非饱和多孔介质有效导热系数模型

Model of Effective Thermal Conductivity of Unsaturated Porous Materials Based on Fractal Theory

多孔介质有效导热系数是研究地源热泵、土壤及岩土热储、材料热质传递的重要参数,运用分形理论,建立了一种预测非饱和多孔介质有效导热系数的分形物理模型和相应的有效导热系数计算公式,基于MATLAB数值分析显示模型计算结果与实验测量值具有较好的一致性,并通过该模型探讨了相关微观参数对多孔介质有效导热系数的影响,结果显示弯曲度分形维数、孔隙率与多孔介质导热系数呈负相关,固液相占比、饱和度、固相基质边长与多孔介质导热系数呈正相关,当孔隙率大于78.4%时,导热系数较小的孔隙相对多孔介质有效导热系数影响较大。

The effective thermal conductivity of porous media is an important parameter for the study of ground source heat pump,soil and geotechnical heat storage,and material heat and mass transfer.Using fractal theory,a fractal physical model for predicting the effective thermal conductivity of unsaturated porous media and the corresponding effective thermal conductivity were established.The thermal conductivity calculation formula,based on MATLAB numerical analysis showed that the calculated results of the model were in good agreement with the experimental measured values,and the influence of the relevant microscopic parameters on the effective thermal conductivity of porous media was discussed through the model.The results show that the fractal dimension of tortuosity.The porosity is negatively correlated with the thermal conductivity of the porous medium,and the solid-liquid phase ratio,saturation,and the side length of the solid matrix are positively correlated with the thermal conductivity of the porous medium.When the porosity is greater than 78.4%,the pores with smaller thermal conductivity are relatively porous The effective thermal conductivity has a greater impact.