Effect of Temperature-Dependent Thermal Conductivity on Spreading Resistance in Flux Channels
Bibliographic record
Abstract
When the thermal conductivity of a material varies with temperature, the governing heat conduction equation becomes nonlinear and the use of constant thermal conductivity may produce unreliable results in thermal analysis. In this paper, analytical solutions for the temperature distribution and thermal resistance of a three-dimensional flux channel with temperature-dependent thermal conductivity are discussed and used to study the effect of the temperature-dependent thermal conductivity on the temperature rise and thermal spreading resistance for different conductivity functions. A single eccentric heat source is considered in the source plane of the flux channel that spreads the heat into a convective heat sink. The analytical solutions of the problem are illustrated by means of the Kirchhoff transform, which is considered a powerful technique for solving nonlinear conduction problems with temperature-dependent thermal conductivity. For validation purposes of the analytical results, the results are compared with numerical solution results obtained by solving the problem based on the finite element method using the ANSYS commercial software package.
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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 | 0.001 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".