Heat Conduction of Walls with a Monotone Temperature Change. Asymptotics and Quasi-Stationarity
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Systematizing the partial solutions of the nonstationarity heat conduction problem of a flat wall in comparison with the general asymptotic solution of this problem, we have found the transverse temperature distributions with any monotone change in the ambient conditions and elucidated the heat conduction properties of the wall under these conditions. The asymptotic solution is given by semiconvergent series and definite integrals and has been investigated for power time dependences with an exponent of 0–2, which has enabled us to justify the concept of quasi-stationarity of the thermal parameters of the wall and obtain asymptotic errors and corrections defining the deviations of these parameters from their stationary values. The features of the average heat flows most resistant to thermal disturbances as to both time and amplitude have been considered.
Keywordsheat conduction of a flat wall variable boundary conditions asymptotic dependences quasi-stationarity heat flow density
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- 1.O. V. Korshunov and V. I. Zuev, Measurement of the thermal resistance of exterior walls, Énergobezop. Énergosberezh., No. 2, 40–45 (2011).Google Scholar
- 2.O. V. Korshunov and V. I. Zuev, Applicability of the quasi-stationary method of determining the thermal resistance of walls, Énergobezop. Énergosberezh., No.3, 27–34 (2011).Google Scholar
- 4.J. V. Bek, B. Blackwell, and Ch. R. St. Clair Jr., Ill-Posed Inverse Heat Conduction Problems [Russian translation], Mir, Moscow (1989).Google Scholar
- 5.O. N. Budadin, A. I. Potapov, V. I. Kolganov, T. E. Troitskii-Markov, and E. V. Abramova, Thermal Nondestructive Testing of Products [in Russian], Nauka, Moscow (2002).Google Scholar
- 6.O. V. Lebedev, O. N. Budadin, S. V. Baranov, and V. G. Avramenko, Thermal fl aw detection of multilayer products on the basis of solving inverse nonstationary heat conduction problems, Kontr. Diagnost., No. 6, 16–23 (2007).Google Scholar
- 7.A. V. Lukov, Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1967).Google Scholar
- 8.A. S. Telegin, V. S. Shvydkii, and Yu. G. Yaroshenko, Heat and Mass Transfer, Ch. 2. Heat Conduction [in Russian], 2nd edn., Akademkniga, Moscow (2002).Google Scholar
- 9.É. M. Kartashov, Analytical Methods in the Theory of Heat Conduction of Solids [in Russian], Vysshaya Shkola, Moscow (2001).Google Scholar
- 10.A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series [in Russian], Nauka, Moscow (1981).Google Scholar
- 11.G. Korn and T. Korn, Handbook of Mathematics [Russian translation], 4th edn., Nauka, Moscow (1977).Google Scholar
- 12.E. von Kamke, Differentialtechungen Lösungsmethoden und Lösungen [Russian translation], Nauka, Moscow (1976).Google Scholar