2. Nomenclature

This is the single, authoritative symbol table for the Pyrolysis.jl Technical Reference Guide and User Guide. Every writer MUST conform to these symbols, meanings, and SI units verbatim. Where a symbol is used differently in different source subsystems, the conflict has been resolved here and the resolution is binding. Conflicts and overloads are called out explicitly in the "Overloaded / reserved symbols" section at the end.

Conventions:

• The spatial coordinate is z (axial, through-thickness). z = 0 is the bottom / substrate (boundary id 2, tag :bottom); z = L is the top / exposed surface (boundary id 1, tag :top). Heat enters from the top; the material shrinks downward. The transverse/lateral plane carries the cross-sectional area A.
• Sign convention for fluxes: positive flux = transport in the +z direction (bottom → top). Divergence (F_R − F_L)·A/V is positive when the quantity flows out of a cell.
• Heat-of-reaction sign convention: h > 0 endothermic (cools), h < 0 exothermic (heats); the volumetric heat source is Q_rxn = −Σ h_r r_r, so endothermic reactions give Q_rxn < 0. (This is the storage convention used internally; note ThermaKin/Gpyro publish h > 0 = exothermic — see overload note H1.)
• "Bulk" density ρ_j is the pure-phase density used by mixing rules and mixture density; "intrinsic/skeletal" density ρ_{i,j} (cell-wall density) is used ONLY in the porosity formula.
• Mass concentration ξ_j (kg/m³) is the primary species state variable, not mass fraction. ξ_j = Y_j ρ.

1. Latin letters

2. Greek letters

3. Subscripts

4. Superscripts and accents

5. Operators

6. Physical constants (fixed values)

7. Overloaded / reserved symbols — resolutions (BINDING)

These symbols are overloaded somewhere in the source subsystems. The resolution below is authoritative; writers must use the disambiguating subscript/context.

• χ (chi) — A1 [pyrolysis progress vs. cross-section ratio]. The volume_change, problem_residual, and geometry subsystems define χ as the pyrolysis progress (dimensionless, cumulative dry-gas mass released per unit initial dry-solid mass). The jacobian KB once glosses it as "cross-section area ratio." Resolution: χ is always pyrolysis progress; the cross-section ratio is A/A_0 = law(χ̄) and is never written as χ.

• θ (theta) — A2 [strain rate vs. stoichiometry]. Internally θ is the volumetric strain rate (s⁻¹), with θ_A radial and θ_L axial. ThermaKin uses θ_i^j for stoichiometric coefficients. Resolution: use ν_{i,j} for stoichiometry everywhere; reserve θ for strain rate. θ_i^j appears only in the ThermaKin-comparison passage and is immediately mapped to ν_{i,j}.

• A — A3 [area vs. pre-exponential factor]. A is the cross-sectional area; the Arrhenius pre-exponential is A_i / A_{αβ} (always subscripted by reaction). In Jacobian/linear-algebra context A also denotes the sparse Jacobian block. Resolution: bare A = area in physics chapters; A_i = pre-exponential (kinetics); A (linear algebra) only inside the Jacobian chapter where the meaning is unambiguous and stated. The FDS/Gpyro pre-exponential Z is mapped to A_i on first use.

• κ vs. K — A4 [permeability]. Use κ for permeability throughout. K (Gpyro permeability) appears only in comparison text and is mapped to κ.

• α — A5 [absorption vs. conversion vs. heat-transfer]. α (or α_eff) = volumetric absorption coefficient (m⁻¹); α_j = mass-basis absorption coefficient (m²·kg⁻¹). Conversion (Gpyro) is α_conv; FDS κ_s maps to α. The mass-transfer "absorptivity" of a surface is also α but always paired with a BC context and Kirchhoff α = ε_eff.

• λ — A6 [gas transfer vs. anything else]. λ is reserved for the gas transfer (diffusion) coefficient (m²·s⁻¹). Do not use λ for thermal conductivity (that is k) or eigenvalues.

• ρ subscripts — A7 [bulk vs. intrinsic]. ρ_j = bulk density (mixing, mixture density); ρ_{i,j} = intrinsic/skeletal density (porosity only). Never write a bare ρ_i for skeletal density without the explicit "intrinsic" qualifier; prefer ρ_{i,j}.

• h — H1 [heat of reaction; sign]. h (kinetics) = heat of reaction per kg of first reactant, with h > 0 endothermic internally; ThermaKin/Gpyro publish h > 0 = exothermic. The conversion to the volumetric source carries the minus sign: Q_rxn = −Σ h_r r_r. The convective coefficient is h_conv, the mass coefficient h_m, the pressure coefficient h_P, all subscripted.

• i — I1 [cell index vs. reaction index]. i is the cell index in discretization/geometry/ALE; in the kinetics chapter i is the reaction index (with j the component index). Each chapter states its convention in its first paragraph. Where both appear together, use i = cell, r = reaction.

• φ — A8 [porosity only]. φ is porosity; do not reuse for view factor (that is F) or any potential. Two historical porosity definitions exist (volume-fraction Σ v_j^gas vs. intrinsic-density 1 − Σ ξ_j/ρ_{i,j}); the intrinsic-density form is canonical and is what φ denotes.

• S — S1 [source vs. Sutherland constant]. S with a subscript (S_conv, S_gen, S_rad, S_j) is a source term; bare S is the Sutherland constant in the viscosity law only.