Repercussions of Increment in Reynolds Number and Half Distance of Major Axis on Magnetohydrodynamic Flow in Elliptical Pipe

Abstract

Analysis has been carried out on velocity configuration for Magnetohydrodynamic (MHD) flow in a straight horizontal pipe of elliptical cross section when Reynolds number and half-length of major axis are adjusted. An electrically conducting, viscous and incompressible fluid flow in the z-direction of a long pipe with elliptical cross-section in x-y plane has been scrutinized. An applied magnetic field is conveyed to the pipe in the y-direction. The fluid is driven by Lorentz force and gravitational force. The governing equations are partial differential equations (pdes) formulated in terms of cylindrical coordinates (r, , z) by amalgamating r-component of Navier-Stokes equation, Ohm’s law, equation of continuity and cross-section of pipe. Navier-Stokes equation is non-dimensionalised, composed in terms of stream function, , converted to an ordinary differential equation (ode) using similarity transformation and evaluated numerically using Finite Element Method (FEM). Results are obtained for velocities for values of Reynolds number, Re? 10.0 and half major axis distance, a 0.0034. Tables and graphs are created and sketched respectively using these findings. The eventualities confess that: When Reynolds number and a half distance of major axis are escalated, velocity of the fluid rises at the centre of the pipe but dwindle to zero towards the periphery of the pipe in both cases. Subsequently, it is anticipated that a pipe of elliptical cross-section would be more beneficial in research on natural phenomena and technological applications than a circular one with the same depth. Fluid velocity and capacity will be higher in the elliptical pipe than in circular pipe resulting in higher MHD effects.