木材横纹有效导热系数的分形模型

Fractal model for predicting effective thermal conductivity perpendicular to fibres of wood

提出了一个二维的分形模型来计算木材横纹有效导热系数.通过分析木材试样的扫描电镜照片,研究了木材横纹剖面的多孔结构特征,采用盒维数法计算了其分形维数.通过分析单一木材细胞的导热过程,采用热阻模拟方法分别推导了弦向和径向有效导热系数的表达式.实验得到各种木材的纤维多孔结构的分形维数约为1.4,由木材纤维孔隙率与分形维数的关系得到了有效导热系数随分形维数变化的表达式.利用分形模型对木材径向有效导热系数进行了计算,并与实验测量结果和文献中的数据进行了比较.结果表明,此分形模型可以对各种木材的横纹有效导热系数进行有效的预测,而且可以推广到不同含水率的情形.

A two-dimensional fractal model was proposed to predict the effective thermal conductivity perpendicular to fibres of wood. The porous structure of wood samples on their cross sections was analyzed using scanning electron microscope images, and their box-counting dimensions were calculated. The heat conduction process of a single cell was studied and the tangential and radial thermal conductivities of wood were obtained by the thermal resistance method. The fractal dimension of porous structure of wood fibres approximately equaled to 1.4. The relationship between thermal conductivity and pore ratio was obtained, from which the formula that described thermal conductivity changing with fractal dimension was derived. According to the proposed fractal model, the radial effective thermal conductivity of wood was calculated and compared with the experimental measurement results and the data in the reference. Comparison shows that the fractal model can effectively predict the effective thermal conductivity perpendicular to fibres of wood, and can be extended to the situation with different hydrous contents.