Numerical Modeling of Thermophysical Processes in the Media with Fractal Structure

Abstract

In this work, investigated are the processes of heat transfer in complex anisotropic media with a fractal structure which are characterized by non-locality in time (memory effect) and non-locality by coordinate (the effect of spatial correlations). The explicit and implicit difference schemes for a nonlocal heat transfer equation using a fractional differentiation apparatus in coordinate in the sense of Riesz have been developed. The difference approximations of the fractional derivative in the time interval is obtained on the basis of the Riemann-Liouville formula. The algorithmic aspects are presented for realization of the obtained difference equations using the predictor-correction method. The software has been developed for numerical simulation of heat transfer in media with fractal structure. The influence of different values of fractional parameters on the processes of heat transfer, depending on the change of coordinates and time, is investigated for given initial conditions and thermophysical characteristics of anisotropic fractal medium. These indicators of fractional differentiation allows for obtaining new parametric functions for processing and interpretation of experimental data of nonlocal transfer processes.