Natural convection of nanofluids in a shallow rectangular enclosure heated from the side
Bibliographic record
Abstract
Abstract This article reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure while the two horizontal ones are assumed insulated. Three types of nanoparticles are taken into consideration: Cu, Al 2 O 3 and TiO 2 . Various models are used for calculating the effective viscosity and thermal conductivity of nanofluids. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity, A and the solid volume fraction of nanoparticles, Φ. In the first part of the analytical study a scale analysis of the present problem is made. In the second part analytical solutions are obtained, in the limit of an infinite layer ( $A\gg 1$ ), for the stream function and temperature fields. The analytical model relies on the assumption of a parallel flow approximation in the core region of the cavity and an integral form of the energy equation in the end regions. In the high Rayleigh number regime a good agreement is obtained between the predictions of the scale analysis and those of the analytical solution. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations based on the lattice Boltzmann method. Cet article présente une étude analytique et numérique de la convection naturelle dans une cavité rectangulaire peu profonde remplie de nanofluides. Les conditions aux limites de Neumann pour la température sont appliquées sur les parois verticales de l'enceinte tandis que les deux parois horizontales sont supposées isolées. Trois types de nanoparticules sont pris en considération: Cu, Al 2 O 3 et TiO 2 . Divers modèles sont utilisés pour le calcul de la viscosité et la conductivité thermique effective du nanofluide. Les paramètres régissant le problème sont le nombre de Rayleigh thermique, Ra, le nombre de Prandtl Pr, le facteur de forme de la cavité, A et la fraction volumique de nanoparticules solides, phi. Dans la première partie de l'étude analytique une analyse d'échelle du problème est réalisée. Dans la deuxième partie les solutions analytiques sont obtenues, dans la limite d'une couche infinie, pour la fonction de courant et les champs de température. Le modèle de la solution repose sur l'hypothèse de l'écoulement parallèle dans la région centrale de la cavité et sur un bilan de conservation d'énergie dans les extrémités. Pour des nombres de Rayleigh assez élevés un bon accord est obtenu entre les prédictions de l'analyse d'échelle et ceux de la solution analytique. Des solutions numériques des équations complètes sont obtenues pour une large gamme des paramètres de contrôle. Un bon accord est observé entre le modèle analytique et les simulations numériques basées sur la méthode de Lattice Boltzmann. © 2011 Canadian Society for Chemical Engineering
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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 | 0.001 |
| 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".