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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...