New classes of exact solutions to nonlinear sets of equations in the theory of filtration and convective mass transfer

Abstract

New classes of exact solutions to nonlinear sets of equations encountered in the theory of filtration and convective mass transfer of reacting media are described. Focus is placed on general first-order sets in which the chemical reaction rates depend on arbitrary functions. General solutions to some first-order systems with power-law nonlinearities are found. A set of new exact solutions with a functional separation of variables involving arbitrary functions is constructed. The results obtained are used for solving the problems of the theory of filtration of one-component and multicomponent suspensions with an arbitrary kinetics of particle accumulation.