## 2 Materials and Methods  
### Numerical Study  
This study examines the compatibility between the radial fan and the heatsink used in an induction hob cooling system, focusing on their impact on electronic component temperatures. To improve analysis time and mesh quality, a simplified model was created. This model includes the radial fan, auxiliary board, customized heatsink, and the tray holding the electronic components, as shown in Figure 1. All components are customized for the Haier Europe Company (Eskisehir, Turkey). The heatsink was placed directly in front of the fan to maximize airflow over its surface. Airflow measurements were taken at the outlet behind the heatsink using probes placed at predefined points. The fan's inlet is located below the bottom casing of the hob, while its outlet directs air toward the metal heatsink inside the tray. The heatsink outlet is positioned near the hob's ventilation channels, allowing hot air to exit through these openings. Figure 1: Simplified induction hob. Three different heatsink types were used in the Design of Experiments and velocity comparison studies. Each had different fin structures and surface areas. In the first phase, these heatsinks were produced using 3D printing with ABS material and mounted on the simplified test setup. ABS was chosen due to its ease of manufacturing, mechanical stability, and cost-effectiveness for airflow studies, despite its low thermal conductivity. Metal printing was not preferred due to project limitations. Air velocity measurements were taken at predefined outlet regions using a TESTO device (TESTO SE, Titiese-Neustadt, Germany) while the fan was running. The prototype heatsinks--Type 1, Type 2, and Type 3--are shown in Figure 2. Design constraints from the supplier and product geometry were considered when shaping the heatsinks. Fin height was fixed at 20 mm to fit within the hob design, and fin thickness was set at 1.3 mm based on manufacturability. Accordingly, Type 1 had 5 fins, Type 2 had 12, and Type 3 had 8 fins. Their effective surface areas were calculated as 0.0835 m\({}^{2}\), 0.1040 m\({}^{2}\), and 0.0683 m\({}^{2}\), respectively. As the second step of the study, a CFD model utilizing the simplified experimental setup was developed [17; 18; 19]. The three types of heatsink models were incorporated into the simulation, where the electronic components attached to them served as heat sources, and the radial fan operated according to its P-Q curve. Through this CFD model, the temperatures occurring on the surfaces of the components were obtained under steady-state conditions. The \"FloEFD\" software package was used to perform the CFD analyses. For turbulence modeling, it uses the k-\(\varepsilon\) model with damping functions, as described by [PERSON] (1981) [20] and [PERSON] et al. [21]. The software generates a Cartesian mesh and utilizes [PERSON]'s universal profiles alongside the \"Two-Scale wall functions\" approach to model the turbulent boundary layer, as noted in the works of [PERSON] et al. [22] and [PERSON] [23]. To achieve spatial discretization, an axis-aligned rectangular grid is applied in regions distant from the geometry boundary, while a Cartesian cut-cell approach is implemented near the geometry boundary. In computational fluid dynamics, the computational domain is divided into control volumes, with conservation equations discretized into algebraic forms to enable numerical solutions. In this study, the continuity equation, one of the fundamental equations used for calculating airflow and heat transfer within the system, was applied to ensure mass conservation. With the operation of the fan, airflow was generated within the system, and the continuity equation ensured that there was neither mass loss nor accumulation. The airflow produced by the fan and its interaction with heatsink surfaces and electronic components were analyzed using the momentum equation. Through this equation, variations in air velocity and direction, forces acting on surfaces, and pressure changes within the system were modeled.