Effect of Inclined Magnetic Field on Stokes Flow Through In-Phase Slip-Patterned Microchannel Using Boundary Element Method

An investigation is conducted on a twodimensional hydrodynamic model of pressure-driven, viscous, incompressible steady creeping flow through a rectangular microchannel that features wall roughness and is influenced by an external inclined magnetic field. The Stokes equations, incorporating the Lorentz force term, are numerically solved using the boundary element method. The wall roughness is mathematically modeled using alternate Navier’s slip and noslip boundary conditions on the surfaces. We investigated streamline contour plots, flow profiles, shear stresses, and pressure gradients for varying the assumed dimensionless parameters to get a complete comprehension of fluid physics. The proposed study has various significant implementations, including regulating and enhancing the mixing and thermal removal inside micro-scaled devices.

I. Introduction

The phenomenon of flow through channels is observed in various domains within the field of fluid mechanics. The existing body of literature has a significant volume of research papers that investigate a wide range of flow conditions, each matching distinct physical scenarios. Various studies considers the Stokes flow within cavities, pipes, and channels [1]–[4]. Stokes flow shows many practical implications in a wide range of real-world scenarios, including polymer processing, dentistry [5], microfluidic devices [6], and microcirculation [7].