A FRACTAL MODEL FOR PREDICTING THE EFFECTIVE THERMAL CONDUCTIVITY OF ROUGHENED POROUS MEDIA WITH MICROSCALE EFFECT

Boqi Xiao, Min Zhang, Hanxin Chen, Jiyin Cao, Gongbo Long and Zheng Zhao
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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

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-10

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.

Keywords: Fractal; Effective Thermal Conductivity; Roughened Porous Media; Microscale Effect (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501140

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DOI: 10.1142/S0218348X21501140

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