Asymptotic Approximation of the Nonsteady Micropolar Fluid Flow through a Circular Pipe

Abstract

We study the nonsteady flow of a micropolar fluid through a thin cylindrical pipe. The asymptotic behaviour of the flow is found via asymptotic analysis with respect to the small parameter ϵ, representing the pipe’s thickness. The asymptotic approximation is derived in the form of the explicit formulae for the fluid velocity and microrotation. We also provide the numerical examples in order to visualize the effects of the micropolar nature of the fluid. The illustrations indicate the influence of the micropolarity on the effective flow of the fluid in the whole domain. In particular, those effects are most clearly observed for the velocity approximation near the boundary of the domain.