▎ Closed-form universal drying curves and quantified discretization-failure boundaries for super-exponentially ▎ vanishing moisture diffusivity in shrinking cylinders: Kirchhoff theory and an exact-Newton finite-volume scheme

Version 2 of the code and data for the manuscript "Closed-form universal drying curves and quantified discretization-failure boundaries for super-exponentially vanishing moisture diffusivity in shrinking cylinders: Kirchhoff theory and an exact-Newton finite-volume scheme" (submitted to the International Journal of Heat and Mass Transfer). This version adds the revision package (revision_v2/): - Closed-form Kirchhoff theory: exact Kirchhoff potential Phi(X) = D0·[X·exp(−a/X) − a·E1(a/X)] with the Lambert-W inverse X = a/[2W(½√(D0·a/Phi))]; Robin-to-Dirichlet boundary degeneracy (Bi_eff → ∞, fundamental eigenvalue → 2.4048); parameter-free universal drying curve in the Kirchhoff time τ = ∫F/R²dt, verified against an 18-case finite-volume matrix; eigenvalue shift B(φ) derived from a nonlinear eigenproblem. - Exact-Newton Kirchhoff finite-volume solver with analytical residual and Jacobian (quadratic convergence; reproduces the baseline t* = 129.10 h). - Failure phase maps: harmonic-mean stagnation in the (a, X_eq) plane with a closed-form criterion; Crank–Nicolson positivity boundary. - Corrected material-constant refit against 18 published drying curves of three medicinal herbs (median RMSE 0.083). The corrected values supersede the earlier refit deposited in version 1 (retained there for provenance). Headline results: universal drying-time prediction within +2.6 % of the finite-volume reference (isothermal, zero fitted parameters); the 2.5-fold shrinkage effect (129.10 h vs 50.82 h) explained by the R(t)⁻² weighting of the Kirchhoff time; analytical sensitivities matching the simulated ones (+32.2 % predicted vs +27.9 % simulated for a0.02 kg/kg target tightening).