## 3 Results  
The purpose of this section is to compare the results obtained through the numerical resolution of the model described in the preceding Section 2 and the experimental data (uniform particle temperature as measured by the two-color pyrometer). Figure 2 gathers the experimental and simulated particle temperatures for the three regulation temperatures of the drop tube furnace. For the regulation temperature of 1100 \({}^{\circ}\)C, Figure 2a shows a very satisfying agreement between the experimental and simulated particle temperatures in the time range 0.25-0.86 s. In this time range, the difference between the maximal experimental (1246 \({}^{\circ}\)C) and simulated (1211 \({}^{\circ}\)C) temperatures is equal to 35 \({}^{\circ}\)C, which represents a relative difference of 2.8%. The times where the maximal temperatures are reached (0.425 s for the experimental curve and 0.404 s for the simulated curve) are very close, the relative difference being equal to 4.9%. The difference between the experimental and simulated temperature curves which is observed before \(t=0.25\) s is due to the fact that the initial condition \(T_{p}(0)=50\)\({}^{\circ}\)C is imposed in the model. The simulated particle temperature rapidly increases from this initial condition to 1050 \({}^{\circ}\)C which is reached at time \(t=0.25\) s. The two-color pyrometer measures a temperature slightly below 1100 \({}^{\circ}\)C inside the drop tube furnace. For the regulation temperature of 1200 \({}^{\circ}\)C, Figure 2b also exhibits a very satisfying agreement between the experimental and simulated particle temperatures in the time range of 0.22-0.62 s. In this time range, the difference between the maximal experimental (1353 \({}^{\circ}\)C) and simulated (1386 \({}^{\circ}\)C) temperatures is equal to 33 \({}^{\circ}\)C, which represents a relative difference of 2.4%. The relative difference between the times corresponding to the maximal temperatures (0.342 s for the experimental curve and 0.310 s for the simulated curve) is equal to 9.4%. \begin{table}
\begin{tabular}{l l l} \hline
**Experimentally Determined Values** & **Calculated Global Values** & **Local Values** \\ \hline \(R_{p}(0)=65\times 10^{-6}\) (m) & \(\rho_{\mathrm{C}}(0)=575.4\times(1-\tau_{\mathrm{asl}}^{0})=434.4\) & \(\rho_{\mathrm{C}}(i,0)=\rho_{\mathrm{C}}(0)=434.4\) (kg.m\({}^{-3}\)) \\  & (kg.m\({}^{-3}\)) & \(\delta m_{\mathrm{C}}(i,0)=\rho_{\mathrm{C}}(i,0)\frac{4\pi}{3}\left(\hat{ \beta}^{-}(i-1)^{3}\right)dr^{3}\) \\ \(A_{\mathrm{C}}(0)=131,800\) (m\({}^{2}\).kg\({}^{-1}\)) & \(m_{\mathrm{ash}}(0)=575.4\times\frac{4}{3}\pi\left(R_{p}(0)\right)^{3}\tau_{ \mathrm{asl}}^{0}\) & \(A_{\mathrm{C}}(i,0)=A_{\mathrm{C}}(0)=131,800\) (m\({}^{2}\).kg\({}^{-1}\)) \\ \hline \end{tabular} \(\delta m_{\mathrm{C}}(i,0)\) being the initial mass of carbon in the volume element \(i\).  
\end{table} 
Table 2: Initial values of the parameters involved in the model. For the regulation temperature of 1300 \({}^{\circ}\)C, Figure 2c, the experimental and simulated particle temperatures again well superimpose in the time range of 0.21-0.85 s. In this time range, the difference between the maximal experimental (1413 \({}^{\circ}\)C) and simulated (1505 \({}^{\circ}\)C) temperatures is equal to 91 \({}^{\circ}\)C, which represents a relative difference of 6.4%. The relative difference between the times corresponding to these maximal temperatures (0.290 s for the experimental curve and 0.271 s for the simulated curve) is equal to 6.6%. For this regulation of 1300 \({}^{\circ}\)C, the computations were stopped at 0.85 s, because the global carbon conversion was higher than 0.99 at that time. This means that at this \"final\" time, the carbon contained in the coal char particle has been almost totally removed from the particle.