Analytical investigation of temperature‐dependent thermal conductivities in functionally graded conical shells: General thermal boundary conditions
Bibliographic record
Abstract
Abstract This investigation, for the first time, analytically provides a solution for steady‐state heat conduction in 2D functionally graded conical shells under general boundary conditions (BCs). The material properties vary in both angular and longitudinal directions according to an arbitrary power‐law function of the longitudinal variable. Furthermore, the thermal conductivity coefficients are assumed to be linearly dependent on temperature, providing a more realistic understanding of heat transfer in functionally graded materials (FGMs). To derive the temperature distribution, this study employs the Kirchhoff transformation, the finite integral transform, and Green's function. An excellent agreement is observed when comparing the results of the present study with available analytical data. To demonstrate the practical applicability of the solution in various industrial scenarios, such as cooling pin fins and spacecraft heat shields, a typical industrial case is analyzed. Additionally, the effects of different parameters on the temperature distribution are studied.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 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 | 0.000 |
| 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 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".