AfanasievA.M. Heat transfer coefficient through a flat two-layer wall in the regime of harmonic change of surface temperature
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https://doi.org/10.15688/mpcm.jvolsu.2026.2.5
Anatoliy M. Afanasiev
Candidate Sciences (Physics and Mathematics), Associate Professor, Department of Mathematical Analysis and Function Theory, Volgograd State University
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https://orcid.org/0000-0003-3703-3167
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. For a flat two-layer wall under boundary conditions of the first kind, a generalization of the concept of the heat transfer coefficient is given for the case when the temperature of one of the surfaces is kept constant, and the temperature of the other surface, along with a constant component, also has a component that varies over time according to a harmonic law. In contrast to the case of fields that remain unchanged over time, the new coefficient is complex, it has the meaning of a frequency response and relates the amplitude and initial phase of temperature fluctuations on one of the wall surfaces to the amplitude and initial phase of the heat flow transmitted through it. The concept of the natural frequency of a two-layer wall is introduced, which characterizes its heat transfer properties in the field of harmonic fields in time, and the oscillation period corresponding to the natural frequency is called the time constant of the plate for thermal processes. The modulus and argument of the complex heat transfer coefficient are presented as functions of a dimensionless variable, the square of which has the meaning of the relative frequency of the heat wave. The dependence of the heat transfer coefficient on the frequency, thermophysical characteristics of the wall layers and their thickness is investigated. The results obtained will find application in the theory of heat exchangers of the regenerative type, in the theory of algorithms for calculating fluctuations in indoor temperature and humidity caused by fluctuations in environmental characteristics, as well as in geocryology for modeling seasonal temperature and humidity fluctuations in freezing-thawing soils.
Key words: mathematical physics, theory of thermal conductivity, harmonic regime, layered medium, plate problem, heat exchangers, regenerative process, heat transfer coefficient.
Afanasiev A.M. Heat transfer coefficient through a flat two-layer wall in the regime of harmonic change of surface temperature is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 29 No. 2 2026, pp. 72-85
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