Abstract
Fractal geometry (fractional Brownian motion—FBM) is introduced to characterize the pore distribution of porous material. Based on this fractal characterization, a mathematical model of heat conduction is presented to study heat conduction behaviors in porous material with a focus on effective thermal conductivity. The role of pore structure on temperature distribution and heat flux is examined and investigated for fractal porous material. In addition, the effects of fractal dimension, porosity, and the ratio of solid-matrix-to-fluid-phase thermal conductivity (ks/kf) on effective thermal conductivity are evaluated. The results indicate that pore structure has an important effect on heat conduction inside porous material. Increasing porosity lowers thermal conductivity. Even when porosity remains constant, effective thermal conductivity is affected by the fractal dimensions of the porous material. For porous material, the heat conduction capability weakens with increased fractal dimension. Additionally, fluid-phase thermal conduction across pores is effective in porous material only when ks/kf < 50. Otherwise, effective thermal conductivity for porous material with a given pore structure depends primarily on the thermal conductivity of the solid matrix.
Highlights
IntroductionThe heat conduction of porous media has drawn particular attention owing to their extensive applications [1,2], such as the thermal insulation material [3], geothermal soil medium [4,5], ceramics, clothing chemical engineering, geophysical exploration and human biomedical engineering
The heat conduction of porous media has drawn particular attention owing to their extensive applications [1,2], such as the thermal insulation material [3], geothermal soil medium [4,5], ceramics, clothing chemical engineering, geophysical exploration and human biomedical engineering.The porous media is a material containing interconnected pores with non-uniform size and shape.In complex structures, the thermal conductivity of a porous material depends on porosity and thermal property and on pore structures
In accordance with the assumptions detailed above, the energy equation of the steady thermal conduction inside the 2D fractal porous material is simplified as: This paper focuses on the role of pore structure on the heat transfer performance of the porous material
Summary
The heat conduction of porous media has drawn particular attention owing to their extensive applications [1,2], such as the thermal insulation material [3], geothermal soil medium [4,5], ceramics, clothing chemical engineering, geophysical exploration and human biomedical engineering. To study soil thermal conduction, it is crucial to understand how pore structure affects the heat conduction behaviors of porous material During recent decades, both theoretical and data-driven research has been used to study thermal conductivity for several types of porous material, typically calculated by network combinations of series and parallel models [6,7,8,9]. A more reasonable reconstruction method, has emerged as a powerful tool to characterize complex structures, one that possesses the features of statistical self-similarity and multi-scale With these features, the fractal dimension, D, determines the heterogeneity of the resulting pore structure of the porous medium. In the current study, a mathematical model of heat transfer through a porous material is presented to study heat conduction behaviors inside the porous material, with special attention paid to thermal conductivity In this model, pore structure is reconstructed using fractal geometry based on fractional. The effects of fractal dimension, porosity, and solid matrix/fluid phase thermal conductivity ratios (ks /kf ) on effective thermal conductivity are evaluated
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