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Present study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.

The numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.

For the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.

The difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

The purpose of this study is to predict the thermal protective performance (TPP) of flame-retardant fabric more economically using machine learning and analyze the factors affecting the TPP using model visualization.

A total of 13 machine learning models were trained by collecting 414 datasets of typical flame-retardant fabric from current literature. The optimal performance model was used for feature importance ranking and correlation variable analysis through model visualization.

Five models with better performance were screened, all of which showed R2 greater than 0.96 and root mean squared error less than 3.0. Heat map results revealed that the TPP of fabrics differed significantly under different types of thermal exposure. The effect of fabric weight was more apparent in the flame or low thermal radiation environment. The increase in fabric weight, fabric thickness, air gap width and relative humidity of the air gap improved the TPP of the fabric.

The findings suggested that the visual analysis method of machine learning can intuitively understand the change trend and range of second-degree burn time under the influence of multiple variables. The established models can be used to predict the TPP of fabrics, providing a reference for researchers to carry out relevant research.

The findings of this study contribute directional insights for optimizing the structure of thermal protective clothing, and introduce innovative perspectives and methodologies for advancing heat transfer modeling in thermal protective clothing.