Intermingled fractal units model and electrical equivalence fractal approach for prediction of thermal conductivity of porous materials

The effective thermal conductivity of porous materials is a function of the intrinsic characteristic of the solid and the fluid phases that occupy the pores, of the volume fraction of the pores, and of their dimensional distribution. This last aspect is less known and studied than the others because the porous microstructure is difficult to define in conventional geometric terms. In this work, an Intermingled Fractal Units model (denominated IFU) is presented, developed by varying some constructive aspects of the Sierpinski carpet. Simple fractals can be used effectively to describe pore size distributions which present a regular growth toward the larger diameters and therefore are not suited to describe very common structures which present one or more peaks in their distribution. But the use of more fractal units means that the IFU is able to effectively simulate the pore size distribution, the volume fractions of the voids as well as the geometry of the microstructure of non-fractal porous materials. By turning IFU model into electrical fractal pattern, it is possible to calculate effective thermal conductivity of the materials. In this approach the value of effective thermal conductivity coefficient derived from the nth stage was used as a default value for the solid phase in the nth + 1 step. This full fractal procedure has been verified with deterministic or random fractal models as well as with some porosity–conductivity experimental data, namely, those obtained from advanced ceramics (Yitria stabilized zirconia) already available in the scientific literature and the results are comparable and very close.