## 2 Geometry and CFD-Thermal Modeling
### Turbulence Modelling
Furthermore, the unified laws of the wall for velocity and temperature profiles in wall coordinates obtained by blending enhanced laminar and turbulent wall functions are applied throughout viscous sublayer, buffer, and fully turbulent regions [73]. The \(Nu\) number distribution on the target plate predicted by the selected turbulence model and near-wall modeling are verified by experimental data of [PERSON] [74] and Gardon and Akfirat [75] for a confined, submerged 2D single turbulent air jet shown in Figure 1. Slot width \(w\) is 6.2 mm, jet to target plate distance is \(6w\), and length of the target plate is \(120w\). At the jet slot, the jet velocity profile is flat, the \(Re\) number is 11,000 and \(I\) is 2%. The target plate has a uniform temperature of 338 K and the air jet temperature at the slot exit is 373 K. Thermophysical properties of air are taken as constant at room temperature and 1 atm pressure. Spent fluid is discharged into the atmosphere. The no-slip boundary condition is applied on all walls. The confinement plate is assumed to be adiabatic. The pressure-velocity coupling algorithm and the pressure-based solver of ANSYS Fluent(r) (version 2019R1) CFD software are utilized. Pressure, momentum, energy, turbulent kinetic energy, and dissipation rate equations are discretized in space by a second-order accurate finite volumes method. Four cartesian meshes consisting of 60 \(\times\) 90, 80 \(\times\) 110, 100 \(\times\) 140, and 120 \(\times\) 160 cells, denoted as M1, M2, M3, and M4, respectively, are generated for grid independence study as shown in Figure 1b. The target plate local \(Nu\) number distributions according to the dimensionless distance from the stagnation point (\(x/w\)) calculated on four meshes at various resolutions are compared in Figure 2. Convergence under grid refinement is achieved for M4 due to negligibly small differences between the results obtained on grids M3 and M4. For grid M4, the highest dimensionless distance from a wall to the centroid of the adjacent grid cell in wall coordinates (\(y+\)) on the target plate is 1.52. The local \(Nu\) number distribution on the target plate calculated by CFD simulation on the grid M4 and experimental data are compared in Figure 3. The result obtained by the realizable \(k-\epsilon\) turbulence model with enhanced wall treatment satisfactorily agrees with the experimental data. The biggest differences occur in the secondary peak region of the  
Figure 1: Confined, submerged 2D single air jet impingement problem: (**a**) solution domain; (**b**) Cartesian mesh. \[\frac{\partial}{\partial t}(\rho\varepsilon)+\frac{\partial}{\partial x_{i}}( \rho\varepsilon\overline{u}_{i})=\frac{\partial}{\partial x_{j}}\left[\left( \mu+\frac{\mu_{t}}{\sigma_{k}}\right)\frac{\partial\varepsilon}{\partial x_{j }}\right]+\rho C_{1}S\varepsilon-\rho C_{2}\frac{\varepsilon^{2}}{k+\sqrt{ \theta}\varepsilon}, \tag{10}\]0 Local \(Nu\) number distributions on the target plate calculated on four meshes with various resolutions. local \(Nu\) number distribution. In the remaining regions, the CFD result is in fair agreement with the experimental data. Similar discrepancies of heat transfer characteristics in the jet stagnation region due to the chosen turbulence model, turbulence production limiter, mesh type, and near-wall grid resolution can be found in the literature [61, 68, 76, 77].