Solution of the boundary value problem of heat and mass transfer by the method of joint application of the integral Laplace transform and the Bubnov-Galerkin variational method for conditions of radiant soil heating

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 emitters. A system of differential equations (in dimensional and dimensionless forms) is presented, reflecting the relationship of thermal and mass transfer processes in colloidal capillary-porous bodies in the case of surface radiant heating. A particular analytical solution of this system of differential equations for an unbounded plate is considered, taking into account cross-processes: the movement of moisture in the soil layer due to temperature difference (thermodiffusion) and the transfer of water vapor energy in a porous medium due to the gradient of the moisture content field (parodiffusion process). On the example of milling peat, taking into account the initial data, the solution of the boundary value problem of heat and mass transfer is obtained by the method of joint application of the integral Laplace transform and the Bubnov-Galerkin variational method, which represents one-dimensional unsteady fields of moisture content and temperature. It is established that under the given initial and boundary conditions, as well as taking into account the thermophysical characteristics of milling peat, the required moisture content values will be achieved in five hours, the temperature in two hours. At the same time, if a regular decrease in moisture content occurs on the coordinate segment z ∈[6.0;12.0  ] cm under the influence of radiant heating, then a slight increase in this value is observed near the soil surface z ∈[0;6.0  ] cm. As for the temperature field of milling peat, there is a regular temperature stratification by the depth of the soil layer, without any temperature anomalies during the entire heating period.

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