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

The optimization of thermal transfers in engineering systems such as heat exchangers requires the analysis of the influence of heat sources upon the temperature at various positions of interest in the studied system. In order to achieve the resolution of the combined modes of heat transfer through these systems, their couplings and the complex 3D geometries involved need to be integrated with full accuracy. Recent developments in probabilistic formulations in the context of transient combined heat transfer (linearized conduction-radiation-convection) have opened a new route to solving such problems with Monte Carlo (MC) algorithms, using state-of-the-art computer graphics digital libraries to handle complex geometries. To estimate the temperature at a probe point of interest, random paths are generated from its position and propagated through the geometry until a known temperature is reached. From a single MC calculation to sample the path statistics, the Symbolic Monte Carlo (SMC) method is used to express the probe temperature as a linear function of the sources. This function can then be used to estimate the probe temperature for any source values, alleviating the need to repeat Monte-Carlo simulations for each source condition, resulting in greatly reduced computation time. This approach is applied to the case of an open-cavity porous medium and computation time insensitivity to the complexity and fineness of the geometry is demonstrated.