Explicit Multipole Formula for the Local Thermal Resistance in an Energy Pile—The Line-Source Approximation

Johan Claesson and Saqib Javed
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Johan Claesson: Building Physics, Lund University, 221 00 Lund, Sweden
Saqib Javed: Building Services, Lund University, 221 00 Lund, Sweden

Energies, 2020, vol. 13, issue 20, 1-24

Abstract: This paper presents a closed-form quite handy formula for the local thermal resistance R b between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy’s mean value theorem of analytical functions is used. The formula for thermal resistance R b0 for the zero-order approximation ( J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation ( J = 0) are shown to be quite small by comparisons with eight-order approximation ( J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance R b0 for the zero-order approximation ( J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance R bmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.

Keywords: energy piles; thermal piles; pile foundations; local thermal resistance; minimum thermal resistance; multipole method; ground source heat pump (GSHP) (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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