## 2 Materials and Methods  
### Preparation of Nanofluid  
Nanofluids were systematically synthesized using a two-step method, with deionized water as the base fluid. CMC (0.4 wt.%) was first dissolved under continuous magnetic \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nanofluid** & **Concentration** & **Results** & **Ref.** \\ \hline CuO/water & 1–5\% \(w/w\) & \(\bullet\) & The results showed that increasing both the inlet air temperature and CuO nanoparticle concentration & \\ CuO/water & 1–5\% \(w/w\) & \(\bullet\) & enhanced the HPHE effectiveness and heat recovery capacity. The highest effectiveness (0.59346) was achieved at 55 \({}^{\circ}\)C inlet air temperature with 5 wt\% & \\  & & CuO concentration. & \\ \hline Graphene oxide/water & 0.1\% \(w/w\) & \(\bullet\) & The GO nanofluid significantly reduced thermal resistance (up to 67\%) at low heat input rates compared to DI water, while both fluids performed similarly at higher heat inputs. & [38] \\ \hline Ag/water & 1\% \(v/v\) & \(\bullet\) & The study demonstrated that using a 1\% silver nanofluid significantly enhanced HPHE performance, achieving up to 10\% higher heat recovery, a maximum effectiveness of 39.25\%, and a 15\% reduction in thermal resistance under optimal thermal load and flow conditions. & [39] \\ \hline ZnO/water & 0–2\% \(w/w\) & \(\bullet\) & ZnO nanofluids enhanced thermal performance by increasing heat transfer coefficients and reducing thermal resistance, achieving a maximum effectiveness of 0.271 at 2\% nanofluid concentration and up to 17.2\% improvement under optimal conditions. & [40] \\ \hline Fe\({}_{2}\)O\({}_{3}\)/water & 0.5–2\% \(w/w\) & \(\bullet\) & Magnetic nanofluids enhanced the thermal performance of an air-to-air HPHE, increasing thermal efficiency to a maximum of 35.3\% and reducing thermal resistance by as much as 71.6\% at 2.0\% nanoparticle concentration. & [41] \\ \hline CuO-Fe/water & \%2 \(w/w\) & \(\bullet\) & The maximum efficiency value of 25.8\% was achieved using a CuO-Fe hybrid nanofluid based on pure water. & [42] \\ \hline Al\({}_{2}\)O\({}_{3}\)-TiO\({}_{2}\)/EG & - & \(\bullet\) & The use of Al\({}_{2}\)O\({}_{3}\)-TiO\({}_{2}\)/EG (50:50) hybrid nanofluids improved thermal performance, achieving a maximum efficiency of 82\% and reducing thermal resistance by up to 53.71\%. & [43] \\ \hline Co\({}_{3}\)O\({}_{4}\) & 1–2\% \(w/w\) & \(\bullet\) & Co\({}_{3}\)O\({}_{4}\) nanofluids significantly enhanced thermal performance, with up to 75.4\% efficiency improvement and 29.3\% exergy-saving efficiency at 2\% concentration. & This work \\ \hline Co\({}_{3}\)O\({}_{4}\)/CB & 2\%/0.4\% \(w/w\) & \(\bullet\) & CB incorporation into 2\% Co\({}_{3}\)O\({}_{4}\) nanofluid further boosted thermal efficiency to 79.2\% and reduced thermal resistance by up to 61.4\% compared to deionized water. & This work \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of recent experimental studies on nanofluid-enhanced HPHEs. stirring to provide the desired rheological behavior and enhance dispersion stability. Co\({}_{3}\)O\({}_{4}\) nanoparticles (Sigma-Aldrich, St. Louis, MO, USA; 99.5% purity, <50 nm particle size) were added to the base fluid at final concentrations of 1.0 wt.% and 2.0 wt.% to prepare the nanofluids. The pH of the dispersion was determined to be approximately 6.5. No visible sedimentation was observed after 24 h. The XRD pattern of the Co\({}_{3}\)O\({}_{4}\) nanoparticles is presented in Figure 2. The diffraction peaks observed at approximately 20 = 31.3\({}^{\circ}\), 36.8\({}^{\circ}\), 44.8\({}^{\circ}\), 59.3\({}^{\circ}\), and 65.2\({}^{\circ}\) correspond to the (220), (311), (400), (511), and (440) planes, respectively. These reflections are in good agreement with the standard spinel Co\({}_{3}\)O\({}_{4}\) phase (JCPDS No. 42-1467). The sharp and intense diffraction peaks also suggest a high degree of crystallinity in the nanoparticle samples.