Matrix Approach to Numerical Modeling of Heat-and-Moisture Transfer Processes in a Medium with a Fractal Structure

Using a fractional-differential apparatus, generalized is the matrix approach of discretization of fractional differential operators for constructing numerical algorithms in order to implement a one-dimensional mathematical model of interrelated heat-and-moisture transfer processes in materials with a fractal structure. Analytical expressions and discretization of derivatives in the sense of Riemann-Liouville, Caputo, and Riesz are presented, which are integrated into the mathematical model of interrelated heat-and- mass transfer in fractal media. Algorithmic aspects of the numerical implementation of the generalized matrix approach are presented for the obtained one-dimensional discrete mathematical model of the interrelated processes of heat-and- moisture transfer in a medium with a fractal structure. Based on the results of numerical study, the patterns of the influence of the fractal structure of the material on the processes of temperature and moisture content changes are outlined. Graphical dependences of changes in the temperature and moisture content of a polymer material over time, taking into account the fractal structure and without taking it into account, are presented.