Using the fractal space-time theory (scale relativity theory), the dynamics of the fluid/nano-particle interface was analyzed. In the general case, the heat transfer through the interface reproduces a d.c. or an a.c. Josephson effects of thermal type, while in the linear approximation, the standard form of heat transfer is given. Consequently, a negative differential thermal conductance appears and an increasing of the heat transfer in nanofluids results.