## 4 Results
This enhancement in performance can be attributed to the improved thermal conductivity and convective heat transfer behavior of the nanofluids. The nanoparticles disrupt the thermal boundary layer and enhance energy transport mechanisms within the fluid, resulting in more efficient heat removal and a significant reduction in thermal resistance. Additionally, higher Reynolds numbers are typically associated with increased turbulence, which reduces the thermal boundary layer thickness and enhances convective heat transfer. [PERSON] et al. reported a maximum 52.3% reduction in thermal resistance using graphene nanofluid at Re = 11,700 (cold) and 11,000 (hot) in an HPHE [59]. Similarly, [PERSON] et al. observed a maximum 71.6% reduction in thermal resistance when magnetic nanofluid was used under Re = 11,450 conditions in the cold duct [41]. These examples align with the trends observed in the current study, further confirming the effectiveness of nanofluids under turbulent flow regimes. Figure 10: Variation in effectiveness (\(\varepsilon\)) with average evaporator wall temperature for deionized water and Co\({}_{3}\)O\({}_{4}\)-based nanofluids. Figure 12 illustrates the variation in exergy loss with respect to the heat capacity rate ratio (\(\rm{C_{h}/C_{c}}\)) for deionized water, 1% Co\({}_{3}\)O\({}_{4}\) nanofluid, and 2% Co\({}_{3}\)O\({}_{4}\) nanofluid. As can be seen, the exergy loss consistently increases with a rising \(\rm{C_{h}/C_{c}}\) across all tested fluids. Exergy loss reflects the irreversibilities arising from heat transfer across finite temperature gradients and viscous dissipation during air flow through the heat exchanger. Although exergy loss to the environment was not explicitly isolated, its contribution is assumed to be implicitly reflected in the total entropy generation observed under steady-state and well-insulated operating conditions. The experimental setup was thermally insulated to minimize external losses, and all measurements were obtained after thermal stabilization. The observed reduction in exergy loss when using nanofluids can be attributed to improved thermal transport mechanisms and more uniform flow behavior, which collectively reduce temperature gradients and entropy generation throughout the system. Among the working fluids, deionized water exhibited the highest exergy loss, while the 2% Co\({}_{3}\)O\({}_{4}\) nanofluid demonstrated the lowest exergy loss across the entire range. Figure 13 presents the exergy-saving efficiency, which quantifies the percentage reduction in exergy loss relative to deionized water, as a function of the \(\rm{C_{h}/C_{c}}\). As the heat capacity rate ratio increases, the exergy-saving efficiency also improves for both the 1% and 2% Co\({}_{3}\)O\({}_{4}\) nanofluids. At a \(\rm{C_{h}/C_{c}}\) of 3, the use of 2% and 1% Co\({}_{3}\)O\({}_{4}\) nanofluids instead of deionized water resulted in exergy loss reductions of 29.3% and 21.5%, respectively. The 2% Co\({}_{3}\)O\({}_{4}\) nanofluid consistently outperformed the 1% concentration, highlighting the beneficial effect of higher nanoparticle loading. This improvement is due to enhanced convective heat transfer and more effective thermal energy utilization, reducing system irreversibility compared to the base fluid. The results indicate that increasing the nanofluid concentration and the hot-side flow rate enhances the system's capability to recover and utilize thermal energy more efficiently, supporting the potential of nanoparticle-enhanced working fluids for improving the thermodynamic performance of air-to-air HPHEs. The use of nanofluids, such as graphene oxide-based formulations, has been shown to significantly reduce exergy losses compared to distilled water in shell-and-tube heat exchangers. This improvement is attributed to enhanced thermal conductivity and reduced entropy generation resulting from the presence of nanoparticles [60].