双材料杆一维稳态热传导泛形模型

采用广义有限Cantor集建立了双材料杆一维稳态热传导问题的泛形模型，得到了泛形双材料杆的温度分布及其等效导热系数的解析表达式，对silty clay loam和L soil土壤的等效导热系数的计算结果与实验结果吻合较好. 结果表明，在需要考虑实际物理对象整数维测度时，使用泛形而非分形可以克服由于分形测度奇异性导致的一系列物理及数学上的困难.

A Ubiquitiformal Model for One-Dimensional Steady State Heat Transfer of a Bi-Material Rod

A generalized finite Cantor set was used to set up a ubiquitiformal model for the one-dimensional steady state heat transfer problem of a bi-material rod. By solving such a ubiquitiform problem, the explicit expressions for the temperature distribution and the equivalent thermal conductivity of the rod were obtained. Numerical results for two kinds of dry soil are in good agreement with previous experimental data. Moreover, the above results imply that ubiquitiform rather than fractal should be used in the need of considering the integral dimensional measure of the actual physical object, which can overcome well both physical and mathematical difficulties resulted from the singularity in fractal measure.