不完全分形多孔介质热导率模型

Thermal Conductivity Model of Incomplete Fractal Porous Media

将多孔介质的物理构成分为具有分形结构的团聚体集合和不具有分形特性的固相和孔隙相,建立了简化单元体模型解释其微观结构。结合多孔介质在干燥过程中热量守恒定律和傅里叶导热定律导出了材料总有效热导率模型。此模型无经验常数,每一个参数都有物理意义。研究结果表明,有效热导率与迂曲分形维数、面积分形维数、孔隙率和热风温度呈反比,与热风速率和时间呈正比。

The porous media was divided into the fractal aggregation and the non fractal solid phase and pore phase, and a simplified cell model was made to show the microstructure. Porosity, areal fractal dimension, tortuosity fractal dimension, tortuosity, solid phase area and pore phase area of incomplete fractal porous were exhibited. The effective thermal conductivity was built combined with thermal energy and Fourier＇s law of heat conduction during drying, thermal energy including the heat which required for solid phase during the drying and the heat coming from the circulating hot air. The model was not based on empirical formulas and assumed thermal resistance, and each symbol had definite physical meaning. The result showed that effective thermal conductivity had a negative correlation with the tortuosity fractal dimension, porosity, areal fractal dimension and hot air temperature, while it has a positive correlation with the hot air rate and time.