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Analytical Solutions for Ground Temperature Profiles and Stored Energy Using Meteorological Data

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Abstract

Analytical solutions to estimate temperature with depth and stored energy within a soil column based upon readily available meteorological data are presented in this paper, which are of particular relevance in the field of ground heat extraction and storage. The transient one dimensional heat diffusion equation is solved with second kind (Neumann) boundary conditions at the base and third kind (Robin) boundary conditions, based on a heat balance, at the soil surface. In order to describe the soil-atmosphere interactions, mathematical expressions describing the daily and annual variation of solar radiation and air temperature are proposed. The presented analytical solutions are verified against a numerical solution and applied to investigate a case-study problem based upon results of a field experiment. It is shown that the proposed analytical approach can offer a reasonable estimate of the thermal behaviour of the soil requiring no information from the soil other than its thermal properties. Comparisons of predicted and measured soil temperature profiles and stored energy transients demonstrate there is reasonable overall agreement. The research contributes a practical approach that can provide surface boundary data that are vital in the thermal analysis of many engineering problems. Applications include: inter-seasonal heat transfer, energy piles and other more established ground source heat utilization methods.

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Acknowledgments

The authors gratefully acknowledge the support given to the second author whose PhD studies were funded by CONACYT (the Mexican National Council of Science and Technology) and SEP (Mexican Secretariat of Public Education). Also the supply by TRL/HA of the source data published in (Carder et al. 2007) is gratefully acknowledged.

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Authors and Affiliations

  1. Cardiff School of Engineering, Cardiff University, Cardiff, CF24 3AA, Wales, UK

    Peter John Cleall, José Javier Muñoz-Criollo & Stephen William Rees

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  1. Peter John Cleall
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  2. José Javier Muñoz-Criollo
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  3. Stephen William Rees
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Correspondence to Peter John Cleall.

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Cleall, P.J., Muñoz-Criollo, J.J. & Rees, S.W. Analytical Solutions for Ground Temperature Profiles and Stored Energy Using Meteorological Data. Transp Porous Med 106, 181–199 (2015). https://doi.org/10.1007/s11242-014-0395-3

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  • DOI: https://doi.org/10.1007/s11242-014-0395-3

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