A new model for heat conduction of nanofluids based on fractal distributions of nanoparticles

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Natural convection heat transfer of nanofluids in a vertical cavity: Effects of non-uniform particle diameter and temperature on thermal conductivity (2010, methodology): “As reported in various studies (Khanafer et al., 2003; Xu et al., 2006; Jang et al., 2007; Tiwari and Das, 2007; Abu-Nada, 2008; Akbari et al., 2008; Abu-Nada and Oztop, 2009), the ranges of variation of these parameters are 10 6 Gr 6 10, 2.”
A Review of Thermal Conductivity Models for Nanofluids (2015, background): “[34] keff kbf = k p+2kbf−2φ(kbf−k p ) k p+2kbf+φ(kbf−k p ) + Hco Nudbf Pr .”
Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation (2017, methodology): “The nanoparticles in nanofluids have been proven to be fractal 9 objects and the distribution of nanoparticles in suspension exhibits the fractal property 10 [28, 55, 57-59].”
Enhanced thermal conductivity of nanofluids: a state-of-the-art review (2010, background): “Xu et al. (2006) proposed another thermal conductivity model for nanofluids, based on the Brownian motion of nanoparticles.”
The Classical Nature of Thermal Conduction in Nanofluids (2008, background): “These include Brownian motion of the nanoparticles [36, 37], fluid convection at the microscales [38-44], liquid layering at the particle-fluid interface [45-50], nanoparticle shape [51, 52], cluster agglomeration [53, 54], or a combination of aforesaid mechanisms [55-59].”