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ABSTRACT
The accurate calculation for heat flux of borehole heat exchanger (BHE) is of great importance for design of ground source heat pump (GSHP); the climatic conditions influence GSHP performance through GHE. In this study, a 2-D heat transfer model for coaxial BHE was built to investigate the effects of multi-climatic parameters on BHE heat transfer and GSHP performance. The outlet temperature, ground temperature profiles and COP of GSHP system for the cooling period were concerned. The effects of climatic conditions under different borehole depths, ground thermal conductivities and flow rates were studied. The studies showed that the outlet temperature from BHE increased about 10% and system COP declined about 5% in cooling mode with considering the effect of climatic conditions. The comparison indicates that the effects of climatic conditions on coaxial BHE are stronger than that on U-tube BHE. Generally, the climatic conditions influence BHE heat transfer mainly through the shallow ground and the influences strengthen with time. The effects can be more significant with a larger ground thermal conductivity, but it weaken with increase of borehole depth. Also, the effects of climatic conditions on BHE and GSHP seem to be independent of flow rate.
Acknowledgments
The authors gratefully acknowledge the National Natural Science Foundation of China for the financial support (grant no. 52006211) and Key Technologies Research and Development Program of Anhui Province (grant no. 202004a07020053) financial support.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Nomenclature
| Variables | = | |
| A | = | area of pipe, m2 |
| d | = | diameter, m |
| f | = | fitness function |
| h | = | convective heat transfer W m−2 K−1 |
| Jdn | = | direct solar radiation, W m−2 |
| Jsh | = | sky radiation, W m−2 |
| L | = | borehole depth, m |
| M | = | number of horizontal grids |
| N | = | number of layers |
| Q | = | heat flux to ground, W |
| Q12 | = | heat flux from inner pipe to outer pipe, W |
| Qa | = | heat flux to the ground surface per unit area, W m−2 |
| Qhc | = | heat flux by heat convection per unit area, W m−2 |
| Qsky | = | heat flux by sky radiation per unit area, W m−2 |
| Qsol | = | heat flux by solar radiation per unit area, W m−2 |
| Qsur | = | heat flux f by surface radiation per unit area, W m−2 |
| Rb | = | borehole thermal resistance, m K W−1 |
| R12 | = | thermal resistance of inner pipe, m K W−1 |
| r1 | = | inner radius of inner pipe, m |
| r2 | = | outer radius of inner pipe, m |
| r3 | = | inner radius outer pipe radius, m |
| r4 | = | outer radius outer pipe radius, m |
| rb | = | radius of borehole, m |
| T0 | = | initial earth temperature,°C |
| T | = | temperature,°C |
| v | = | fluid velocity, m/s |
| w | = | mass flow rate, kg/s |
| Xd | = | tube spacing of U-tube BHE, m |
| z | = | vertical coordinate, m |
| ∆t | = | time interval, s |
| ∆ri | = | space interval in z-direction, m |
| Greek letters | = | |
| α | = | thermal diffusivity, m2 s−1 |
| ε | = | convergence criterion |
| θ | = | solar altitude, deg |
| λ | = | thermal conductivity, W m−1 K−1 |
| ρc | = | volumetric heat capacity, J m−3 K−1 |
| σ | = | Stephen–Boltzmann constant |
| τ | = | time, h |
| Subscripts | = | |
| 1 | = | inner pipe |
| 2 | = | outer pipe |
| a | = | ambient |
| b | = | borehole |
| c | = | cooling |
| f | = | fluid |
| g | = | grout |
| h | = | heating |
| p | = | pipe |
| s | = | ground |
| sur | = | ground surface |
| w | = | borehole wall |
| in | = | inlet of BHE |
| out | = | outlet of BHE |
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