Monte Carlo functional estimation of the radiative source term in a semi-transparent medium: A faster coupled conductive-radiative model resolution

The estimation of thermo-physical properties of materials at high temperatures requires the development of robust and fast -enough direct models that takes into account the strong coupling between conduction and radiation. The interest in using the Monte Carlo method to obtain a conduction-radiation model in a semi -transparent material solved in a reduced computational time is addressed in this study. An academic configuration that consists of an absorbing/emitting and non -scattering gray medium with steady-state conduction is investigated since this study is meant to be a proof of concept. It is demonstrated that the radiative source term of the heat equation may be estimated as a function of the temperature field to the fourth power, using a Finite Differences algorithm and a single Monte Carlo simulation of radiation. The results of the numerical study show that, on the one hand, they are in good agreement with those found in the literature and, on the other, that the coupled model can be resolved in a significantly shorter amount of computational time than with traditional methods thanks to the functional estimation of the radiative source term. In fact, in each of the fifteen analyzed cases, the coefficients of the function were determined in approximately 6 s using the Monte Carlo method using a laptop with standard computational resources. The computation of the function and its application revealed that, depending on the studied configuration, a resolution with the finite differences-functional Monte Carlo algorithm can be around twenty to one thousand times faster than a classic Finite Differences-Monte Carlo algorithm. Due to these characteristics, as well as the fact that the functional estimation is insensitive to geometry complexity and can be extended to configurations with heterogeneous radiative properties, it becomes possible to utilize this method in inversion procedures, since the direct model must be evaluated numerous times.