Heat Conduction in Porous Media Characterized by Fractal Geometry

Zilong Deng, Xiangdong Liu, Yongping Huang, Chengbin Zhang and Yongping Chen
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Zilong Deng: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, Jiangsu, China
Xiangdong Liu: School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China
Yongping Huang: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, Jiangsu, China
Chengbin Zhang: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, Jiangsu, China
Yongping Chen: Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Environmental Science and Engineering, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

Energies, 2017, vol. 10, issue 8, 1-14

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 ( k s / k f ) 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 k s / k f < 50. Otherwise, effective thermal conductivity for porous material with a given pore structure depends primarily on the thermal conductivity of the solid matrix.

Keywords: heat conduction; thermal conductivity; porous material; fractal (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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