## 2 Methodology
### CFD Model  
The fabric cooling process in the stenter machine is modeled using the Finite Volume Method (FVM). Solid models of the last section of the stenter machine, where the cooling process occurs, are created by simplifying the geometry in order to reduce computation costs and data storage. In this case, instead of modeling all injector channels in a single simulation (total of 12 injector channels, 6 injector channels at upper level and 6 injector channels at bottom level), each pair of injector channels (1 injector channel at upper level and 1 injector channel at bottom level) is separately modeled. All CFD simulations are conducted using commercial CFD software ANSYS Fluent 14.0.  
Mesh and Simulation DetailsThis study utilizes Reynolds-Averaged Navier-Stokes (RANS) governing equations for mass, momentum, and energy in CFD analysis. Additionally, the Realizable k-\(\epsilon\) turbulence model equations are employed in simulations. The velocity inlet boundary condition is defined for the two inlet surfaces of the fluid domain given in Figure 2. A total of four outlet surfaces, two in the (+) x-direction and two in the (-) x-direction, located between the injector channels and fabric, are defined as pressure outlet boundary conditions. Surfaces identified as symmetry boundary conditions can be clearly seen in Figure 2. In order to avoid computational costs and data storage issues, two surfaces in the (+) z-direction and two surfaces in the (-) z-direction are considered symmetry boundary conditions. Wall boundary condition with no slip shear is applied to all other surfaces. All CFD simulations are conducted with air treated as an ideal gas and as a Newtonian fluid.  
Simulations are solved under unsteady-state conditions because the fabric movement should be carefully integrated into CFD models. The fabric velocity toward (+) z-direction is 0.3 m/s, as obtained from the stenter machine control panel. It is supposed that the fabric moves as a flat surface. The velocity value of the porous zone movement is set to 0.3 m/s in the CFD model. Since the distance of the fabric movement is 0.47 m and the fabric velocity (V\({}_{\text{f}}\)) is 0.3 m/s in the models, simulations are carried out for 1.57 s (0.47 m/0.3 m.s\({}^{-1}\) = 1.57 s). In all simulations, time step size is 0.001 s, and the number of time steps is therefore 1570. In other two analyses examining the effect of fabric velocity (V\({}_{\text{f}}\) = 0.25 m/s and V\({}_{\text{f}}\) = 0.35 m/s), the number of time steps varies naturally depending on the fabric velocity. In the present study, the fabric considered as porous media is lycra fabric, and its thermophysical properties [20] are illustrated in Table 2. Based on the assumption that the fabric is isotropic in all directions, the fabric porous zone has 1.4 \(\times\) 10\({}^{7}\) viscous resistance provided by the manufacturer.  
Figure 4: Mesh model of the injector channel.  
At initial condition of unsteady-state CFD simulations, the temperatures of both fluid domain and airflow at the inlet surface are 26.85 \({}^{\circ}\)C, while temperature of fabric porous zone is 130 \({}^{\circ}\)C. The SIMPLE algorithm is utilized to obtain the solution of pressure-velocity coupling. By using the Second Order Upwind Scheme, all scalars in each fluid domain are spatially discretized. All scaled residuals except energy are computed using double-precision calculations until \(10^{-4}\) is reached. Finally, \(10^{-6}\) residual criteria are aimed and obtained for energy equation.