A study on the pressure-driven flow of magnetized non-Newtonian Casson fluid between two corrugated curved walls of an arbitrary phase difference

Pressure-driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure-driven flow of magnetized Casson fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field and volumetric flow rate, taking the corrugation amplitude as the perturbation parameter. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. The velocity exhibited a declining trend due to an increase in the Casson fluid parameter. For a sufficiently large corrugation wavenumber, the flow rate decreases, and the phase difference becomes irrelevant. However, the reduction in flow can be minimized by decreasing the channel radius of curvature. In general, a smooth curved channel will give the maximum flow rate for a large corrugation wavenumber. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices like stents.