Solution of the boundary value problem of heat and mass transfer using the Fourier method of finite integral transform for radiant soil heating conditions

The purpose of the research is to find, predict and regulate the temperature and humidity regime of the soil for the conditions of radiant heating of cultivation facilities using dark-type ceiling infrared radiators. In the work, without intermediate mathematical transformations, a generally accepted system of differential equations (both in dimensional and dimensionless forms) is presented, taking into account the main and cross processes of heat and mass transfer in dispersed media. For this system of equations, a particular analytical solution is considered, which takes into account not only the main phenomena of heat and mass transfer that occur independently of each other, but also the effect of water vapor transfer on the formation of the temperature field of the soil layer. Using the example of milling peat, the results of solving this problem are presented in the form of one-dimensional unsteady fields of temperature and moisture content. Taking into account the given unambiguity conditions (geometric, physical, initial and boundary conditions), it is established that the required values of moisture content and temperature will be reached in six hours. At the same time, there is practically no change in moisture content during the time period under consideration on the coordinate segment z ∈[0;6,0]sm. The solution of the mathematical problem, implemented in a software environment, allows you to control the thermal and humidity conditions of the soil by regulating the heat flow on its surface (in the case of an obvious relationship between the magnitude of the heat flux and the intensity of evaporation from the soil surface). Due to the fact that the solution proposed in the article is a particular one and does not take into account thermal diffusion in the soil layer, i.e.the influence of temperature differences on moisture transfer seems appropriate and of scientific interest to consider further the general solution of the system of differential equations of interrelated heat and mass transfer.

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