# Table 1 Empirical models used for thermo-physical properties modelling

Property Model
Gas phase heat capacity (Ragland et al. 1991) $$C_{p,g} \left( {T_{g} } \right) = 990 + 0.122T_{g} - 5680T_{g}$$ (J/kg K)
Solid phase heat capacity (Jurena 2012) $$C_{p,wet} = \frac{{C_{p,dry} + 4.19M}}{1 + M} + A$$ (kJ/kg K)
$$A = \left( {0.02355T - 1.32M - 6.191} \right)M$$
$$C_{p,dry} = 0.1031 + 0.003867T$$
Porosity (Wakao and Kaguei 1982) $$\varepsilon_{0} = \frac{{V_{g} }}{V}$$
$$\varepsilon = \varepsilon_{0} + \left( {1 - \varepsilon_{0} } \right)\mathop \sum \nolimits_{i} f_{i} \left( {Y_{i,0} - Y_{i} } \right)\varepsilon_{0} = 0.5$$
i-char, volatile
Gas phase density 1.3 (kg/m3)
Solid phase density 500 (kg/m3)
Kinematic viscosity $$v = 1.523$$
Effective thermal conductivity of the bed (Ragland et al. 1991; Wakao and Kaguei 1982; Jasak 1996) $$\lambda_{e} = \lambda_{e,0} + aPrRe\lambda_{g}$$ (W/mK)
a = 1 along the bed, 0.5 along bed height
Emissivity 0.9
Gas phase diffusion coefficient (Ragland et al. 1991; Wakao and Kaguei 1982; Jasak 1996; Jasak 1996) $$D_{i,e} = D_{i,0} + ad_{p} \left| {v_{g} } \right|$$ (m2/s)
For temperature < 100 K and Pmax = 70 atm
$$D_{AB} = \frac{{\left( {0.0027 - 0.0005M_{AB} } \right)T^{3/2} M_{AB}^{1/2} }}{{P\sigma_{AB}^{2} \varOmega_{D} }}$$
$$\sigma_{AB} = \frac{{\sigma_{A} + \sigma_{B} }}{q}$$ (Å) $$\varOmega_{\text{D}} = \left( {44.54T^{0 - 4.909} + 1.911T^{0 - 1.575} } \right)^{0.1}$$
$$T^{0} = kT/\varepsilon_{AB} \varepsilon_{AB} = \left( {\varepsilon_{A} \varepsilon_{B} } \right)^{1/2}$$
$$M_{AB} = \left[ {\left( {1/M_{A} } \right) + \left( {1/M_{B} } \right)} \right]^{ - 1}$$
Solid phase diffusion coefficient (Patankar 1980) 1.4833 × 10−6 (m2/s)
Fuel particle properties
Diameter of particle Assuming; $$\frac{surface\;area}{volume} = 240\left( {\text{constant}} \right)$$
$$d_{p} = \frac{{6\left( {1 - \varepsilon_{b} } \right)}}{240} = 0.025\left( {1 - \varepsilon_{b} } \right)$$ (m)