The surface of a thick pressboard part can dry while its centre remains wetter. Heating and chamber pressure set removal boundaries; water must still travel from the interior. Betie and colleagues describe the one-dimensional Fick model and its constant-diffusivity slab solution [1].
Use thickness to identify the difficult part
For a simple homogeneous slab, a diffusion model is ∂c/∂t = D∂²c/∂x², where c is moisture content on a consistent kg-water/kg-dry-material basis for this homogeneous illustration, x distance in metres, time t seconds and D diffusivity in m²/s. A characteristic time scales with ℓ²/D, where ℓ is the relevant travel distance to an exposed surface.
At unchanged D and boundary conditions, doubling that distance increases the characteristic scale fourfold. This illustrates thickness sensitivity; it is not a factory cycle-time rule. Real D can depend on temperature and moisture, and a covered face can change the travel distance from half thickness to an edge path.
An oil or gas observation cannot resolve the centre concentration in the unequilibrated slab below. Preserve the solid-material sampling region and its temperature when comparing moisture evidence. [2]
Recompute the thickness time scale
For an independent ideal slab calculation, assume uniform initial moisture 2.0% of dry mass, both broad surfaces instantly held at 0.10%, fixed temperature and constant D = 1×10⁻¹⁰ m²/s. At t = 10,000 s, half-thickness ℓ = 1 mm gives Fo = Dt/ℓ² = 1; ℓ = 2 mm gives Fo = 0.25. The centre solution is (c−cs)/(c0−cs) = (4/π)Σ[(-1)ⁿ/(2n+1)]exp[−(2n+1)²π²Fo/4]. Summing the series gives centre moisture 0.305% and 1.402%. Against an assumed 0.50% centre criterion, only the thinner slab passes this ideal screen although both surfaces read 0.10%. At 40,000 s the thicker slab reaches the same 0.305%. Validate D, actual temperature/moisture dependence and exposed paths before setting a factory duration.
Compare measurements by depth and boundary
| Evidence | What it describes | What remains unresolved |
|---|---|---|
| Surface temperature | Accessible thermal boundary | Centre temperature during heating or evaporation |
| Chamber pressure/dew point | Gas removal environment at the sample point | Moisture remaining deep in pressboard |
| Thin witness coupon | That coupon’s removal response | Thicker or shielded component response |
| Representative internal evidence | Defined depth or validated model estimate | Other geometries outside the demonstrated scope |
Identify the thickest and most shielded insulation in the load, not just the largest visible part. Record whether its broad faces are exposed, clamped or bonded. Those boundaries can matter as much as nominal thickness.
References
- A. Betie, F. Meghnefi, I. Fofana and Z. Yeo, Modeling the Insulation Paper Drying Process from Thermogravimetric Analyses, Energies 11, 517, 2018, section 2. DOI: 10.3390/en11030517.
- S. R. Arsad et al., Water Content in Transformer Insulation System: A Review on the Detection and Quantification Methods, Energies 16, 1920, 2023. DOI: 10.3390/en16041920.