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Analytical Modeling of Advection–Conduction Heat Transfer Outside Borehole Heat Exchangers Under Dirichlet Boundary Conditions.

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Title: Analytical Modeling of Advection–Conduction Heat Transfer Outside Borehole Heat Exchangers Under Dirichlet Boundary Conditions.
Authors: Wei, Ting1 (AUTHOR), Wang, Lijuan2 (AUTHOR) wlj@ahsdxy.edu.cn, Ren, Honglei1,3 (AUTHOR), Lin, Fei1,3 (AUTHOR)
Source: Energies (19961073). May2026, Vol. 19 Issue 9, p2206. 19p.
Subject Terms: *Fourier transforms, *Boundary value problems, *Mathematical analysis, *Heat convection, *Numerical analysis, *Geothermal wells, *Groundwater flow, *Ground source heat pump systems
Abstract: For heat transfer outside borehole heat exchanger (BHE) arrays in aquifers, existing analytical models mostly adopt Neumann or Robin boundary conditions, whereas constant-temperature (Dirichlet) boundaries are more practical and convenient for monitoring in engineering applications. Considering the coupled effects of heat advection and conduction induced by groundwater seepage, and based on the engineering reality that vertical heat flow is much smaller than horizontal heat flow, this study idealized the BHE array as a constant-temperature boundary and established a one-dimensional simplified model. The advection term of the governing equation was removed through the exponential transformation of the dependent variable, and an analytical solution was derived using Fourier transformation. A three-dimensional coupled hydro-thermal numerical model was established in FEFLOW for validation. The results indicate that relative errors between analytical and numerical solutions remain below 3% outside the BHE array; however, the analytical method is inapplicable inside the array due to significant thermal interference, and independent field validation is precluded by prior thermal disturbances. The proposed solution features fast computation and clear physical interpretation, providing a simple and efficient tool for rapid estimation of temperature variations during preliminary feasibility studies of ground-source heat-pump projects. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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Header DbId: enr
DbLabel: Energy & Power Source
An: 193716102
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Analytical Modeling of Advection–Conduction Heat Transfer Outside Borehole Heat Exchangers Under Dirichlet Boundary Conditions.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Wei%2C+Ting%22">Wei, Ting</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Lijuan%22">Wang, Lijuan</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> wlj@ahsdxy.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ren%2C+Honglei%22">Ren, Honglei</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lin%2C+Fei%22">Lin, Fei</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Energies+%2819961073%29%22">Energies (19961073)</searchLink>. May2026, Vol. 19 Issue 9, p2206. 19p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink><br />*<searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Heat+convection%22">Heat convection</searchLink><br />*<searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Geothermal+wells%22">Geothermal wells</searchLink><br />*<searchLink fieldCode="DE" term="%22Groundwater+flow%22">Groundwater flow</searchLink><br />*<searchLink fieldCode="DE" term="%22Ground+source+heat+pump+systems%22">Ground source heat pump systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: For heat transfer outside borehole heat exchanger (BHE) arrays in aquifers, existing analytical models mostly adopt Neumann or Robin boundary conditions, whereas constant-temperature (Dirichlet) boundaries are more practical and convenient for monitoring in engineering applications. Considering the coupled effects of heat advection and conduction induced by groundwater seepage, and based on the engineering reality that vertical heat flow is much smaller than horizontal heat flow, this study idealized the BHE array as a constant-temperature boundary and established a one-dimensional simplified model. The advection term of the governing equation was removed through the exponential transformation of the dependent variable, and an analytical solution was derived using Fourier transformation. A three-dimensional coupled hydro-thermal numerical model was established in FEFLOW for validation. The results indicate that relative errors between analytical and numerical solutions remain below 3% outside the BHE array; however, the analytical method is inapplicable inside the array due to significant thermal interference, and independent field validation is precluded by prior thermal disturbances. The proposed solution features fast computation and clear physical interpretation, providing a simple and efficient tool for rapid estimation of temperature variations during preliminary feasibility studies of ground-source heat-pump projects. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.3390/en19092206
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
        StartPage: 2206
    Subjects:
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Heat convection
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Geothermal wells
        Type: general
      – SubjectFull: Groundwater flow
        Type: general
      – SubjectFull: Ground source heat pump systems
        Type: general
    Titles:
      – TitleFull: Analytical Modeling of Advection–Conduction Heat Transfer Outside Borehole Heat Exchangers Under Dirichlet Boundary Conditions.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Wei, Ting
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          Name:
            NameFull: Wang, Lijuan
      – PersonEntity:
          Name:
            NameFull: Ren, Honglei
      – PersonEntity:
          Name:
            NameFull: Lin, Fei
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          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 19961073
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            – Type: volume
              Value: 19
            – Type: issue
              Value: 9
          Titles:
            – TitleFull: Energies (19961073)
              Type: main
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