THE HEAT TRANSPORT IN NANOFLUIDS: A THEORETICAL APPROACH THROUGH THE FRACTAL THEORIES A mathematical model of the heat transport in nanofluids using the fractal theories (the scale relativity theory in the topological dimension DT = 2) is established. Through a scale covariance form of the Newton’s equation, a Navier-Stokes type equation with an imaginary viscosity coefficient and particularly a Schrödinger’s type equation are obtained. Some applications of the model are given like the heat transport through an effective thermal conductivity, by Brownian motion or by liquid layering at liquid-nanoparticle interface. It results that the heat transport in nanofluids is performed through an unique mechanism, the above standard sequences mentioned being imposed by the interaction scales. Moreover, the quantum thermal conductance of electrons in an one-dimensional wire is obtained.