## 4 Results  
The performance of the air-to-air HPHE was experimentally evaluated under different conditions. All tested conditions were within the turbulent flow regime, as confirmed by the calculated Reynolds numbers for both the hot and cold air streams. Figure 8 shows the variation in the convective heat transfer coefficient concerning different heat capacity rate ratios for deionized water and 1% and 2% Co\({}_{3}\)O\({}_{4}\) nanofluids. The heat transfer coefficient is a key indicator of convective heat transfer performance and depends on both the thermophysical properties of the working fluid and the flow dynamics. According to Figure 8, when the hot-side air velocity increases, the heat transfer coefficient enhances. This enhancement results from intensified convective heat transfer in the evaporator section. Higher hot air velocity increases the Reynolds number, reduces thermal boundary layer thickness, and results in more effective heat absorption by the working fluid inside the heat pipes. In addition to velocity, air temperature also affects the Reynolds number by altering air properties. Specifically, increasing temperature leads to a rise in dynamic viscosity and a simultaneous decrease in density, both of which contribute to a reduction in the Reynolds number. Therefore, the combined effect of air temperature and velocity governs the overall flow regime. Moreover, the use of nanofluids significantly improves the heat transfer coefficient compared to deionized water. At all velocity ratios, both 1% and 2% Co\({}_{3}\)O\({}_{4}\) nanofluids demonstrate superior thermal performance. The 2% Co\({}_{3}\)O\({}_{4}\) nanofluid consistently yielded the highest heat transfer coefficient values, validating its effectiveness in promoting convective heat transfer within the heat pipe system. Under all test conditions, the hot and cold air channels exhibited turbulent flow, ensuring stable external convective heat transfer. This consistent air flow regime provides a reliable thermal boundary for evaluating the relative performance of different nanofluid working fluids inside the heat pipe. Figure 9 illustrates the variation in thermal efficiency and improvement rates for deionized water and nanofluids containing 1% and 2% Co\({}_{3}\)O\({}_{4}\) under different Reynolds number conditions. As shown in Figure 9, the highest efficiency was obtained at a hot-side Reynolds number of 13,500 and a cold-side Reynolds number of 6000 for all tested fluids. Under these conditions, the thermal efficiency reached 21.0% for the 1.0% Co\({}_{3}\)O\({}_{4}\) nanofluid and 24.2% for the 2% Co\({}_{3}\)O\({}_{4}\) nanofluid, while deionized water exhibited a lower efficiency of 14.8%. The highest improvement rates were recorded at Re = 14,200 (hot side) and 10,400 (cold side), reaching 62.7% for the 1% Co\({}_{3}\)O\({}_{4}\) nanofluid and 75.4% for the 2% Co\({}_{3}\)O\({}_{4}\) nanofluid, compared to deionized water. This condition corresponds to a favorable flow ratio, allowing for effective heat absorption in the evaporator and sufficient residence time in the condenser, thus facilitating optimal heat transfer. The trend in the figure demonstrates that increasing the Reynolds number in the hot channel, when combined with a relatively lower Reynolds number in the cold channel, promotes higher  
Figure 8: Heat transfer coefficients of deionized water, 1% Co\({}_{3}\)O\({}_{4}\) nanofluid, and 2% Co\({}_{3}\)O\({}_{4}\) nanofluid at various heat capacity rate ratios (C\({}_{\text{h}}\)/C\({}_{\text{c}}\)). efficiency by enhancing the temperature gradient across the heat exchanger. Additionally, the higher nanoparticle concentration further amplifies this effect by increasing thermal conductivity and disrupting thermal boundary layers, thereby improving heat absorption and dissipation throughout the heat exchanger.