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 (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.

Thermal Conduction Simulation Based on Reconstructed Digital Rocks with Respect to Fractures

“…In this study, the thermal conductivity ratios of the solid to water and air were 12.34 and 284.62, respectively. A previous study [55] reported that fluid thermal conduction could cross pores effectively in porous media when the solid to fluid thermal conductivity ratio was less than 50. Therefore, when the fluid is conductive (water saturated), the fracture's negative effect on ETC is less than that under nonconductive conditions (air saturated).…”

“…With incremented fracture length, the thermal conduction is obstructed by the fractures gradually. As the difference between the solid and fluid thermal conductivities is significant, compared to the matrix, the pore space is almost not conductive [55]. Therefore, the fractures can disturb the temperature field in an obvious way, especially when the fracture with a large length and aperture is vertical to the heat flux direction.…”

Numerical Investigation on Heat-Transfer and Hydromechanical Performance inside Contaminant-Insensitive Sublimators under a Vacuum Environment for Spacecraft Applications

“…The issues of the phase change and the heat and mass transfer in porous substrates have been studied in the previous literature, and these studies are useful to sublimator research and are classified into two categories, described as follows. The first category is the influence of structure parameters, flow characteristics, fluid properties, physical parameters and heat-transfer characteristics on heat-and-mass transfer performance in porous substrate [30][31][32][33][34][35][36]. Hanlon et al researched the influences of the thin film evaporation, the particle size, the porosity, and the wick structure thickness on the evaporation heat transfer in sintered wick structure based on a two-dimensional heat-transfer model [37].…”

Multiple-relaxation-time lattice Boltzmann simulation for adsorption processes of carbon dioxide in a fixed-bed

“…Comparing with the time-consuming and economical undesirable experimental method, the numerical simulation method, as a popular research tool from the microscopic to macroscopic scales (Huang et al , 2015; Deng et al , 2017a, 2017b; Ahmed et al , 2017), has attracted much interest for describing the dynamic adsorption behaviors in the fixed bed because of its simplification and high efficiency (Xu et al , 2013). Using the numerical solution of the coupling momentum-, mass-, and energy-conservation equations, the mathematical simulation studies have been applied to predict the complete dynamic processes including the flow, mashe/sheat transfer and adsorption behaviors in the fixed bed (Shafeeyan et al , 2014).…”

“…In the past decades, lattice Boltzmann (LB) model has been used to solve the complex fluid flow and heat/mass transfer problems successfully, because of several significant advantages compared with the conventional numerical methods, such as the simplicity of the algorithm, the linear convective operator, and the high efficiency for parallel performance (Kefayati et al , 2012; Deng et al , 2017a, 2017b). Recently, many attempts have been made to study the fluid transport and adsorption behaviors in the microscopic pore scale.…”