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Parameters of the carslaw-jaeger equation describing the temperature distribution in the ground

Publication date: 20.09.2018

Technical Transactions, 2018, Volume 9 Year 2018 (115), pp. 67-78

https://doi.org/10.4467/2353737XCT.18.132.8971

Authors

,
Barbara Larwa
Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology
https://orcid.org/0000-0003-1762-6694 Orcid
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,
Monika Gwadera
Instytut Inżynierii Chemicznej i Procesowej, Wydział Inżynierii i Technologii Chemicznej, Politechnika Krakowska
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,
Izabela Kicińska
Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology
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Krzysztof Kupiec
Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology
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Titles

Parameters of the carslaw-jaeger equation describing the temperature distribution in the ground

Abstract

Temperatura gruntu zmienia się z głębokością oraz w czasie. Zmienność czasowa ma charakter harmoniczny. Równanie opisujące zmiany temperatury gruntu zawiera cztery parametry: średnioroczną temperaturę powierzchni gruntu, roczną amplitudę temperatury powierzchni gruntu, kąt fazowy oraz dyfuzyjność cieplną gruntu. Na podstawie wyników pomiarów przedstawionych w literaturze wyznaczono parametry równania kombinowaną metodą opierającą się na regresji liniowej, opisaną w literaturze. Metoda ta prowadzi jednak do otrzymania niejednoznacznej wartości współczynnika dyfuzyjności cieplnej. Stwierdzono, że znacznie lepsze wyniki daje metoda regresji nieliniowej, prowadząc do otrzymania dokładnych i jednoznacznych wartości wszystkich parametrów równania. 

 

The ground temperature changes with depth and time. Time variability is considered as a harmonic function. The equation describing changes of the ground temperature contains four parameters: the average annual  temperature of the surface of the ground, the annual amplitude of the temperature of the ground surface as well as the phase angle of the temperature and thermal diffusivity of the ground. Based on the results of the measurements presented in the literature, the parameters of the equation using the combined method on the basis of linear regression, described in the literature, were determined. This method, however, leads to an ambiguous value of the thermal diffusivity. It was found that the nonlinear regression method gives much better results, leading to obtaining precise and unambiguous values of all parameters of the equation.

References

[1]       Kurevija T., Vulin D., Krapec V., Influence of undisturbed ground temperature and geothermal gradient on the sizing of borehole heat exchangers, Proceedings of the World Renewable Energy Congress, Linkoping, Sweden, 8–13 May 2011, 1360–1367.

[2]       Carslaw H.S., Jaeger J.C., Conduction of Heat in Solids, second ed., Clarendon Press, Oxford 1959.

[3]       Kusuda T., Achenbach P.R., Earth temperature and thermal diffusivity at selected stations in the United States, National Bureau of Standards Report Nr 8972, June 1965.

[4]       Badache M., Eslami-Nejad P., Ouzzane M., Aidoun Z.,  A new modeling approach for improved ground temperature profile determination, Renewable Energy 2016, 85, 436–444.

[5]       Popiel C.O., Wojtkowiak J., Temperature distributions of ground in the urban region of Poznan City, Experimental Thermal and Fluid Science 2013, 51, 135–148.

[6]       Krarti M., Lopez-Alonzo C., Claridge D.E., Kreider J.F., Analytical model to predict annual soil surface temperature variation, Journal of Solar Energy Engineering 1995, 117, 91-99.

[7]       Gwadera M., Larwa B., Kupiec K., Undisturbed ground temperature – different methods of determination, Sustainability 2017, 9, 2055.

[8]       Carslaw H.S., Introduction to the mathematical theory of the conduction of heat in solids, MacMillan and Co., Limited, London 1921.

[9]       Rees S.J. (Ed.), Advances in Ground-Source Heat Pump Systems, Elsevier 2016.

         

Information

Information: Technical Transactions, 2018, Volume 9 Year 2018 (115), pp. 67-78

Article type: Original article

Titles:

Polish:

Parameters of the carslaw-jaeger equation describing the temperature distribution in the ground

English:

Parameters of the carslaw-jaeger equation describing the temperature distribution in the ground

Authors

https://orcid.org/0000-0003-1762-6694

Barbara Larwa
Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology
https://orcid.org/0000-0003-1762-6694 Orcid
Contact with author
All publications →

Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology

Instytut Inżynierii Chemicznej i Procesowej, Wydział Inżynierii i Technologii Chemicznej, Politechnika Krakowska

Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology

Chair of Chemical and Process Engineering, Faculty of Chemical Engineering and Technology, Cracow University of Technology

Published at: 20.09.2018

Article status: Open

Licence: None

Percentage share of authors:

Barbara Larwa (Author) - 25%
Monika Gwadera (Author) - 25%
Izabela Kicińska (Author) - 25%
Krzysztof Kupiec (Author) - 25%

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Parameters of the carslaw-jaeger equation describing the temperature distribution in the ground

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