Temperature Fields Generated by a Circular Heat Source: Solution of a Composite Solid of Two Different Isotropic Semi-Infinite Media
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Bibliographic record
Abstract
Abstract The problem of a three-dimensional (3D) heat flow from a circular heat source (CHS) embedded inside a composite solid of two isotropic but different semi-infinite media is solved for the first time in this paper. This CHS asymmetrical measurement setup is useful when two identical samples are not available for measurement. Two different time-dependent temperature fields are derived for the composite semi-infinite media, as well as their corresponding heat fluxes. The derivation of the 3D solution uses first principles with basic assumptions and employs the Hankel and Laplace transforms. The Laplace inversion theorem is used to find the inverse Laplace transform of the temperature functions, since no tabulated inverse transform functions are available for this case. The solution is exact with no approximations and is given in an integral form, which can easily be evaluated numerically. This solution is a generic one and can be applied to more complex asymmetrical setups, such as the case involving thermal contact resistances.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it