Analytical Solutions for Transient Thermal Spreading Resistance of a 3-D Flux Channel
Bibliographic record
Abstract
In microelectronic devices, the moment a high-power current is transmitted into the system, heat is simultaneously generated, and the thermal field keeps developing until it reaches a steady-state field after a period of time. In this work, transient analytical solutions for the temperature field and thermal resistance of a rectangular 3-D flux channel are obtained. The flux channel is assumed to have a small heat source on the top surface, whereas convective effects are considered on the bottom surface and lateral edges. The time-dependent solutions are presented explicitly as infinite Fourier series forms. In addition, the solutions are also presented in dimensionless forms as generalized solutions. Moreover, an existing, well-established simple model that represents the profile of the transient thermal spreading resistance for a semi-infinite flux tube is used to verify the presented forms of the analytical solutions, and the results compare very well when considering a flux channel of large thickness. Further, the solutions are used to study the behavior of temperature and thermal resistance over time for some dimensional and nondimensional problems.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".