Stability Analysis of Magnetoconvection in a Fluid-Porous System with Thermal Effects
Bibliographic record
Abstract
This study investigates the linear and nonlinear stability analysis of thermal convection in a fluid layer overlying a highly porous material, subjected to a vertical magnetic field and maintained at a constant wall temperature.A two-layer approach is adopted, where the Darcy-Brinkman model is used to describe fluid flow within the porous medium.The influence of the magnetic field on both linear and nonlinear stability is analysed.The Chebyshev-Tau-QZ spectral method is employed to solve the coupled ordinary differential equations, formulated as an eigenvalue problem.This approach is particularly advantageous for fluid-porous convection problems due to its high accuracy.Nonlinear stability analysis is conducted using the energy method, and the results are validated against existing literature.The magnetic field shows stabilizing effect and with increase in depth ratio also revealed stabilizing effect.The findings of this study have significant applications in geophysical fluid dynamics, magnetohydrodynamics, and industrial processes such as thermal insulation, cooling systems, and crystal growth, where heat transfer in porous-fluid systems plays a critical role.
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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 | 0.000 | 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 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".