Heat Conduction in Porous Media Characterized by Fractal Geometry

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.

Keywords

• heat conduction
• thermal conductivity
• porous material
• fractal