## 2 Materials and Methods
### Characterizations  
Transmission electron microscopy (TEM) study was conducted using a JEOL JEM 1010 apparatus (Tokyo, Japan) working at 100 kV acceleration voltage. The studied samples were obtained by depositing a diluted solution of the nanoparticles on a thin carbon-coated copper grid. The patterns of the X-ray diffraction (XRD) analysis were obtained by a Siemens D-5000 powder X-ray diffractometer (Karlsruhe, Germany) with CuK\(\alpha\) radiation (wavelength of 1.54056 A) throughout the 20 range of 5\({}^{\circ}\) to 100\({}^{\circ}\) and compared with the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cluster** & **Base Fluid** & **Nanofluid Name** \\ \hline A (97 nm) & Water & CoFe\({}_{2}\)O\({}_{4}\) 97 nm/W \\ A (97 nm) & Propylene glycol & CoFe\({}_{2}\)O\({}_{4}\) 97 nm/PG \\ A (97 nm) & Propylene glycol:water at 35:65 mass ratio & CoFe\({}_{2}\)O\({}_{4}\) 97 nm/PG:W \\ B (155 nm) & Water & CoFe\({}_{2}\)O\({}_{4}\) 155 nm/W \\ B (155 nm) & Propylene glycol & CoFe\({}_{2}\)O\({}_{4}\) 155 nm/PG \\ B (155 nm) & Propylene glycol:water at 35:65 mass ratio & CoFe\({}_{2}\)O\({}_{4}\) 155 nm/PG:W \\ C (192 nm) & Water & CoFe\({}_{2}\)O\({}_{4}\) 192 nm/W \\ C (192 nm) & Propylene glycol & CoFe\({}_{2}\)O\({}_{4}\) 192 nm/PG \\ C (192 nm) & Propylene glycol:water at 35:65 mass ratio & CoFe\({}_{2}\)O\({}_{4}\) 192 nm/PG:W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of designed nanofluids. crystallographic information files of the crystallographic open database. The gathered data were refined with the Le Bail technique via the Rietica program. Raman spectra were obtained from powdered materials on a glass slide substrate, using a Renishaw in Via Reflex Raman Microscope (Gloucestershire, UK). Experiments were performed at ambient temperature with an excitation wavelength of 633 nm. Magnetic tests were conducted by a Quantum Design MPMS XL7 SQUID physical property measurement system (San Diego, CA, USA) supported with a vibrating-sample magnetometer. Field-dependent magnetization curves were recorded at 300 K, with an external field of up to 7 T. The specific surface area (SSA) of the clusters was characterized by a Micromeritics ASAP 2020 analyzer (Norcross, GA, USA) using nitrogen physisorption at 77 K and applying the Brunauer-Emmett-Teller (BET) theory. Before each analysis, the materials were degassed for 240 min at 513 K in vacuum. The stability of the nanofluids was assessed via dynamic light scattering using a Malvern Instruments ZetasizerNano ZS (Malvern, UK). The average Z-size (i.e., the intensity-weighted average hydrodynamic size obtained from a cumulant fit of the intensity autocorrelation function) of the samples was determined over 16 days at 173\({}^{\circ}\) scattering angle and 298.15 K. The analysis was carried out for the 0.1 wt% CoFe\({}_{2}\)O\({}_{4}\) 97 nm/W, CoFe\({}_{2}\)O\({}_{4}\) 97 nm/PG:W, CoFe\({}_{2}\)O\({}_{4}\) 192 nm/W, and CoFe\({}_{2}\)O\({}_{4}\) 192 nm/PG:W nanofluids with a double objective, which was to observe the behaviour (1) with an increasing amount of PG in the base fluid and (2) with the increasing size of the clusters. Two samples with different conditions were analysed for each cited nanofluid. One remained in static state after preparation (hereinafter, static nanofluid) and the other was mechanically stirred for 60 s at 2000 rpm before measurement (hereinafter, shaken nanofluid) using a VELP ZX3 vortex mixer (Usmate Velate, Italy). The thermal conductivities of the base fluids and nanofluids at 293.15, 303.15 and 313.15 K were obtained using a Thermtest THW-L2 device (Hanwell, NB, Canada) with a Peltier EchoTherm IC20 XR dry bath (Hartkirchen, Austria), which ensured a constant temperature. The experimental method of the thermal conductivity meter employs the transient hot wire approach, as per ASTM D7896-19 [29]. The principal element of the device is a 60 mm long and 0.1 mm diameter alumel wire, which is submerged in a container containing roughly 20 mL of sample.