New ways of experimental data processing by generalized complex variables that are characteristic of the drying process are presented. The authors presented the results of a study of heat and moisture exchange in the convective drying of thin flat moist capillary-porous materials. As a result of the processing of the experimental data, equations were obtained for determining the densities of heat fluxes, average integral temperatures, drying time and moisture evaporation rate in the second drying period. The relationship between the densities of heat fluxes in the first and second periods and the temperature change in the second period is revealed. The dependence for calculating the temperature of the material in the period of the falling drying rate taking into account the heat that is expended to heat the wet body is presented. The equations for determining the temperature in the second period by the temperature coefficient of drying, the rate of heating of the wet material and the rate of heating of the wet body are presented as well. An equation for determining the drying time by the value of the rate of loss of moisture content of the material is given. A mathematical expression for calculating the intensity of moisture evaporation in the first and second drying periods depending on the ratio of moisture content in the first period and the current in the second moisture content one is set. The conditions of a regular regime for heat and moisture exchange for a second drying period are adduced. The authors consider the possibility of determining the rate of heating of wet material by the heating rate using the graphical differentiation of the temperature function, which is described by the curve, as a function of time in the second drying period. The problems of using the methods of the theory of the regular regime for heating wet bodies during the investigation of the drying process are considered. The formulas for determining the rate of heating of the body and the rate of loss of moisture content are given. The accuracy of the experimental data processing and the reliability of the experimental equations obtained for all the materials under study are verified. As a result of the research, all the basic kinetic characteristics necessary for the calculation of heat and moisture exchange in the drying process have been determined.
The results of the study of heat and mass transfer in the processes of heat treatment and drying processes of thermal insulating materials when the values of the Biot heat exchange criterion are less than one and the main factor is the interaction of the evaporation surface of the material with the environment (external problem) are presented. It was assumed that at low temperature gradients over the cross section of a wet body, thermal transfer of matter can be neglected, and phase transformations are absent (Posnov's criterion is equal to zero). By processing the experimental data on convective heat treatment of materials carried out by the least squares method, experimental equations for calculating the kinetics of drying have been obtained. Equations are given for determining the duration of drying, material temperature, heat flux density. On the basis of the theory of regular thermal regime, equations for the rate of heating of a solid and the rate of decrease in moisture content have been obtained. The verification of the reliability of the obtained equations and comparison of the calculated values of the parameters with the experimental ones are presented. An experimental dependence of the relative drying rate on the dimensionless moisture content has been established. The dependence of the generalized drying time on the relative moisture content is given. Also, based on the analysis of the experimental data on the thermal conductivity coefficients for wet thermal insulation materials, the dependences of the thermal conductivity coefficients on moisture content and temperature have been established. As a result of solving the criterion heat transfer equation, the values of the heat transfer coefficients for the period of the decreasing drying rate are obtained. The values of the Biot criterion in the processes of drying porous ceramics and asbestos are determined, too. It has been determined that the ratio of the moisture content loss rate to the drying rate in the first period does not depend on the drying mode and is a function of the initial moisture content.
In the work, the authors investigated the possibility of using the results of analytical solutions of the linear differential equations of unsteady heat conduction with constant heat transfer coefficients to calculate the temperature of the material during heat treatment of leathers. Heat treatment of natural leathers as heat-sensitive materials is carried out under mild temperature conditions and high air moisture contents, the temperature does not undergo significant changes, and the heat transfer coefficients change almost linearly. When using analytical solutions, the authors made the assumptions that for small temperature gradients over the cross section of a thin body, the thermal transfer of matter can be neglected and for values of the heat and mass transfer Biot criteria less than unity, the main factor, limiting heat and mass transfer, is the interaction of the evaporation surface of the body with the environment; so, in solving the differential heat equation we can restrict ourselves to one first member of an infinite series. In this case, a piecewise stepwise approximation of all thermophysical characteristics with constant values of these coefficients at the calculated time intervals was applied, which made it possible to take into account the change in the transfer coefficients throughout the entire heat treatment process. Processing of experimental data showed that in low-intensity processes with reliable values of the transfer coefficients, it is possible to use the results of solutions of differential equations of unsteady heat conduction in heat transfer calculations. The results of the study of heat transfer during drying of leather confirm the laws of temperature change established experimentally. Together with experimental studies of drying processes, analytical studies are of great practical importance in the development of new methods for calculating heat and mass transfer in wet bodies.
In the paper, the authors analyzed the solution of the differential equation of non-stationary heat conduction for an unbounded plate during the heat exchange of plate surfaces with the surrounding medium according to Newton’s law at a constant temperature of the medium. To use the results of solving the equations in the drying of thin flat materials, the dependence of the heat transfer coefficients on temperature and moisture content was studied. As a result of studying and analyzing a number of literature sources, the regularities of the change in the heat transfer coefficients during drying are established with high reliability. Studies of drying of thin wet plates of white and red clays with known heat transfer coefficients have shown that for small values of the heat transfer criterion of the Bio and small temperature gradients over the section of a thin material, application of the results of solutions of the heat transfer equations gives completely satisfactory agreement between the calculated and experimental values of the temperatures and the duration of drying. It is established that for small Bio numbers, the main factor is the external heat and mass transfer of the surface of the material with the surrounding medium and the rate of drying depends little on internal mass transfer. It is shown that the use of numerical methods for solving differential equations is possible with varying degrees of approximation only for accurate and reliable dependences of heat and mass transfer coefficients on moisture content and temperature. For a number of materials with known heat transfer coefficients, the use of analytical methods in calculations is of considerable interest and brings the theory closer to the practice of drying.
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