Research on the Fractal Convective Heat Transfer Coefficient of Porous Media Based on the Pipe Ball Model

Porous media, compared to traditional materials, have advantages such as light weight, high specific surface area, and high porosity, making them highly valuable in the field of convective heat transfer. Investigating the convective heat transfer mechanisms of porous media is of significant importance. In this paper, based on the pipe ball model, the internal flow within porous media is treated as a combination of turbulent flow through pipes and external flow around spheres, thus a convective heat transfer model for porous media is established. Utilizing fluid mechanics theory and fractal theory, a fractal criterion equation for the convective heat transfer coefficient in this model is derived. A comparison with experimental data shows that when the Reynolds number is less than 10, the fractal formula has significant deviations from the experimental data, and these deviations gradually decrease as the Reynolds number increases. The calculated results match well with experimental data within the Reynolds number range of 10-10
⁶
. Comparing the results with over 100 sets of literature experimental data, it was found that within the Reynolds number range of 10 to 10
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and porosity range of 0.383 to 0.583, 62 sets of data had relative deviations within 60%, accounting for 45.74 % of the total.