Nonlinear thermal convection of a non-Fourier fluid
Bibliographic record
Abstract
Purpose – The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike existing methodologies, the spectral modes are not imposed arbitrarily. They are systematically identified by expanding the spectral coefficients in terms of the relative departure in the post-critical Rayleigh number (perturbation parameter). The number and type of modes is determined to each order in the expansion. Non-Fourier effects become important whenever the relaxation time (delay in the response of the heat flux with respect to the temperature gradient) is of the same order of magnitude as process time. Design/methodology/approach – In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A perturbation approach is developed to solve the nonlinear spectral system in the post-critical range. Findings – The Nusselt number increases with non-Fourier effect as suggested in experiments in microscale and nanofluid convection. Originality/value – Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.001 | 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 teacher head, 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".