532.546A model of colmatage-suffosion filtration of disperse systems in a porous medium is analyzed numerically based on a new kinetic equation for saturation of the pore space with settled particles.Modeling of the phenomena of precipitation of particles from a disperse medium in its filtration in a porous medium and clogging of the pores with these particles (colmatage of the pores) and unclogging of the pores under the action of different forces (suffosion) is of great importance for various technological processes. Some mathematical models of colmatage-suffosion filtration of disperse systems in porous media are given in [ 1,2]. These models' drawbacks were discussed in [3,4]. In the latter works, based on a balance equation for the concentration of particles suspended in the filtered liquid, new kinetic equations of active porosity [5,6], and a generalized Darcy law a model of colmatage-suffosion filtration that is devoid of the mentioned drawbacks of the models of [ 1, 2] is proposed and studied. At the same time it is noteworthy that in [2] a balance equation is written in a more general form than in [3,4], where the change in the saturation of the pore space with the settled particles and the "free" liquid not connected with the settled mass, the change in the volume concentration of the suspended solid substance in the moving mixture, etc. are taken into account separately. In [7] instead of a kinetic equation for the change in the active porosity [5,6] it is proposed that a kinetic equation for the saturation of the pore space with settled particles in the loose body where allowance is made not only for colmatage and suffosion effects but also for sedimentation precipitation of the particles be used. In [8] a model of colmatage-suffosion filtration of multicomponent systems is proposed and issues of correct formulation of the problem and the existence of invariant and self-similar solutions are discussed. In [9], based on the model of [3,4], the joint influence of the effects of convective diffusion, colmatage, and suffosion on the concentration of particles in the flow, the active-porosity profiles, the filtration rate, and other filtration characteristics was investigated, and the range of qualitative agreement between the obtained theoretical results and the experimental data given in [2] was determined. Just as in [3,4], a material-balance equation for particles suspended in a liquid is used as the balance equation in [8,9]. In this work a model based on the balance equation of [2], the kinetic equation of [7], and a generalized Darcy law is investigated. In light of the foregoing the proposed model takes into account in a more general form the filling of the pore volume with the filtered liquid, the settled particles, and the "free" liquid not connected with the settled mass and takes into consideration at the same time the effects of colmatage, suffosion, sedimentation precipitation of the particles, etc. After the formulation of the model a specific problem is considered whose numerical solution ...

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The Laplace transform is used to obtain a unique equation for describing essentially nonsteady heat or mass transfer in a heterogeneous medium. The equation is used to analyze the heating of a half-space through a plane boundary.A detailed survey of the methods used to describe nonsteady heat transfer in dense granular media can be found in [i]. The possibilities of the methods are discussed in connection with experimental data on the heating of different types of layers from a flat wall. The methods take two approaches, each of which is largely phenomenological. The first approach involves taking the solutions of the system of equations of heterogeneous transfer with a time-independent interphase heat-transfer coefficient and extending them to the region of heat-transfer time scales in which this system is invalid [i]. The second approach is based on the use of an ordinary parabolic heat-conduction equation [2] with allowance for the additional thermal resistance near the wall. This leads to the formulation of a boundary condition of the third kind for the wall.Although useful empirical formulas for the heat flux from the wall can be obtained by appropriate selection of the coefficients in the equations for interphase heat flow or the boundary condition, neither method adequately describes the physics of the transport process. In fact, as was shown in [3], the above system can be used only when the transience of the flow is slight. The best evidence of the conditional nature of studies that have employed the second approach is that physically substantiated attempts to refine the thermal resistance (see [4][5][6], for example) have only worsened the agreement between the theoretical and experimental results. Generalization of methods of the steady-state theory to essentially nonsteady transport processes requires direct analysis of the exchange of the continuous phase with individual elements of the discrete phase, as was proposed in [3]. Calculations of this type were performed in [7,8] (as well as [9]) for the rows of particles closest to the wall.To simplify the problem, we propose to ignore the nonuniformity of the temperature distribution over the particle surface and to assume it to be equal to the mean temperature of the continuousphase at the point corresponding to the center of the particle. The validity of these assumptions was discussed in [3]; the assumption of uniformity of temperature at scales on the order of the dimensions of a particle is a necessary condition for the applicability of continuum methods in the description of heat transfer in heterogeneous media. Some ramifications of further generalizations are discussed below.The equation of convective heat transfer in the continuous phase is written in the standard form edlcl --~+uv TI:-~,,ATl--nq.(1)To calculate the heat flux q from the continuous phase to a single particle in the approximation being examined, we have the usual problem of the heat conduction inside a particle with a boundary condition of the first kind. If the particles are sph...