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A Fractal Model For Predicting The Effective Thermal Conductivity Of Roughened Porous Media With Microscale Effect

Author

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  • BOQI XIAO

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • MIN ZHANG

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • HANXIN CHEN

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • JIYIN CAO

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • GONGBO LONG

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • ZHENG ZHAO

    (��State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, P. R. China)

Abstract

The effective thermal conductivity (ETC) of roughened porous media (RPM) is of interest in a number of applications of heat transfer. In this work, a fractal analytical model for the ETC of RPM with microscale effect is proposed. The proposed fractal model is expressed in terms of relative roughness, the molecular mean free path, porosity, fractal dimensions (pore area fractal dimension and tortuosity fractal dimension), maximum pore diameter, capillary straight length, and the thermal conductivity of the solid matrix and gas. It is observed that the dimensionless ETC of RPM decreases with increasing relative roughness, pore area fractal dimension and tortuosity fractal dimension. Besides, it is found that the dimensionless ETC of RPM increases with thermal conductivity ratio of gas phase over solid phase. In addition, it is found that the dimensionless ETC of RPM is slightly dependent on the relative roughness and tortuosity fractal dimension when kg/ks < 1. The determined dimensionless ETC of RPM is in good agreement with experimental data and existing models reported in the literature. With the proposed fractal model, the physical mechanisms of heat transport through RPM with microscale effect are better elucidated. Every parameter in the fractal analytical model has clear physical meaning, with no empirical constant.

Suggested Citation

  • Boqi Xiao & Min Zhang & Hanxin Chen & Jiyin Cao & Gongbo Long & Zheng Zhao, 2021. "A Fractal Model For Predicting The Effective Thermal Conductivity Of Roughened Porous Media With Microscale Effect," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-10, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501140
    DOI: 10.1142/S0218348X21501140
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    Cited by:

    1. Yang, Shanshan & Wang, Mengying & Zou, Mingqing & Sheng, Qiong & Cui, Ruike & Chen, Shuaiyin, 2023. "Permeability coupling model of multiple migration mechanisms in rough micro-fractures of shales," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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