## 3 Results and Discussion  
### Torrefaction  
As mentioned, all the experiments were carried out by placing the tubular reactor in the muffle furnace set at 400 \({}^{\circ}\)C. In order to determine the heat transfer regime of the system behavior, the Biot number (_Bi_), which relates to the heating regime of the material, and the thermal Thiele modulus (_M_), relating to the propagation of the reaction within the sample, were determined as:  
\[Bi=\frac{h}{\lambda/L_{c}}. \tag{3}\]  
\[M=\frac{R^{\dagger}}{\lambda/\left(c_{p}L_{c}^{2}\right)}. \tag{4}\]  
The parameters are summarized in Table 1 below. Note that the thermal conductivity for stainless-steel was significantly greater than the value for the CE material [28]. Furthermore, the diameter of the reactor was significantly smaller compared to the size of the furnace chamber; thus, the influence of the stainless-steel tube on the heat convection from the furnace wall to the sample surface was neglected. The _Bi_ and \(M\) for this experimental setup were obtained for the CE material. Since _Bi_ equaled 0.15, which was smaller than one, this indicated that the samples were thermally thin, and the heat conduction into the sam \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Source** \\ \hline \(h\), W/m\({}^{2}\)-K & 10 & [25] \\ \hline \(\lambda\) for CE material, W/m-K & 0.2 & [26] \\ \hline \(\rho\) (apparent), kg/m\({}^{3}\) & 1150 & Measured in this study \\ \hline \(c_{p}\) (apparent), J/kg-K & 1600 & [27] \\ \hline \(L_{c}\) diameter, m & 0.003 & Measured in this study \\ \hline \(Bi\) & 0.15 & Current result \\ \hline \(M\) & 0.009 & Current result \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimated values for the parameters to determine the Bi and M. CE, Convergen Energy, LLC. the heat convection from the furnace wall to the sample surface. For \(M\) equal to 0.009, it indicated that the reaction rate was much smaller than the heat conduction into the sample. Therefore, the reaction rate was governed by the heat convection from the furnace to the sample surface, after which the temperature of the particle became uniform instantly. The analysis of the same experimental setup was done by [PERSON] et al., 2020, and the temperature of the sample particle could be defined as:  
\[\frac{T_{w}-T(t)}{T_{w}-T_{o}}=e^{-t/\tau} \tag{5}\]  
where _Tw_, \(T_{o}\), and \(\tau\) represent the furnace wall temperature, the initial temperature of the sample, and the characteristic time, respectively [24]. \(\tau\) can be defined as:  
\[\tau=\frac{mc_{p}}{hA}. \tag{6}\]  
For this specific experiment setup, the characteristic time was calculated to be 120.3 s. The waste consisted of both fiber and plastics, and the previous study showed that fiber and plastic behaved differently during the torrefraction [13]. In order to obtain a preliminary correlation to study the behavior of the torrefraction behavior of this waste material, we assumed two first-order reactions. This is a rather common assumption in biomass and plastic torrefraction, which represented the degradation of fiber and plastic during the torrefraction experiment [29; 30; 31]. A similar correlation was developed and implemented successfully by [PERSON] et al., 2018 [10]. The correlation between mass loss and time was represented by the following equation:  
\[\alpha=1-(a_{1}A_{1}^{*}e^{-\frac{T_{a_{1}}}{T(t)}}+a_{2}A_{2}^{*}e^{-\frac{T_ {a_{2}}}{T(t)}}) \tag{7}\]  
where \(\alpha\), \(a\), \(A^{*}\), and \(T_{a}\) are the mass loss, scalar for fiber and plastic, pre-exponential factor, and characteristic time, respectively. The values of the parameters were determined by fitting Equation (6) to the experimental results, and the results are shown in Table 2.  
With the model developed above, the temperature transient, as well as the mass loss were plotted as a function of time as shown in Figure 1. The dotted line indicates the correlation between the mass loss of the material and time.