Flow of fractal fluid in pipes: Non-integer dimensional space approach

Abstract

Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer dimensional space. A generalization of the Navier–Stokes equations for non-integer dimensional space, its solution for steady flow of fractal fluid in a pipe and corresponding fractal fluid discharge are suggested.