Nonzero boundary condition for the unsteady micropolar pipe flow: Well-posedness and asymptotics

Abstract

In this paper, we consider the unsteady flow of a micropolar fluid through a thin pipe with the nonzero boundary condition for microrotation. We first prove the well-posedness of the corresponding initial-boundary value problem governing the flow. Then, using asymptotic analysis with respect to the pipe’s thickness, we construct the higher-order approximation of the solution. The proposed approximation is given in explicit form, taking into account the effects of the boundary conditions, the micropolar nature of the fluid as well as the time derivative. A detailed study of the boundary layers in the vicinity of the pipe’s ends is also provided along with a numerical example illustrating the behaviour of the derived asymptotic solution.