## 2 Materials and Methods  
The different analysed nanofluids, 0.005 wt% and 0.05 wt% dispersions of sulfonic acid-functionalized graphene nanoplatelets (S-GnP), and polycarboxylate chemically modified graphene nanoplatelets (P-GnP, NanoInnova Technologies S.L., Madrid, Spain) in tridistilled water, W, were designed by a two-step method. Firstly, the required quantities of nanopowder and water were weighed in a balance Mettler AE-200 (Mettler Toledo, Greifensee, Switzerland), 0.1 mg uncertainty, and appropriately mixed. Then, the resulting mixtures were submitted to ultrasonication in an ultrasonic bath Ultrasound (JP Selecta S.A., Barcelona, Spain) during 120 min at 20 kHz.  
Elemental analyses (C, H, N, S and O) were performed by an elemental analyser Flash 2000 (Thermo Fisher Scientific, Cambridge, UK). For the C, H, N, S detection, around 1-2 mg of each dry nanopowder were placed in tin capsules. Then, the samples were subjected to combustion at 1173 K, separating the subsequent combustion gases by column chromatography with He as carrier gas. Lastly, the presence of CO\({}_{2}\), H\({}_{2}\)O, NO\({}_{2}\) and SO\({}_{2}\) (corresponding to the presence of C, H, N and S, respectively) were detected by an integrated thermal conductivity detector (TCD). For the O detection, around 1-2 mg of each nanoadditive were placed silver capsules. Then, the samples were submitted to pyrolysis at 1333 K, separating the resulting gases by column chromatography with He as carrier gas. Finally, the presence of O, combined with C as CO, was chromatographically separated from other products and detected by TCD.  
Dynamic light scattering (DLS) analyses to characterize the polydispersity of the nanoadditive were developed by a Zetasizer Nano ZS (Malvern Instruments Ltd., Malvern, UK). The pH of the different-loaded dispersions was assessed through a Sension+PH3 pH-meter (Hach, CO, USA) with a combination pH electrode, code 5010.  
The rheological behaviour of the samples (283.15 to 323.15 K) was studied by a rheometer Physica MCR 101 ([PERSON], Graz, Austria) coupled with a cone-plate geometry CP50-1, determining the flow curves in the 10 to 1000 s\({}^{-1}\) shear rate range. The expanded uncertainty (k = 2) of the experimental dynamic viscosities is 3% [27; 37].  
Thermal conductivities (293.15 K) were experimentally measured by the transient hot wire method through a KD2 Pro thermal analyzer (Decagon Devices, Pullman, WA, USA) coupled with a KS-1 probe. The expanded uncertainty (k = 2) of these measurements is 3% [27].  
Densities for each nanofluid set (288.15 to 313.15 K) were experimentally determined by a densimeter DMA 500 ([PERSON], Graz, Austria) based on the oscillating U-tube technique. The expanded uncertainty (k = 2) of these measurements is 0.1% [38; 39].  
To provide a comprehensive physical profile, linear and non-linear optical properties of the studied nanofluids were summarized from a previous study [21]. These properties were obtained by a commercial double beam ultraviolet-visible (UV-Vis) spectrophotometer Lambda 900 (PerkinElmer, Waltham, MA, USA) [40; 41] and a home-made laser experimental setup to perform high light-intensity tests. The main element of this setup, the light source, is a pulsed nanosecond Nd:YAG laser Q-smart 850 (Quantel, Les Ulis, France) that provides 6 ns pulses at three wavelengths (1064, 532 and 355 nm). More details about the experimental apparatus can be found elsewhere [21].