C to two granular materials and to compacted molding sand with quite a good fitting between the experimental and modeled curves.