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The enhanced thermal conductivity of nanofluids justifies their application to traditional niches of heat transfer fluids. For Newtonian materials, however, viscosity, pressure drop, and ultimately, pumping power, also increase with nanoparticle concentration. A different behavior, though, may be observed with non-Newtonian nanofluids. This possibility motivated the present work, in which aqueous solutions of refrigeration secondary fluid and prime-mover coolant were enriched by graphene nanoparticles (thickness: 0.55-3.74 nm; average length: 5-10 μm). Viscosity variation with shear stress was experimentally investigated for temperatures within (−10 C < T < 25 C). Shear thinning and shear thickening were observed and described in detail by means of flow curves for each fluid sample (base fluid and nanofluids). The patterns for the curve fitting parameters of a modified version of the Herschel-Bulkley equation were analyzed, tabulated, and modeled. Finally, the relative apparent viscosity data were compared with four classical models. HIGHLIGHTS:• Synthesis of graphene non-Newtonian heat transfer nanofluids.• The spectrum of temperatures ranged from -10 C to 25 C.• Shear thinning and shear thickening were observed and described in detail.• Herschel-Bulkley-like equation was observed, parameters patterns were modeled.• Relative apparent viscosity data were compared with four classical models.