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.