ANALYTICAL SOLUTION FOR FREE PARABOLIC FLOW OVER A FLAT PLATE UNDER A MAGNETIC FIELD

Abstract

The study of conductive fluid flow influenced by magnetic fields is known as magnetohydrodynamics (MHD). Nowadays, MHD research has expanded and specialized into various branches with different applications. This paper analyzes free parabolic flow over a flat plate with a constant rotation perpendicular to the surface in the presence of a magnetic field. The flow is assumed to be laminar, steady, incompressible, and viscous under a uniform external magnetic field. The novelty of this study is deriving the governing equations and fluid behavior affected by the magnetic field on a flat plate. To achieve this, the nonlinear partial differential momentum equation is converted into a nonlinear ordinary differential equation using similarity transformation and simplified based on problem conditions. Then, the velocity field is determined analytically. The results from this approach are compared with numerical solutions for evaluation and validation, showing excellent agreement. The influence of magnetic field strength and the curvature angle of the parabolic velocity profile on the fluid velocity distribution is investigated. Increasing the Hartmann number flattens the velocity profile and raises the kinetic energy within the boundary layer. Furthermore, increasing the curvature angle of the free flow increases the tangential velocity.