On the objective rate of heat and stress fluxes. Connection with micro/nano-scale heat convection
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Bibliographic record
Abstract
In this paper, the derivation of the convected derivatives for the heat fluxand stress tensor is revisited. A kinematic approach is adopted based onmaterial invariance. These upper-convected derivatives are used in theliterature to generalize Newton's law of viscosity and Fourier's heat law ofheat. The former constitutive law represents the behaviour of a viscoelasticfluid of the Boger type obeying the Oldroyd-B model, and the latterrepresents fluids obeying the Maxwell-Cattaneo's heat equation. Theinvariance of the derivatives under orthogonal transformation is also shown.Although the presentation here is limited to the derivatives of vector andsecond-rank tensor fluxes, the formulation can be generalized to generatethe convected derivative of a tensor flux of arbitrary rank. Finally, theconnection with micro- or nano-channel flow is noted.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it