Determination of the Applied Thermal Tortuosity of Porous Media with Macroscopic Geometric Parameters Using a Neural Network Model

Abstract The tortuosity of a porous medium has a significant effect on heat transfer through it, but this effect is difficult to quantify. In this study, we have developed the concept of applied thermal tortuosity and the thermal tortuosity function which characterizes the effect of porous medium geometry and the thermal conductivity ratio on the averaged path length of heat conduction in a porous medium. We have also proposed new macroscopic geometric parameters of porous media that can better describe the complexity of the porous media geometry. The relationship between the macroscopic geometric parameters and the developed thermal tortuosity function was established by using a neural network model. We used the developed thermal tortuosity function to calculate effective thermal conductivity, which can be applied in the thermal energy equation. Computations were performed for arbitrary two-dimensional porous media. Despite the model’s uncertainties, the developed neural network model is significantly more accurate than empirical correlations for determining the effective thermal conductivity. Optimization of the neural network architecture can further improve the accuracy of the model, but the problem of uncertainty cannot be completely solved. The study shows the importance of embedding the established knowledge of transport in porous media into the neural network model to improve its accuracy.