Toward the Use of Symbolic Monte Carlo for Conduction-Radiation Coupling in Complex Geometries

Abstract

We address the interest of using Symbolic Monte Carlo to obtain a reduced model for conduction-radiation coupling in complex geometries. Symbolic Monte Carlo was successfully used for radiative transfer in a decoupled manner, but no attempt has yet been reported to extend its use to radiation coupled with other modes. Here we show that from a unique Monte Carlo simulation of radiation coupled with conduction in a semi-transparent solid surrounded by a convective flow, it is possible to build a formulation of the local temperature as function of the convective heat transfer coefficient, for instance, including the evaluation of uncertainty. This reduced model (a transfer function) enables to decrease the computation time when the function needs to be evaluated plenty of times for different values of the parameters as in optimization or control algorithms.

A Monte Carlo-Based Strategy to Assess Complex Kinetics: Application of the Null-Reaction Method to DAEM

“…In order to achieve this, one needs to express the kinetic rate constant, k E , as an expected value. The question is open, but recent studies − showed that the temperature could be expressed as an expected value in k E .…”

“…For future investigations, the coupling of chemical kinetics with a thermal model (such as a heat equation) will be considered. This is a concept that has already been demonstrated in radiation physics by coupling the radiative transfer to the absorption coefficient model, while other research coupling heat transfer phenomena is ongoing. − …”

Solving transient coupled conductive and radiative transfers in porous media with a Monte Carlo Method: Characterization of thermal conductivity of foams using a numerical Flash Method

“…The complete methodology and the particular configuration of the flash method are detailed. Compared to previous studies [25][26][27], the present problem requires a transient solution. Thus, a validation case is provided for a 3D geometry which could be useful as a benchmark case for further algorithmic improvements.…”

“…This approach has been validated for conductive and radiative transfers by comparison with a deterministic method. Ibarrart et al [26] extended this to consider coupled conductive, advective and radiative heat transfers while Penazzi et al [27] studied the case of a semi-transparent medium. Assuming the linearity of heat transfers is a not limiting factor because only a small increase of the equilibrium temperature of the medium is required in most of the characterization methods, including the flash method.…”

Transfer function estimation with SMC method for combined heat transfer: insensitivity to detail refinement of complex geometries

“…To the best of our knowledge, the SMC method was previously developed only for radiative heat transfer. Recent developments have now extended the use of this method to combined heat transfer [Penazzi, 2019]. Previously, [Villefranque, 2019] showed the insensitivity of computation time to mesh refinements for the resolution of radiative transfer with the MC method in the field of atmospheric radiation.…”