Afanasyev A.M., Bakhracheva Yu.S. The Problem of Heat and Mass Transfer of a Half-Space with an Air Flow with Periodic Changes in Air Temperature
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https://doi.org/10.15688/mpcm.jvolsu.2024.2.2
Anatoly M. Afanasyev
Doctor of Sciences (Engineering), Professor, Department of Information Security,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Yulia S. Bakhracheva
Candidate of Sciences (Engineering), Associate Professor, Department of Information Security,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. A system of differential equations, boundary and initial conditions for calculating temperature and moisture content fields in a homogeneous halfspace, the boundary of which is blown by an air flow, is formulated. The heat exchange of the boundary with the air medium occurs according to the Newtonian law, and mass transfer — according to the Dalton evaporation law. In the initial state, the air and the material have the same temperature, and water vapor, both near the surface of the material and outside the boundary layer, is in a saturation state, so there is no exchange of heat and moisture between the air and the material. At some point, the air temperature begins to produce small harmonic fluctuations near its initial value. For a mathematical model of heat and mass transfer, in which the movement of moisture to the surface is considered to be caused only by a drop in moisture content, i.e. the phenomenon of thermal diffusion is neglected, an asymptotic time view of the temperature and moisture content fields is obtained. The moisture content field has the form of a damped harmonic wave, and the temperature field is represented by the superposition of two waves of the same type, which have the same frequency, but different attenuation coefficients and phase velocities. The calculation of the basic wave parameters for a material with clay characteristics is carried out, and the results obtained are compared with experimental data. The constructed solution is a generalization of the Fourier formulas known in the literature, which are valid only in a situation when the material does not contain moisture, and according to the harmonic law, not the air temperature changes, but the surface temperature. The results obtained in the article will be used in geocryology as a theoretical tool in the study of seasonal fluctuations in the thermal and physical state of the soil, which is an important task in planning economic activities in the field of the distribution of frozen rocks.
Key words: heat and mass transfer, Lykov equations, a problem for a halfspace, harmonic regime, damped waves, penetration depth, delay time, geocryology.
The Problem of Heat and Mass Transfer of a Half-Space with an Air Flow with Periodic Changes in Air Temperature by Afanasyev A.M., Bakhracheva Yu.S. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 27 No. 2 2024, pp. 14-29
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