Bounding of Effective Thermal Conductivity of Two-Phase Materials
Bibliographic record
Abstract
In this paper, we propose a new approach to obtain the upper and lower bounds for the effective thermal conductivity of real two-phase systems. The developed expressions are based upon the series and parallel combination of resistors. To incorporate the effect of random distribution of inclusions in the continuous matrix as well as the wide difference in the thermal conductivity of the constituents, a non-linear second-order correction term is introduced. This correction term is used to replace the volume fraction of inclusions in parallel and perpenducular thermal conductivity equations. The obtained upper and lower bounds are then compared with the Hashin and Shtrikman bounds [ and it is found that the modified bounds are narrower as compared to other previously developed bounds for effective thermal conductivity. The modified upper and lower bounds are then used in Chaudhary and Bhandaris model to predict the effective thermal conductivity of real two-phase materials. The predictions of the effective thermal conductivity using the modified relations match well with the experimental results.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".