Certain exact solutions in problems of soil desalination

Application of an equivalent equation to description of heat- and mass-exchange processes determined by differential equations in the domain with a moving boundary

“…Here we consider models of the (1)-(2); type for domains with a moving boundary. In this connection, equations in [3,4] can be interpreted as the simplest (monomial) approximation N = C of expansion (4). The process of mass transfer occurs only in flow channels * .…”

“…Finally, trinomial expansion of series (4) yields EE (5). Thus, the EE may be assumed to be a natural generalization of the model [3][4][5] with relation (2). We introduce new variables and parameters: * In [7], it is proposed that the nonstationary term in the flow part be also disregarded in this approximation.…”

“…Within the framework of the models of [3][4][5], the use of variational and projection methods [32,33] for the domain with a moving boundary will require a certain investigation, which points to a certain advantage of application of the EE. For example, with the L. V. Kantorovich method [32], we can find, using functional (17), the approximate solution of Eq.…”

“…The process of mass transfer occurs only in flow channels * . Boundary conditions on the moving boundary are formulated there in the form of hypotheses and assumptions [1, 3,4]. Quite diverse modes of coupling of the variables N and C in an actual porous body [26] enable us to consider other conditions at x = Ut ⁄ ε.…”

“…We know of mathematical models from the literature for analysis of a number of mass-exchange processes (desalination of soils, flushing of sediments, and others) on the basis of a two-component diffusion model where the equation in the flow part of a porous material describes the process in the domain with a boundary moving according to the law 0 < x < Ut [1][2][3][4][5]. Solution of the problems on the basis of such models involves artificial techniques [3][4][5] of extension of the solution beyond the domain of its determination and of analysis of a certain (derived) integral equation, which makes it difficult to solve the problems in other cases. In so doing, when one is able to find the solution, it is expressed by three quadratures related to conversion of integral transforms with composite (nonstandard) variables.…”