## 4 Results
The effective thermal conductivities of the nanofluids containing 1% and 2% w/w Co\({}_{3}\)O\({}_{4}\) in a 0.4% CMC-water base fluid were calculated as approximately 0.616 W/m\(\cdot\)K and 0.619 W/m\(\cdot\)K, respectively, while their viscosities at a shear rate of 10 s\({}^{-1}\) were estimated as 0.0454 mPa\(\cdot\)s and 0.0456 mPa\(\cdot\)s. These results indicate that increasing the nanoparticle concentration slightly enhances both the thermal conductivity and viscosity, which reflects the typical trade-off between improved heat transfer performance and increased flow resistance. Some parameters affect the effectiveness of the HPHE. Higher air inlet temperatures improve the effectiveness [56; 57]. This trend aligns with findings of the study, which reported that the effectiveness of the evaporator and condenser sections is enhanced by increasing the hot-side air inlet temperature. It was also observed that increasing the air flow rate on the hot side positively influenced the effectiveness on the evaporator side [58]. Figure 10 illustrates the variation in the thermal effectiveness (\(\varepsilon\)) with the average evaporator wall temperature for deionized water and Co\({}_{3}\)O\({}_{4}\)-based nanofluids. An increase in the average evaporator wall temperature tends to enhance the system's effectiveness, as higher wall temperatures generally facilitate improved heat transfer rates. However, when compared at similar operating conditions, nanofluids exhibit superior effectiveness values even at lower evaporator wall temperatures relative to deionized water. The addition of nanofluids enables the achievement of higher thermal performance despite lower wall temperature levels. Figure 10 also shows that the use of nanofluids leads to a reduction in wall temperatures within the evaporator section. This decrease in the wall temperature indicates that the evaporation process occurs more efficiently at lower temperatures when Co\({}_{3}\)O\({}_{4}\) nanofluids are used compared to deionized water. The enhanced thermal performance of the nanofluids results from their superior thermal conductivity and improved convective heat transfer characteristics. These properties allow for more effective heat absorption from the surrounding air, resulting in lower surface temperatures during evaporation. This behavior demonstrates the ability of nanofluids to recover heat from  
Figure 9: Thermal efficiency values of the tested working fluids under different Reynolds number conditions, along with the corresponding improvement rates of nanofluids relative to deionized water. lower temperature sources, making them highly beneficial for increasing the thermal performance of heat-pipe-based heat exchangers. An enhanced particle concentration appears to promote greater disruption of the thermal boundary layer, further supporting effective energy exchange. The results confirm that the inclusion of Co\({}_{3}\)O\({}_{4}\) nanoparticles significantly improves thermal effectiveness, with the 2% concentration consistently yielding the best performance. Figure 11 presents the variation in thermal resistance and corresponding improvement rates for deionized water, 1% Co\({}_{3}\)O\({}_{4}\) nanofluid, and 2% Co\({}_{3}\)O\({}_{4}\) nanofluid across different Reynolds number combinations. The thermal resistance is a critical parameter that inversely correlates with heat transfer performance, and lower values indicate more efficient heat transfer. As shown in the figure, the thermal resistance of the heat pipe system decreases significantly when nanofluids are used instead of deionized water. The lowest thermal resistance values for all working fluids were recorded at a hot-side Reynolds number of 14200 and a cold-side Reynolds number of 10400. Under this condition, the thermal resistance dropped significantly to its minimum, and the corresponding improvement rates were calculated as 36.8% for the 1% Co\({}_{3}\)O\({}_{4}\) nanofluid and 50.2% for the 2% Co\({}_{3}\)O\({}_{4}\) nanofluid, relative to deionized water.