On hydromagnetic two-phase gas-liquid flow in ciliary channel: An application of a metachronal rhythm

The study of two-phase flows, encompassing gas-liquid plays a pivotal role in various industrial and biomedical applications. It investigates the behavior of an annular two-phase flow within ciliary channels, separated by compressible and incompressible flow regimes, in the presence of a magnetic field. The compressible flow is confined in the core region surrounded by the liquid phase. To analyze the flow characteristics, continuity, and momentum equations are considered for both phases. The compressible phase involves significant changes in density, requiring consideration of compressibility effects and the equation of state. Velocity and stresses are assumed to be equal at the interface. The system of mathematical equations is solved analytically by using the regular perturbation technique. The behavior of each phase with the input parameters is described thoroughly. The magnetic parameter is found to decrease while the Reynolds number increases for the velocity profile. The study's outcomes can contribute to the advancement of multiphase flow research by offering a versatile platform for innovation in biomedical engineering, with a thorough examination of the intricate relationship between ciliary motion, compressible and incompressible fluids, and MHD effects in ciliary channels.