## 2 Mathematical Model
All the external surfaces exposed to the surroundings were assumed to lose heat through convection. The convective heat transfer coefficient was set equal to 10 W/m\({}^{2}\) K (value within the range of natural convection), and the ambient temperature to 300 K.  
The ideal gas law was used to compute the fluid density. The fluid viscosity and thermal conductivity were assumed to vary with temperature according to the laws reported--for nitrogen--in Canu [40]. The specific heat capacity for each species was calculated as a piecewise fifth-power polynomial function of temperature. The mixture-averaged specific heat capacity was computed as a mass-fraction average of the pure species heat capacities. The wall thermal conductivity was assumed to be constant. Cordierite, stainless steel, silicon carbide (SiC), and cast iron were considered as materials. Table 3 details the values of thermal conductivity for the outer and inner walls adopted in the computations run by varying the inlet gas velocity. The value of thermal conductivity for SiC was taken from [41]. The values 10 W/m K and 50 W/m K are typical of thermal conductivity for stainless steel and cast iron, respectively [29]. Simulations were performed using a uniform grid with square cells. In order to check the grid independence, three cell sizes were tested: 0.08 mm-coarse grid; 0.04 mm-intermediate grid; 0.02 mm-fine grid. The maximum wall temperature was assumed as a criterion for convergence. For the case All Cordierite (see Table 3) at V\({}_{\text{in}}\) = 0.5 m/s, Figure 2 shows the axial profiles of temperature along the center line of the inner wall, where the maximum temperature was attained, as computed by varying the grid resolution. Reducing the cell size from 0.04 mm to 0.02 mm resulted in variations of the wall temperature lower than 5%, without affecting its maximum value. Thus, the intermediate grid, with cell size equal to 0.04 mm, was employed in this work. The conservation equations were solved semi-implicitly with a segregated solver. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm was adopted to treat the pressure-velocity coupling. The spatial discretization used second-order schemes for all terms. Convergence was confirmed by: (1) the residual of each equation going below 1 \(\times\) 10\({}^{-12}\); (2) the global mass and energy balances being satisfied at the end of each simulation; (3) the constancy of temperature and propane mole fraction monitored at various locations for at least 1 \(\times\) 10\({}^{4}\) iterations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Thermal Conductivity of the** & **Thermal Conductivity of the** & **Nomenclature** \\
**Outer Wall [W/m K]** & **Inner Wall [W/m K]** & **Nomenclature** \\ \hline
2 & 2 & All Cordierite \\
32.8 & 32.8 & All SiC \\
32.8 & 2 & SiC + Cordierite \\
23.3 & 23.3 & As SiC + Cordierite 1  \\
10 & 10 & All Stainless Steel \\
10 & 2 & Stainless Steel + Cordierite \\
50 & 50 & All Cast Iron \\
50 & 2 & Cast Iron + Cordierite \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of thermal conductivity for the outer and inner walls adopted in the computations.