## 2 Experimental Measurements
### Boundary Conditions  
The boundary conditions of the model used in this study were examined in detail and presented in Figure 3. The geometric properties of the heated block were determined as a 3.75 cm square base and a height of 1.27 cm. The block containing the TPMS structure has the same dimensional characteristics. A diameter of 1 cm was used for the inlet and outlet cylinders. The regions where the heat flux was applied are marked with red arrows in Figure 3a, and a constant heat flux of 30.8 kW/m\({}^{2}\) was applied in these areas. The fluid temperature at the system's inlet was designated as \(T_{int}\), while the applied inlet velocity was defined as \(u_{int}\), and the calculated outlet temperature was represented as \(T_{out}\). Adiabaticwall conditions were established for all boundaries within the computational domain, effectively preventing heat transfer, except for the surfaces subjected to heat flux, which enabled a focused assessment of heat transfer performance in specific regions. Based on these specified parameters and conditions, the boundary conditions were mathematically formulated. A uniform velocity (\(u=u_{in}\)) is applied at the inlet region in the \(x\)-direction, and the fluid enters the test section at a constant temperature (\(T_{in}\)). An open boundary condition is applied at the outlet, where stresses are set to zero. The bottom surface of the Al block is exposed to a constant heat flux (\(q^{\prime\prime}\)). All external surfaces are assumed to be adiabatic, satisfying the condition of zero temperature gradient normal to the surface (\((\partial T_{Surface})/\partial n=0\)). In the present fluid dynamics analysis, no-slip boundary conditions are imposed on all surfaces. Figure 3b illustrates the precise positioning of thermocouples within the experimental setup. Seven thermocouples (TC-1, TC2, \(\ldots\), TC-7) are strategically placed at specific intervals along the flow path, beginning at 4.2 mm from the inlet and extending to 29.4 mm, with equidistant spacing of 4.2 mm between consecutive measurement points. This systematic arrangement enables comprehensive temperature monitoring throughout the TPMS structure, facilitating detailed analysis of temperature gradients and thermal performance characteristics. The thermocouples are positioned 0.1 cm below the interface inside the solid block to accurately capture the heat transfer dynamics between the TPMS structure and the cooling fluid while minimizing flow disturbance. The effect of gravity was neglected in our TPMS model under forced convection conditions. Previous studies have quantified gravity's influence in similar heat transfer systems. [PERSON] et al. (2021) reported that in forced convection through TPMS structures with \(Re\) exceeding 2000, the contribution of natural convection due to gravity is typically less than 2% of the total heat transfer coefficient [33]. Similarly, [PERSON] et al. (2022) demonstrated that for gyroid TPMS structures under forced convection with flow rates above 20 cm\({}^{3}\)/s, the Richardson number (\(\mathrm{R_{i}}\)) remains below 0.1, indicating that buoyancy effects are negligible compared to forced convection [10]. These findings from the literature  
Figure 3: Test section: (**a**) 3D layout of gyroid porous structure, (**b**) thermocouple positions. support our approach to neglecting gravity effects in the current study's turbulent flow regime. The boundary conditions of the model used in this study were examined in detail and are presented in Table 3. Table 3 provides a comprehensive overview of all boundary conditions applied in the numerical simulation, including their mathematical representations and physical interpretations. The model has a porosity ratio of 0.7. Due to the simulation of the TPMS as a solid structure, the permeability value was not evaluated in this investigation. In the experiments, the calculated temperature (\(T\)) was measured 0.1 cm below the interface inside the solid Al block.