On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index

TL;DR

This paper proves the existence of classical solutions for steady, chemically reacting generalized Newtonian fluid flows with concentration-dependent power-law indices in two dimensions, under specific conditions.

Contribution

It establishes the existence of classical solutions for a coupled system of fluid flow and concentration equations with variable power-law index, a novel result for this class of fluids.

Findings

Existence of classical solutions in 2D periodic case.

Valid for power-law index greater than one.

Applicable to chemically reacting fluids with concentration-dependent properties.

Abstract

Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier--Stokes equations and convection - diffusion equation with diffusivity dependent on the concentration and the shear rate. Cauchy stress behaves like power-law fluid with the exponent depending on the concentration. We prove the existence of a classical solution for the two dimensional periodic case whenever the power law exponent is above one and less than infinity.