Flow of a Micropolar Fluid Through a Channel with Small Boundary Perturbation

Abstract

Abstract The aim of this paper is to investigate the effects of small boundary perturbations on the flow of an incompressible micropolar fluid. The fluid domain is described as follows: we start from a simple rectangular domain and then perturb part of its boundary by the product of a small parameter ϵ and some smooth function h. Using formal asymptotic analysis with respect to ϵ, we derive the effective model in the form of the explicit formulae for the velocity, pressure and microrotation. The asymptotic solution clearly acknowledges the effects of the boundary perturbation and the micropolar nature of the fluid. The obtained results are illustrated by some numerical examples confirming that the considered perturbation has a nonlocal impact on the solution.