Abstract
Considering that the motion of microphysical object takes place on continuous but non-differentiable curves, i.e. on fractals, effects of nanoparticle clustering on the heat transfer in nanofluids using the scale relativity theory in the topological dimension are analyzed. In the one-dimensional differentiable case, the clustering morphogenesis process is achieved by cnoidal oscillation modes of the speed field and a relation between the radius and growth speed of the cluster is obtained. In the non-differentiable case, the fractal kink spontaneously breaks the vacuum symmetry by tunneling and generates coherent structures. Since all the properties of the speed field are transferred to the thermal one and the fractal potential (fractal soliton) acts as an energy accumulator, for a certain condition of an external load (e.g. for a certain value of thermal gradient) the fractal soliton breaks down (blows up) and releases energy. As result, the thermal conductibility in nanofluids unexpectedly increases.
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