Modelling of heat transfer within heterogeneous media by Brownian walkers. (March 2022) - Gonneau, Vincent; Rochais, Denis; Enguehard, Franck
Highlights: The displacement of Brownian walkers carrying enthalpy according to the Itô-Taylor algorithm is used to simulate quantitatively transient conduction heat transfer within heterogeneous media. All classical linear boundary conditions (Dirichlet, Neumann and Newton) are treated with a complete stochastic approach. Stochastic transmission criteria were demonstrated in order to determine the behaviour of a walker meeting an interface between two constituents or a boundary submitted to a newton condition. The so-called "rear face flash" experimental technique over a homogeneous medium could be quantitatively reproduced with this model. Abstract: This work concerns the modelling of transient thermal conduction within a heterogeneous medium by the movement of Brownian walkers. The material structure is voxelised, and each walker transports an elementary enthalpy during its displacement within the structure. This enthalpy transport represents the conductive flow and makes it possible to simulate the conduction in a transient state with a quantitative stochastic approach. A study of the impact of the value of the time step is carried out to fix the choice conditions of this parameter, in particular in the presence of strong contrasts in thermophysical properties, and as such to define a validity framework of the diffusion model. Then several academic problems related to the behaviour of walkers are resolved in order to be able to account for different thermal solicitations and conditions at the boundaries (Dirichlet, Neumann, Newton) with Brownian walkers. These results have in particular made it possible to reproduce the so-called "rear face flash" experimental technique using a model by Brownian walkers over a homogeneous medium. Then, a stochastic transmission criterion based on the thermal effusivities is demonstrated to treat the meeting of a walker with an interface between two constituents within a heterogeneous medium. This work, focused on the mastery of the dynamics of Brownian walkers within heterogeneous media for the correct simulation of transient conduction, is a first step towards the modelling of the transient conduction-radiation coupling by means of Brownian walkers coupled to ray tracing techniques at the local scale of a voxelised structure.