Mathematical simulation of heat and mass transfer, phase conversions, and shrinkage for optimization of the process of drying of thermolabile materials

Abstract

A mathematical model and a numerical method for calculation of the processes of heat and mass transfer, phase conversions, and shrinkage in drying of colloidal capillary-porous bodies are presented. The model and method allow one to conduct polyvariant calculation of the fields of temperature, volumetric concentration, and pressure in each of the components of the bound substance. A method of dehydration of thermolabile materials that makes it possible to minimize the time of drying and provide savings of energy and resources is presented.Drying of disperse materials, which is widely used in different branches of industry and agriculture, requires great energy and material consumption. In connection with this, a modern trend in the development of drying technologies is the saving of energy and resources and enhancement of the dehydration process with the high quality of the finished product being preserved.The possibility of enhancement of the process of drying of thermolabile materials due to increase in the heatcarrier temperature is limited, since the effect of elevated temperatures on these materials leads to their destruction or irreversible qualitative changes. In dehydration of thermolabile materials, at each instant of time the body temperature must be lower than some maximum permissible value T * . If the maximum permissible temperature is relatively low, dehydration of thermolabile materials at a constant temperature of the drying agent T sur = T * is impractical. This is due to the fact that at low temperatures the time of the drying process increases greatly, its efficiency decreases, and the quality of the product can deteriorate. Therefore, development of a highly efficient technology of drying of thermolabile materials is related to the necessity of varying the heat-carrier temperature during drying.Most thermolabile materials are colloidal capillary-porous bodies the volume of which can decrease severalfold in drying. Shrinkage phenomena can greatly affect the dynamics of the processes of heat and mass transfer and phase conversions. In mathematical models used for describing the processes of drying [1][2][3][4][5], shrinkage of material is usually disregarded.In the present paper, we state the mathematical model and the numerical method of calculation of heat and mass transfer, phase conversions, and deformation in dehydration of porous bodies, on the basis of which a new method of drying of thermolabile materials is developed. This method provides a minimum time of the process and decrease in energy losses at the given values of the maximum permissible temperature and the maximum temperature of the drying agent.Mathematical Model. We consider an isotropic, colloidal, capillary-porous body that deforms as a result of heat and mass transfer processes, phase conversions, or under the action of outer forces. In Cartesian coordinates, we denote x 1 , x 2 , and x 3 in terms of x i (t) = x i [t, x 1 (0), x 2 (0), x 3 (0)] (i = 1, 2, 3), i.e., the coordinates of the point of this body at a time instant ...

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