Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics935210.18469/1810-3189.2021.24.2.13-21Research ArticleGeneralization of the Fourier problem of temperature waves in half-spaceAfanasyevAnatoly M.<p>Doctor of Technical Sciences, Associate Professor, Professor of the Information Security Department, Institute of Priority Technologies</p>a.m.afanasiev@yandex.ruBakhrachevaYulia S.<p>Candidate of Technical Sciences, Associate Professor of the Department of Information Security, Institute of Priority Technologies</p>bakhracheva@yandex.ruVolgograd State University06092021242132106092021Copyright © 2021, Afanasyev A., Bakhracheva Y.2021<p>The problem of asymptotic fluctuations of temperature and moisture content in a half-space whose boundary is blown by an air flow with a temperature varying according to the harmonic law is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange of the first kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal changes in the thermophysical state of frozen rocks and soils, in the theory of building structures to study the thermal regime of indoor premises with fluctuations in ambient temperature, in the theory of drying by electromagnetic radiation to study the processes of heat and mass transfer in oscillating modes.</p>diffusion equationharmonic modehalf-space problemasymptotic solutionharmonic wavescomplex amplitude methodheat and mass transferLykov equationsgeocryologyFourier lawselectromagnetic dryingoscillating modesуравнение диффузиигармонический режимзадача для полупространстваасимптотическое решениегармонические волныметод комплексных амплитудтепломассопереносуравнения Лыковагеокриологиязаконы Фурьеэлектромагнитная сушкаосциллирующие режимы[Born M., Vol'f E. Fundamentals of Optics / Trans. from English. Moscow: Nauka, 1970, 856 p. (In Russ.)][Nikol'skij V.V., Nikol'skaja T.I. Electrodynamics and Radio Propagation. Moscow: Nauka, 1989, 544 p. (In Russ.)][Ango A. Mathematics for Electrical and Radio Engineers. Foreword by Louis De Broglie. Moscow: Nauka, 1967, 780 p. (In Russ.)][Rudobashta S.P., Kartashov E.M., Zuev N.A. Heat and mass transfer during drying in an oscillating electromagnetic field. Teoreticheskie osnovy himicheskoj tehnologii, 2011, vol. 45, no. 6, pp. 641–647. (In Russ.)][Rudobashta S.P., Zueva G.A., Kartashov E.M. Heat and mass transfer during drying of a spherical particle in an oscillating electromagnetic field. Teoreticheskie osnovy himicheskoj tehnologii, 2016, vol. 50, no. 5, pp. 539–550. DOI: https://doi.org/10.7868/S0040357116050109 (In Russ.)][Rudobashta S.P., Zueva G.A., Kartashov E.M. Heat and mass transfer during drying of a cylindrical body in an oscillating electromagnetic field. Inzhenerno-fizicheskij zhurnal, 2018, vol. 91, no. 1, pp. 241–251. (In Russ.)][Mors F.M., Feshbah G. Methods of Theoretical Physics. T. 2. Moscow: Izd-vo inostr. lit., 1960, 886 p. (In Russ.)][Lykov A.V. Heat Conduction Theory. Moscow: Vysshaja shkola, 1967, 600 p. (In Russ.)][Tihonov A.N., Samarskij A.A. Equations of Mathematical Physics. Moscow: Nauka, 1966, 724 p. (In Russ.)][Permafrost (Short Course)/ ed. by V.A. Kudrjavtsev. Moscow: Izd-vo MGU, 1981, 240 p. (In Russ.)][Cheverev V.G. General Permafrost. Water-Conducting Properties of Soils / ed. by V.A. Kudrjavtsev. Moscow: Izd-vo MGU, 1978, 464 p. (In Russ.)][Lykov A.V. Drying Theory. Moscow; Leningrad: Energija, 1968. 471 p.][Lykov A.V. Heat and Mass Transfer: A Reference Book. 2nd ed., Rev. and Additional. Moscow: Energija, 1978, 480 p. (In Russ.)][Afanas'ev A.M., Siplivyj B.N. On the boundary conditions of mass transfer in the form of Newton's and Dalton's laws. Inzhenerno-fizicheskij zhurnal, 2007, vol. 80, no. 1, pp. 27–34. (In Russ.)][Tihonov A.N., Vasil'eva A.B., Sveshnikov A.G. Differential Equations. Moscow: Nauka, 1985, 231 p. (In Russ.)][Rudobashta S.P., Zueva G.A., Zuev N.A. Influence of thermal diffusion on oscillating infrared drying kinetics. Izv. vuzov. Himija i him. tehnologija, 2016, vol. 59, no. 4, pp. 83–87. DOI: https://doi.org/10.6060/tcct.20165904.5322 (In Russ.)][Kundas S.P. et al. Modeling the Processes of Thermal and Moisture Transfer in Capillary-Porous Media. Minsk: In-t teplo- i massoobmena im. A.V. Lykova NAN Belarusi, 2007, 292 p. (In Russ.)][Afanas'ev A.M., Siplivyj B.N. Electromagnetic drying theory: asymptotic solution of the initial-boundary value problem for a rectangular region. Physics of Wave Processes and Radio Systems, 2012, vol. 15, no. 1, pp. 77–83. (In Russ.)]