Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes revisited: Boundary-layer-in-time effects

Abstract

In this paper, we revisit the problem of the time-dependent micropolar fluid flow in a thin pipe system considered in Pažanin et al. (2024) [29]. We remove the restriction that the inflow/outflow and the external source functions vanish for small values of time and extend the analysis to non-homogeneous initial conditions. This requires the construction of the boundary-layer-in-time and the boundary-layer-in-space-and-in-time correctors in the asymptotic expansion of the solution. Consequently, we propose a new asymptotic approximation of higher order of accuracy for a general case with strong coupling between velocity and microrotation. The error estimates are also proved justifying the use of the derived effective model and indicating its range of applicability.