## 2 Model Description  
Figure 1 shows a schematic diagram of an SAH with baffles attached on the back plate. The baffles are placed opposite the absorber plate with parameters including the spacing \(P\), height \(e\), and angle \(a\). In practical applications, the baffle can be made of galvanized steel  
and welded to the back plate to extend the lifespan. The SAH duct has a height \(H=20\) mm, length \(L=500\) mm, and width \(W=300\) mm. The 250 mm duct is placed upstream of the test section for the fully developed flow, and the 150 mm duct is located at the exit of the test section for flow mixing and elimination of the reverse flow per ASHRAE standard 93-97. The geometries of the baffle in this study are investigated for the following four levels: baffle spacings \(P=40\) mm, 80 mm, 120 mm, and 160 mm; baffle heights \(e=7.5\) mm, 10 mm, 12.5 mm, and 15 mm; and baffle inclination angles \(a=30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), and \(120^{\circ}\). These parameters correspond to the baffle spacing ratios \(P_{r}=P/H=2\), 4, 6, and 8 and the baffle blockage ratios \(B_{r}=e/H=0.375\), 0.500, 0.625, and 0.750. Meshing is performed as illustrated in Figure 2. The walls in the test section are highly refined to handle the flow phenomena adjacent to the walls and the laminar sub-layer at the absorber plate. Furthermore, a grid adaption for a \(y^{+}\) value of approximately unity is performed for the absorber plate to better predict heat transfer related to the laminar sub-layer [7; 23]. The boundary conditions applied to the computed domain include the velocity inlet at the left wall and the pressure outlet at the right wall of Figure 1. A constant heat flux of 1000 W/m\({}^{2}\) is set for the absorber plate to heat the air. The remaining surfaces are walls with no-slip conditions. For turbulent flows, boundary conditions of turbulence intensity  
Figure 1: SAH duct baffled on back plate. Figure 2: Meshing with refinement of the walls in the test section. of 5% and turbulent viscosity ratio of 10 are used for the inlet and the outlet. From the area-weighted averages including the absorber plate temperature (\(T_{ap}\)), the air temperature at the outlet (\(T_{o}\)), and the pressures at the inlet (\(p_{1}\)) and outlet (\(p_{2}\)) of the test section, the magnitudes of the thermal-hydraulic parameters are deduced as follows:  
The heat gain of the air from the absorber plate is given as [22]:  
\[\dot{Q}=\dot{m}c_{p}(T_{o}-T_{i})=hA_{ap}(T_{ap}-T_{f}), \tag{1}\]  
where:  
\(\dot{m}\) is the air mass flow rate;  
\(c_{p}\) is the specific heat at a constant pressure;  
\(h\) is the convection heat transfer coefficient;  
\(T_{i}\) is the air temperature at the inlet, and \(T_{i}\) = 300 K is used in the current study;  
\(A_{ap}\) is the absorber plate area, and \(A_{ap}\) = \(L\times W\);  
\(T_{f}\) is the mean temperature of the air, and \(T_{f}\) = 0.5(\(T_{i}+T_{o}\)). The Nusselt number is computed from the convection heat transfer coefficient as:  
\[Nu=\frac{hD_{h}}{k}, \tag{2}\]  
where \(D_{h}\) is the hydraulic diameter, \(D_{h}=\frac{4 WH}{2(W+H)}\), and \(k\) is the thermal conductivity of the air. The friction factor of the air flowing through the baffled duct is calculated from the following Darcy-Weisbach equation [21]:  
\[f=\frac{p_{1}-p_{2}}{\frac{L}{D_{h}}\frac{\rho U^{2}}{2}}, \tag{3}\]  
where \(\rho\) and \(U\) are the air density and air velocity at the inlet, respectively. In this research, the thermophysical properties of the air are assumed to be constants, and their values are as follows: \(\rho\) = 1.225 kg/m\({}^{3}\), \(k\) = 0.0242 W/m-K, \(c_{p}\) = 1006.43 J/kg-K, and dynamic viscosity \(\mu\) = 1.7894 \(\times\) 10\({}^{-5}\) kg/m-s.  
Two-dimensional numerical simulation is performed on the baffled ducts using the standard \(k\)-\(\epsilon\) turbulence model with enhanced wall treatment. The governing equations, i.e., the continuity, momentum, energy, and transport equations employed in the standard \(k\)-\(\epsilon\) model, are resolved by Ansys Fluent 16 (Ansys Inc.).