Mathematical Investigation of Acoustic Streaming in presence of Magnetic field over Two and Three dimensional geometries

Abstract

This study is made to understand and enhance the performance of acoustofluidics devices to expedite the burgeoning of powerful medical and chemical devices. Two effects are mainly recognized in the field of acoustofluidic; the acoustic radiation force and the acoustic streaming. The acoustic radiation force acts on suspended particles and is caused by acoustic wave scattering on the particle. The acoustic radiation force is generated during the transfer of energy from the acoustic wave to the suspended particle, which causes the particle to travel in a translational direction relative to the fluid. Acoustic streaming is generated during the transfer of momentum from the acoustic wave to the fluid. In the present work, we look into the problem of acoustic streaming for two dimensional solid porous and rough surface geometries in presence of magnetic field, which is being investigated by invoking successive approximation within the frame work of boundary layer approximation. Our main objective is to model the standing wave and Rayleigh Streaming in the presence of magnetic field and to investigate the pattern of acoustic streaming through different structures. The magnetic field induced by the current is assumed to be negligible in comparison with applied magnetic field. Since the boundary layer approximation is valid, the method of successive approximation is used to analyze the flow. The process of successive approximation is based on the following physical reasoning. Here we select a system of co-ordinates, which is at rest with respect to the body, and assuming that the fluid moves with respect to the body at rest, we can assume that the velocity is composed of two terms. vy=vy(1)+vy(2)+vy(3)+Under these conditions the first approximation, vy(1) satisfies the linear differential equation for the given boundary condition. The second approximation for vy(2)can be obtained by replacing the convective terms from vy(1) and taking into account the convective pressure term can be solved with the given boundary...