ANALYTICAL MODEL AND SOLUTION OF LAYERED HEAT TRANSFER OF GROUND HEAT EXCHANGER CONSIDERING INTERFACIAL THERMAL RESISTANCE EFFECT

Zhou Xiangyun; Hu Shixiang; Zhang Xiayang; Gao You; Sun De'an

doi:10.19912/j.0254-0096.tynxb.2024-0310

PDF(2671 KB)

Acta Energiae Solaris Sinica ›› 2025, Vol. 46 ›› Issue (6) : 712-720. DOI: 10.19912/j.0254-0096.tynxb.2024-0310

ANALYTICAL MODEL AND SOLUTION OF LAYERED HEAT TRANSFER OF GROUND HEAT EXCHANGER CONSIDERING INTERFACIAL THERMAL RESISTANCE EFFECT

Zhou Xiangyun¹, Hu Shixiang¹, Zhang Xiayang^2,3, Gao You^2,3, Sun De'an⁴

Author information +

History +

Abstract

The ground heat exchanger was simplified as a finite solid cylindrical heat source, and an analytical model of layered soil heat transfer considering the interfacial thermal resistance effect was established. The finite Hankel and Laplace transforms were used to obtain the Laplace domain solutions to the temperature of each soil layer. The correctness of the proposed model was verified by comparing with the numerical solution and existing analytical solution. The influence of interfacial thermal resistance on the temperature distribution of near-field layered soil was evaluated. The results show that the interface temperature above the soil layer increases due to heat accumulation, and the interface temperature below the soil layer decreases due to heat flow because of the existence of thermal resistance effect. The temperature distribution at the interface of soil layer shows a hopping phenomenon. The influence of thermal contact resistance on temperature response increases with increasing the heat transfer time, but decreases with increasing the radial distance. The greater the difference of the thermal conductivity between adjacent soil layers, the greater the influence of thermal contact resistance on the temperature distribution.

Key words

geothermal energy / heat transfer of layered stratum / ground heat exchanger / interfacial thermal contact resistance / semi-analytical solution

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Zhou Xiangyun, Hu Shixiang, Zhang Xiayang, Gao You, Sun De'an. ANALYTICAL MODEL AND SOLUTION OF LAYERED HEAT TRANSFER OF GROUND HEAT EXCHANGER CONSIDERING INTERFACIAL THERMAL RESISTANCE EFFECT[J]. Acta Energiae Solaris Sinica. 2025, 46(6): 712-720 https://doi.org/10.19912/j.0254-0096.tynxb.2024-0310

References

[1] SPITLER J D, GEHLIN S E A. Thermal response testing for ground source heat pump systems—an historical review[J]. Renewable and sustainable energy reviews, 2015, 50: 1125-1137.
[2] 孙畅, 张磊, 张广宇, 等. 太阳能-地源热泵系统控制策略及运行特性研究[J]. 太阳能学报, 2024, 45(1): 95-101.
SUN C, ZHANG L, ZHANG G Y, et al.Study on control strategy and operation characteristics of solar-ground source heat pump system[J]. Acta energiae solaris sinica, 2024, 45(1): 95-101.
[3] 赵军, 段征强, 宋著坤, 等. 基于圆柱热源模型的现场测量地下岩土热物性方法[J]. 太阳能学报, 2006, 27(9): 934-936.
ZHAO J, DUAN Z Q, SONG Z K, et al.A method for in situ determining underground thermal properties based on the cylindrical heat source model[J]. Acta energiae solaris sinica, 2006, 27(9): 934-936.
[4] 战国会, 俞亚南. 地源热泵有限长圆柱面和圆柱体热源模型[J]. 浙江大学学报(工学版), 2011, 45(6): 1104-1107.
ZHAN G H, YU Y N.Finite long cylindrical surface and cylinder source model of ground source heat pump[J]. Journal of Zhejiang university (engineering science), 2011, 45(6): 1104-1107.
[5] 苏华, 聂伟伟, 李茜, 等. 地源热泵竖埋管换热器热工参数反演方法研究[J]. 太阳能学报, 2023, 44(10): 481-487.
SU H, NIE W W, LI Q, et al.Research on thermal parameter inversion method for vertical borehole heat exchanger of ground source heat pump[J]. Acta energiae solaris sinica, 2023, 44(10): 481-487.
[6] YANG J, YAN Z G, LI X X, et al.A unified model and analytical solution for borehole and pile ground heat exchangers[J]. International journal of heat and mass transfer, 2020, 152: 119559.
[7] INGERSOLL L R, ZOBEL O J, INGERSOLL A C.Heat conduction with engineering, geological, and other applications[J]. Physics today, 1955, 8(3): 17.
[8] CARSLAW H, JAEGER J.Conduction of heat in solids[M]. Oxford UK: Oxford University Press, 1959.
[9] PHILIPPE M, BERNIER M, MARCHIO D.Validity ranges of three analytical solutions to heat transfer in the vicinity of single boreholes[J]. Geothermics, 2009, 38(4): 407-413.
[10] MAN Y, YANG H X, DIAO N R, et al.A new model and analytical solutions for borehole and pile ground heat exchangers[J]. International journal of heat and mass transfer, 2010, 53(13/14): 2593-2601.
[11] 曾和义, 刁乃仁, 方肇洪. 地源热泵竖直埋管的有限长线热源模型[J]. 热能动力工程, 2003, 18(2): 166-170, 216.
ZENG H Y, DIAO N R, FANG Z H.A model of finite-length linear heat-source for the vertical embedded pipe of a ground-source heat pump[J]. Journal of engineering for thermal energy and power, 2003, 18(2): 166-170, 216.
[12] ABDELAZIZ S L, OZUDOGRU T Y, OLGUN C G, et al.Multilayer finite line source model for vertical heat exchangers[J]. Geothermics, 2014, 51: 406-416.
[13] PAN A Q, MCCARTNEY J S, LU L, et al.A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground[J]. Energy, 2020, 200: 117545.
[14] 张琳邡, 张东海, 周扬, 等. 分层岩土中地埋管换热器传热解析模型与分析[J]. 太阳能学报, 2022, 43(10): 378-385.
ZHANG L F, ZHANG D H, ZHOU Y, et al.Analytical mode and analysis of heat transfer of ground heat exchangers in layered stratum[J]. Acta energiae solaris sinica, 2022, 43(10): 378-385.
[15] ZHANG Y P, WU W B, ZHANG H K, et al.A novel soil-pile interaction model for vertical pile settlement prediction[J]. Applied mathematical modelling, 2021, 99: 478-496.
[16] TIO K K, KOK CHUAN T.Thermal resistance of two solids in contact through a cylindrical joint[J]. International journal of heat and mass transfer, 1998, 41(13): 2013-2024.
[17] 王才进, 武猛, 蔡国军, 等. 基于多元分布模型预测土体热阻系数[J]. 岩石力学与工程学报, 2023, 42(增刊1): 3674-3686.
WANG C J, WU M, CAI G J, et al.Prediction of soil thermal resistivity based on multivariate distribution models[J]. Chinese journal of rock mechanics and engineering, 2023, 42(Sup 1): 3674-3686.
[18] WEN M J, TIAN Y, LI L C, et al.An imperfect thermal contact problem for consolidation of bilayered saturated soil subjected to ramp-type heating[J]. International journal of heat and mass transfer, 2022, 190: 122755.
[19] CHO W J, KIM J S, CHOI H J.Hydrothermal modeling for the efficient design of thermal loading in a nuclear waste repository[J]. Nuclear engineering and design, 2014, 276: 241-248.
[20] CRUMP K S.Numerical inversion of Laplace transforms using a Fourier series approximation[J]. Journal of the ACM, 1976, 23(1): 89-96.