Analytical fractal models of transport parameters for open-cell metal foam

Open-cell metal foam is widely used in enhanced heat transfer, separation and purification due to their advantages of high porosity and high specific surface area. In the process of metal foam application, it is necessary to accurately predict the permeability and thermal conductivity of metal foam. However, the random pore distribution and complex structure of metal foams make it difficult to calculate the permeability and thermal conductivity, and the fractal theory can well characterize the random pore distribution of metal foams. Therefore, in this paper, the characteristic size and pore size of the metal foam are characterized through fractal theory, and then the permeability and thermal conductivity analytical model of the metal foam is established by using the characteristic parameters. Then, the effective permeability of the rough surface of the metal foam is considered and the analytical model is derived. Finally, the thermal conductivity analytical model considering the metal foam coating and hollow is established. All models are analytical models that do not contain empirical parameters and fitting parameters, and have good prediction accuracy compared with experimental test results and previous analytical models.