Effects of varying heat transfer rates for borehole heat exchangers in layered subsurface with groundwater flow
Bibliographic record
Abstract
The existence of groundwater flow adds a convective heat component to shallow geothermal heat pump systems, significantly improving heat transfer efficiency. Numerous analytical and numerical methods have been proposed to assess the impact of groundwater flow on ground heat exchangers. However, numerical simulations often require significant resources and time, while conventional analytical solutions overlook the time and depth-varying heat transfer rates, leading to inaccurate temperature predictions. This study proposes a computationally efficient semi-analytical solution by extending the line source solution and coupling it with a thermal resistance model. This approach addresses variations in heat transfer rate over time and depth, overcoming the limitations of conventional analytical solutions. Compared to a three-dimensional numerical model constructed in COMSOL Multiphysics, the average absolute percentage error (MAPE) of borehole wall temperatures for a U-shaped borehole heat exchanger (BHE) is approximately 1 %, across a wide range of water flow velocities and thermal conductivity ratios between two contacting geological layers. A significant advantage of the proposed solution is its computational efficiency. The proposed solution can complete long-term simulations with over 9,000 time steps in about 10 min, as opposed to numerical models that typically require several hours. The excellent computational efficiency and substantial accuracy make the proposed solution a simple and effective tool for the design and optimization of BHEs in engineering applications.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".