Flow of Fractal Fluid in Pipes: Non-Integer Dimensional Space Approach

TL;DR

This paper develops a mathematical framework using non-integer dimensional space calculus to analyze steady Poiseuille flow of fractal fluids in pipes, extending classical fluid dynamics to fractal media.

Contribution

It introduces a generalized Navier-Stokes equation for fractal fluids in non-integer dimensions and provides solutions for steady pipe flow and fluid discharge.

Findings

Derived a generalized Navier-Stokes equation for fractal fluids

Obtained analytical solutions for steady flow in pipes

Extended classical fluid dynamics to fractal media

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.