Flow of an incompressible micropolar fluid through an elliptic pipe under a constant pressure gradient

Abstract

The study of the flow through pipes and channels either closed or open is a classical problem. In this paper, we make a theoretical investigation of the flow of an incompressible micropolar fluid through a straight elliptic pipe of uniform cross section under a constant pressure gradient. In any micropolar fluid flow problem, there is a need to determine two independent flow field vectors which includes, velocity vector and microrotation vectorwhich are governed by a coupled system of partial differential equations. Herein the components of these vectors are determined in terms of Mathieu functions. The arbitrary constants that arise in the solution are determined by solving an infinite non homogeneous system of linear equations adopting a numerical procedure. The variation of the volume flow rate through a cross section of the pipe is numerically studied with respect to the material parameters, geometric parameters and the pressure gradient. The results are presented through graphs. Key words: Flow, micropolar fluid, elliptic pipe, constant pressure gradient, Mathieu functions, volume flow rate.