Combined Impact of Temperature-Dependent Heat Source and Gravity Fluctuation on the Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer
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Bibliographic record
Abstract
This paper investigates the combined influence of temperature-dependent heat sources and gravitational fluctuations on the onset of double-diffusive reaction-convection in an anisotropic porous medium. The momentum equation is modelled using the Darcy-Brinkman approach, and linear stability analysis is conducted using normal mode analysis to formulate the eigenvalue problem. Four gravity functions linear, parabolic, cubic and exponential are analysed and the critical Rayleigh numbers for stationary and oscillatory modes are derived using a single-term Galerkin approximation. The results reveal that temperature-dependent heat sources, gravity variations, anisotropy and the Damköhler number significantly affect convection instability thresholds. Notably, exponential gravity fluctuations provide the highest system stability, delaying the onset of convection. These findings offer valuable insights into the stability behaviour of anisotropic porous systems, with applications in optimising geothermal energy systems, industrial heat management, porous media-based chemical reactors, groundwater filtration, subsurface energy storage and thermal insulation systems. Major Findings: The findings revealed that temperature-dependent heat sources and exponential gravity fluctuations delay convection onset, enhancing system stability. Linear, parabolic, and cubic gravity variations promote instability, reducing stability thresholds. Anisotropy amplifies system sensitivity to governing parameters, while the Damköhler number significantly influences instability. Exponential gravity fluctuations emerge as the most stabilizing factor.
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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