Table 2.
Comparison of the heat transfer models for iron, the most studied of the elemental particles
| Property | Starke [91]‡ | Kock [58] | Eremin–Gurentsov [59, 71, 74, 97, 99] |
Sipkens–Singh [60, 61] |
Sipkens–Hadwin [73]* |
|---|---|---|---|---|---|
|
Density, ρ (kg/m3) |
7700 | 7700 |
8200–0.6 T/K Ref. [97] uses 7700 |
8171–0.650 T/K [124] | 8171–0.650 T/K [124] |
|
Specific heat capacity, cp (J/kg·K) |
650 [125] | 824 [125] | f(T), piecewise smooth [125] | 835 [123] | f(T), piecewise linear [123] |
| Thermal accommodation coefficient, α | 0.33 (Ar) |
0.13 (Ar) 0.13 (N2)† |
0.01 (He) 0.1 (Ar) 0.13 (CO) |
Typically inferred in a specific study | 0.236 (Ar) |
|
Eq. degrees of freedom, (4 + ζint) |
4 (only Ar) | 4† | (1 – γ) / (1 + γ) | 4 + ζint | 4 (only Ar) |
|
Heat of vaporization, ΔHv (kJ/mol) |
– | 375.8 | 375.8 | Watson eq | Román eq |
| Vapor pressure, pv (kPa) | – |
Clausius–Clapeyron eq pref = 3.337 kPa Tref = 2500 K [96] |
Clausius–Clapeyron eq pref = 3.337 kPa Tref = 2500 K [96] Ref. [71] includes Kelvin eq |
Clausius–Clapeyron eq pref = 101.3 kPa Tref = 3134 K ΔHv,ref = 6090 kJ/mol [126], includes Kelvin eq |
Clausius–Clapeyron eq pref = 101.3 kPa Tref = 3073 K ΔHv,ref = 6571 kJ/mol [126], includes Kelvin eq |
| Surface tension, [N/m] | – | – | 2.40–2.85 · 10–4 T/K [127] | f(T) [128]i | 1.865 [128] |
Temperatures are in Kelvin. The surface tension contributes to the evaporation submodel whenever the Kelvin equation is implemented for the vapor pressure. Equivalent (eq.) degrees-of-freedom refers to the quantity (4 + ζint) in Eq. (17). The quantity γ, relevant to the Eremin–Gurentsov model, refers to the ratio of the specific heat capacities of the gas, whose value was not explicitly stated in those works. Thermal accommodation coefficients were typically inferred and then used in subsequent studies
†Note that in the absence of accounting for the internal degree of freedom for N2, the Kock model thermal accommodation coefficient will not match the corresponding physical quantity (correction results in α = 0.09)
‡Starke model was developed only for low fluences
*Sipkens–Hadwin model is the optimal model of those presented in that work, as chosen via Bayesian model selection
if(T) = 1.865 – (T/K – 1823) · 0.35 · 10−3