Analytical Solution of Heat Pulse Method in a Parallelepiped Sample Space with Inclined Needles
Bibliographic record
Abstract
The heat pulse method enables estimation of soil thermal diffusivity ( k ), volumetric heat capacity ( C ), thermal conductivity, and water content. The heater needle and temperature‐sensing needle may deflect during probe insertion into soils. The impact of needle deflection on estimates of C and k has not been fully studied theoretically or experimentally. We defined θ to be the polar angle of needle deviation from the z axis and φ to be the azimuthal angle in the x–y plane. Transient‐state analytical solutions were derived for an inclined and pulsed finite line source in a parallelepiped sample with zero surface temperature and adiabatic boundary conditions. For a heat pulse sensor with 6‐mm needle spacing and a heater needle of 4‐cm length in a given parallelepiped (5 by 5 by 5 cm, assumed to be filled with air‐dry sand), model errors in C and k were about −11.3 and 12.1%, respectively, for an inclined heater needle with θ = 1° and φ = 0°. Model errors in C and k were about −11.2 and 12.1%, respectively, for an inclined sensor needle with θ = 1° and φ = 180°. When −6 ≤ θ ≤ 6° for either the heater or the sensor needle, the temperature curves could be approximated rather well by a pulsed infinite line source model with a modified probe spacing that accounted for the inclination. For various heating durations and strengths, the errors in both k and C were relatively constant when all other parameters were fixed; however, the errors in both C and k decreased monotonically and slowly as k increased. The model errors in C and k were similar for four soil conditions with different thermal properties in the range −6 ≤ θ ≤ 2°.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".