Afanasyev A.M., Siplivyy B.N. Mathematical Model of Electromagnetic Drying with Boundary Conditions of Mass Transfer on the Basis of Dalton’s Law of Evaporation
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Afanasyev Anatoliy Mikhaylovich
Doctor of Technical Sciences, Professor, Department of Information Security,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Siplivyy Boris Nikolaevich
Doctor of Technical Sciences, Professor, Department of Theoretical Physics and Wave Processes, Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. The drying electromagnetic waves with boundary conditions of mass transfer are analyzed on the basis of the laws of Newton and Dalton. In the Newton’s
model the rate of moisture evaporation from the surface of the sample is proportional to the difference between the current moisture content on the surface and the equilibrium moisture content of material. In the Dalton’s model the evaporation rate is proportional to the difference of partial pressure of water vapor through the thickness of the boundary layer. Under conditions of Newton’s intensity drying there is a function of moisture content on the surface, and under the conditions of Dalton – the temperature function is on this surface. It is shown that the mass transfer by Newton’s law leads to a contradiction of the regularity of the period of constant drying rate. In contrast, the use of boundary conditions of mass transfer on the basis of Dalton’s law of evaporation leads to a complete accordance with the experiment. This statement is proved by the direct construction of solutions of initial-boundary value problem for the fields of temperature and moisture content during the electromagnetic drying of the plate.
model the rate of moisture evaporation from the surface of the sample is proportional to the difference between the current moisture content on the surface and the equilibrium moisture content of material. In the Dalton’s model the evaporation rate is proportional to the difference of partial pressure of water vapor through the thickness of the boundary layer. Under conditions of Newton’s intensity drying there is a function of moisture content on the surface, and under the conditions of Dalton – the temperature function is on this surface. It is shown that the mass transfer by Newton’s law leads to a contradiction of the regularity of the period of constant drying rate. In contrast, the use of boundary conditions of mass transfer on the basis of Dalton’s law of evaporation leads to a complete accordance with the experiment. This statement is proved by the direct construction of solutions of initial-boundary value problem for the fields of temperature and moisture content during the electromagnetic drying of the plate.
Key words: mathematical modeling, electromagnetic drying, Dalton’s law of evaporation, period of constant drying rate.
Mathematical Model of Electromagnetic Drying with Boundary Conditions of Mass Transfer on the Basis of Dalton’s Law of Evaporation by Afanasyev A.M., Siplivyy B.N. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №6 (25) 2014 pp. 69-80
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