The first part of a heating trace can reveal a local difference before heat has spread widely. That advantage comes with a constraint: the temperature slope depends on the region’s effective heat capacity as well as the heat input. Comparing unmatched regions can therefore misidentify the source of a faster rise.
For a simplified lumped region, C dT/dt = P − Q_out. C is effective heat capacity in joules per kelvin, P is heat input in watts, and Q_out is net heat leaving in watts. If Q_out is small over a justified initial interval, the slope approximates P/C. The approximation requires a defined region and a suitable thermal response.
Define when the source begins
Record actual excitation through its ramp. Time zero should correspond to a known source history, rather than the camera’s first frame. If background loss changes gradually, a slope during that ramp does not represent constant heating.
Preserve initial temperature and prior cooling history. A previously heated region can have a different internal temperature distribution even when its surface looks similar to the reference.
| Window check | Observation | Reason to revise the interval |
|---|---|---|
| Excitation onset | Measured electrical or magnetic history | Source still changing |
| Camera response | Timing and radiometric stability | Instrument response dominates slope |
| Local thermal boundary | Geometry and neighboring temperatures | Heat transfer is no longer negligible |
| Effective heat capacity | Comparable sampled material and volume | Regions are thermally unmatched |
| Repeat trials | Slope variability | Difference is not resolved reproducibly |
The selected interval should satisfy the comparison’s assumptions, not merely contain the straightest-looking line.
Compare regions with known thermal differences
An edge, clamp contact and interior surface can have different heat capacities and paths to surrounding material. If the diagnostic comparison uses them, include those differences in the model or choose a better-matched reference.
For a buried source, surface temperature may lag the source. An early surface slope can then be governed by heat arrival rather than initial local generation. A known-depth reference or a validated thermal model is needed before converting it to source power.
Check the slope’s stability against the fitting interval
Fit several justified adjacent windows and examine how the estimated slope changes. Large sensitivity can indicate a ramp, diffusion, camera artifact or an overly short noisy interval. Retain the raw time trace and the selected window in the record.
Emissivity and reflections remain relevant even when only a slope is used. If a reflection changes during the excitation sequence, the apparent slope can be unrelated to specimen heating. Verify surface and viewing conditions with an appropriate control. [1]
The result should report a thermal slope under its actual source and boundary history. When the P/C approximation is demonstrated, it can support a relative heating comparison. When it is not, the trace remains useful evidence of a differing thermal response, but it should not be presented as a direct wattage measurement of a lamination fault.
Compare slopes using catalogue-based steel mass
Catalogue nominal thickness is 0.23 mm and assumed density 7,650 kg/m³ [2]. Assume region A contains 20 sheets and region B 40 sheets, each 100 × 100 mm, with equal specific heat 500 J/(kg·K) and negligible initial heat outflow. Masses are 0.3519 and 0.7038 kg. Assumed slopes of 0.020 K/s and 0.010 K/s both imply 3.519 W from P = mc dT/dt. The twofold slope difference therefore does not show different heating. Use matched regions or quantify effective heat capacity, onset and outflow; propagate mass and fitted-slope uncertainty [3] before calling a slope change a fault-power change.
Manufacturing controls. Layer count, local thickness, coating contact, clamp heat sinking and duct geometry control thermal mass and heat escape. A visible surface region may sample less or more material than its geometric footprint suggests; validate the effective volume over the chosen interval.
References
- Deisenroth, D. C. et al., Measurement Uncertainty of Surface Temperature Distributions for Laser Powder Bed Fusion Processes, Journal of Research of NIST 126, 126013, 2021, sections 1.5 and 2.1; DOI: 10.6028/jres.126.013.
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je_03_202004, 2020, Specifications; Size and Form Tolerances.
- JCGM, JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement, 2008.