Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations

Parameter Identification of the Fractional-Order Mathematical Model for Convective Mass Transfer in a Porous Medium

Fractional calculus is an essential tool in studying new phenomena in hydromechanics and heat and mass transfer, particularly anomalous hydromechanical advection-dispersion considering the fractal nature of the porous medium. They are valuable in solving the urgent problem of convective mass transfer in a porous medium (e.g., membranes, filters, nozzles, convective coolers, vibrational prillers, and so on). Its solution allows for improving chemical engineering and technology workflows, refining process models for obtaining porous granular materials, realizing the convective cooling of granular and grain materials, and ensuring the corresponding apparatuses' environmental safety. The article aims to develop a reliable convective mass transfer model for a porous medium and proposes a practical approach for its parameter identification. As a result, a general scientific and methodological approach to parameter identification of the fractional convective mass transfer model in a porous medium was proposed based on available experimental data. It mainly used Riemann-Liouville fractional time and coordinate derivatives. The comprehensive application of the Laplace obtained the corresponding general solution transform with respect to time and a coordinate, the Mittag-Leffler function, and specialized functions. Different partial solutions in various application case studies proved this solution. Moreover, the algorithm for practically implementing the developed approach was proposed to evaluate parameters for the considered model by evaluation data. It was reduced to the two-parameter model and justified by the available experimental data.