Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface
Bibliographic record
Abstract
The boundary layer heat and mass transfer of nanofluids over an isothermal stretching sheet is analyzed using a drift-flux model. The relative slip velocity between the nanoparticles and the base fluid is taken into account. The nanoparticles’ volume fractions at the surface of the sheet are considered to be adjusted passively. The thermal conductivity and the dynamic viscosity of the nanofluid are considered as functions of the local volume fraction of the nanoparticles. A non-dimensional parameter, heat transfer enhancement ratio, is introduced, which shows the alteration of the thermal convective coefficient of the nanofluid compared to the base fluid. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using the fourth-order Runge–Kutta and Newton–Raphson methods along with the shooting technique. The effects of six non-dimensional parameters, namely, the Prandtl number of the base fluid Prbf, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, variable thermal conductivity parameter Nc and the variable viscosity parameter Nv, on the velocity, temperature, and concentration profiles as well as the reduced Nusselt number and the enhancement ratio are investigated. Finally, case studies for Al2O3 and Cu nanoparticles dispersed in water are performed. It is found that increases in the ambient values of the nanoparticles volume fraction cause decreases in both the dimensionless shear stress f″(0) and the reduced Nusselt number Nur. Furthermore, an augmentation of the ambient value of the volume fraction of nanoparticles results in an increase the heat transfer enhancement ratio hnf/hbf. Therefore, using nanoparticles produces heat transfer enhancement from the sheet.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.001 |
| 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 source (direct Gemma or distilled Codex), 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".