## 2 Materials and Methods
### Numerical Study
The heat loads generated by the electronic components within the system were transferred to the environment through convection, facilitated by the airflow and the heatsinks. This heat transfer process was modeled based on the energy equation, allowing for the calculation of both the component  
Figure 2: Types of heatsinks. surface temperatures and the overall cooling performance of the system. Within this context, the fundamental conservation equations employed in this study are presented below. In Equation (1), \(\rho\) is fluid density, \(t\) is fluid time, and \(\overset{\rightarrow}{V}\) is velocity component. In Equation (2), \(u\), \(v\), and \(w\) are the velocity components of Cartesian coordinates. \[\frac{\partial\rho}{\partial t}+\
abla.\left(\rho\overset{\rightarrow}{V} \right)=0 \tag{1}\]  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{ \partial(\rho v)}{\partial y}+\frac{\partial(\rho w)}{\partial z}=0 \tag{2}\]  
\[\frac{\partial(\rho v)}{\partial t}+\
abla.(\rho v)=-\
abla p+\
abla.\tau+f \tag{3}\]  
\[\tau=\mu\left(\
abla v+(\
abla v)^{T}-\frac{2}{3}\mu(\
abla.v)I\right) \tag{4}\]  
In Equations (3) and (4) shown above, \(p\) is the pressure, \(\tau\) is the stress tensor, \(\mu\) is the dynamic viscosity,\(f\) is the external force, and \(\
abla\). \((\rho vv)\) is the convective momentum transfer. In Equation (5) below, \(e_{t}\) is the total energy, \(q\) is the total heat flux, and \(\varphi\) is the dissipation due to viscosity. \[\frac{\partial(\rho e_{t})}{\partial t}+\
abla.(\rho ve_{t})=-\
abla.q+\varphi \tag{5}\]  
For modeling the turbulence, the RANS model was used with the \(k-\varepsilon\) model. Turbulence kinetic energy and turbulence dissipation are given in Equations (6) and (7) below. \[\frac{\partial(\rho k)}{\partial t}+\frac{\partial(\rho ku_{i})}{\partial x_{ i}}=\frac{\partial}{\partial x_{i}}\left(\left(\mu+\frac{\mu_{t}}{\sigma_{k}} \right)\frac{\partial k}{\partial x_{j}}\right)+P_{k}-\rho\varepsilon \tag{6}\]  
Figure 1:0  
In the equations above, \(\rho\) is the density, \(k\) is the turbulence kinetic energy, \(\mu_{t}\) is the turbulent viscosity, \(\sigma_{k}\) is the Prandtl number, \(P_{k}\) is turbulent energy creation, \(\varepsilon\) is the turbulent dissipation, and \(C_{1\varepsilon}\) and \(C_{2\varepsilon}\) are the empirical constants. The coefficient of empirical constants for the \(k-\varepsilon\) model is given in Equation (8) below:  
Figure 1:1  
Considering the properties of air as an ideal gas, state Equation (9) was used in conjunction with the energy conservation equation. The internal energy was modeled based on the constant-volume specific heat assuming incompressible flow conditions at low Mach numbers. Figure 1:2  
Figure 1:3  
In Equations (9) and (10) shown above, \(p\) is the pressure [Pa], \(\rho\) is the density, \(R\) is the ideal gas constant, \(T\) is the absolute temperature, \(e\) is the density of internal energy, \(q\) is the heat flux, and \(\Phi\) is the viscos dissipation. Airflow Phase:  
In the airflow study phase of the CFD analysis, the airflow generated by the radial fan was modeled based on its actual P-Q (pressure-flow rate) performance curve, provided by the manufacturer. Rather than explicitly modeling the internal rotating blades of the fan using computationally intensive rotating region methods such as the Multiple Reference Frame (MRF) technique, the fan's performance was directly represented through a pressure jump boundary condition corresponding to its operational curve. Utilizing the P-Q curve approach offered several advantages over conventional MRF methods. First, it significantly reduced the computational cost by eliminating the need to resolve complex rotating blade geometries. Second, it allowed for the representation of real fan behavior under varying system resistance conditions, thereby improving the practical accuracy of airflow predictions.