A Finite Difference Thermal Model of a Cylindrical Microwave Heating Applicator Using Locally Conformal Overlapping Grids: Part I-Theoretical Formulation
Bibliographic record
Abstract
In this paper, we present a versatile mathematical formulation of a newly developed 3-D locally conformal Finite Difference (FD) thermal algorithm developed specificallyfor coupled electromagnetic (EM) and heat diffusion simulations utilizing Overlapping Grids (OGFD) in the Cartesian and cylindrical coordinate systems. The motivation for this research arises from an attempt to characterize the dominant thermal transport phenomena typically encountered during the process cycle of a high-power, microwave-assisted material processing system employing a geometrically composite cylindrical multimode heating furnace. The cylindrical FD scheme is only applied to the outer shell of the housing cavity whereas the Cartesian FD scheme is used to advance the temperature elsewhere including top and bottom walls, and most of the inner region of the cavity volume. The temperature dependency of the EM constitutive and thermo-physical parameters of the material being processed is readily accommodated into the OGFD update equations. The time increment, which satisfies the stability constraint of the explicit OGFD time-marching scheme, is derived. In a departure from prior work, the salient features of the proposed algorithm are first, the locally conformal discretization scheme accurately describes the diffusion of heat and second, significant heat-loss mechanisms usually encountered in microwave heating problems at the interfacial boundary temperature nodes have been considered. These include convection and radiation between the surface of the workload and air inside the cavity, heat convection and radiation between the inner cavity walls and interior cavity volume, and free cooling of the outermost cavity walls.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".