Operator Method of Nonstationary Temperature Field Calculation in Environment With an Isolated Cylindrical Pipe

Voldemārs Barkāns, Gints Turlajs, Aivars Cers, Roberts Veselauskis, Daniels Turlajs, Sigurds Jaundālders

Abstract


The following research is important for the understanding of thermal conductivity processes in the setting typical for thermal pumps and for bringing calculations nearer to the real situation. Considering a non-stationary process, the temperature field is described in the polar coordinate system by using Laplace’s equation and corresponding mixed-type boundary data. The solution was obtained by the Laplace transform method, applying an integral function of complex variables. The inverse Laplace transform and the original temperature are expressed as an integral. For the integration, a closed contour, which rules out branching and provides an integral of an analytic function, is employed. Cauchy’s theorem is applied to the calculations. As a result, indefinite integrals have been derived for temperature estimation in the heat pipe coating and the surrounding environment, depending on the fluid temperature within the heat pipe. 


Keywords:
Heat pumps; Laplace transform; thermal conductivity

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References


H. S. Carslaw and J. C. Jaeger, Teploprovodnostj tverdih tel. Moscow: Nauka, 1964, 487 p. (in Russian)

H. S. Carslaw and J. C. Jaeger, Operacionnie metodi v prikladnoj matematike, Moscow: IL, 1948, 293 p. (in Russian)

M. A. Lavrentjev and B. V. Šabat, Metodi teorii funkcij kompleksnogo peremennogo, Moscow: Nauka, 1958, 678 p. (in Russian)

V. Barkāns, A. Cers, N. Zeltinsh, and G. Turlajs, “Non-Stationary Temperature Field in a Tube Surrounding Environment,” Modern science: researches, ideas, results, technologies, no. 2(13), Dnepropetrovsk, Ukraine, NPVK Triakon, pp. 34–37, 2013.

V. Barkāns, “Operator Method for Nonstationary Temperature Field Calculation in Thick-Walled Cylindrical Heat Pipe Environment,” Power and Electrical Engineering, vol. 33, pp. 5–11, 2016. https://doi.org/10.7250/pee.2016.001

G. N. Watson, Teorija besselevih funkcij. Moscow: IL, 1949, 787 p. (in Russian)

G. Doetsch, Rukovodstvo k prakticheskomu primeneniju preobrazovanija Laplassa i Z-preobrazovanija, Moskva: Nauka, 1971, 288 p. (in Russian)

A. Gray and G. B. Matthews, Funkcii Besselja i ih prilozhenija k fizike i mehanike, Moscow: IL, 1953, 372 p. (in Russian)

E. Janke, F. Emde, and F. Losch, Specialjnije funkcii, formuli, grafiki, tablici, Moscow: Fizmat-giz, 1968, 344 p. (in Russian)

V. P. Isachenko, V. A. Osipova, and A. S. Sukomel, Teploperedacha, Moscow: Energija, 1969, 440 p. (in Russian)

V. Katsura, K. Nagano, and S. Takeda, “Method of calculation of the ground temperature for multiple ground heat exchangers,” in Proc. Applied Thermal Engineering, vol. 28, no. 14–15, pp. 1995–2004, 2008. https://doi.org/10.1016/j.applthermaleng.2007.12.013




DOI: 10.7250/pee.2017.001

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