Afanasev A.M. Steady-State Heat Transfer Through a Flat Wall in the Mode of Harmonic Surface Temperature Change
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https://doi.org/10.15688/mpcm.jvolsu.2025.3.7
Anatoliy M. Afanasev
Doctor of Sciences (Engineering), Professor, Department of Information Security, Volgograd State University
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https://orcid.org/0000-0003-3703-3167
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. A steady-state temperature field in a flat wall is investigated in a situation where harmonic fluctuations in the temperature of one of the surfaces are superimposed on a constant temperature difference between the wall surfaces. The concept of a complex coefficient of heat transfer over a variable component, the concept of a frequency characteristic of the plate and the corresponding characteristic period of oscillation, which is called the time constant of the plate for thermal processes, is introduced. This value turns out to be a function of the thermophysical characteristics of the wall material and its thickness. 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, and the inverse value has the meaning of the relative depth of penetration. It is shown that for oscillations with periods exceeding the time constant of the plate, heat transfer through it occurs in approximately the same way as in the case of stationary fields. If the oscillation period is less than the time constant, then with an increase in this inequality, the intensity of the heat flux transmitted through the plate decreases monotonously and tends to zero. As an example, the heat transfer characteristics in the harmonic mode for walls made of copper and building bricks are calculated. 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, in the theory of methods for determining the thermophysical characteristics of materials based on measurement data, i.e. when solving inverse problems of the theory of thermal conductivity.
Key words: mathematical physics, theory of thermal conductivity, planelayered media, heat waves, harmonic mode, frequency response, heat transfer coefficient, heat exchangers.
Steady-State Heat Transfer Through a Flat Wall in the Mode of Harmonic Surface Temperature Change by Afanasev A.M. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 28 No. 3 2025, pp. 76-89
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