Geometry effects on a micropolar fluid flow in a wavy curved channel

This study examines the effects of geometry on the steady flow of an incompressible viscous fluid with rigid microparticles. The flow is confined within a curved channel characterized by sinusoids defined by amplitude, wavelength and phase shift. Homogeneous boundary conditions are used to express the behaviours of the fluid and particle velocity vectors at the prescribed boundaries. Through the analytical solutions of the flow model, the modification in the flow field due to the effects of the geometric parameters as well as the physical parameters is elucidated. The results notably indicate that, for small relative amplitude and arbitrary wavelength, the presence of boundary waviness can induce an additional component of angular velocity, consequently, the flow is subjected to the influence of more than one length scale parameter. However, for long wavelength and arbitrary amplitude, the mentioned angular velocity component does not exist, and the flow becomes influenced by a single length scale parameter. Furthermore, the presence of microparticles in the fluid reduces its flow when compared to the flow of a Newtonian fluid. Nevertheless, the tendency of the micropolar flow enhancement is observed, depending on the parameters characterizing the rheology of the fluid and geometry of the boundaries of the flow domain.