Effect of the Magnetic Field on the Flow of a Liquid Metal and Heat Transfer in a Curved Cylindrical Annular Duct with Uniform Wall Temperatures

Panteleimon Bakalis ,P Hatzikonstantinou

doi:10.15344/2455-7412/2016/120

Abstract

The laminar fully developed magnetohydrodynamic (MHD) and thermal flow of a liquid metal into a curved annular duct of circular cross section, subjected to a transverse external magnetic field, is studied in the present work. The cylinders are maintained at different uniform temperatures, thus buoyancy forces between the walls are created. Applying our computational methodology, computational results are obtained for different values of curvature (0-0.2), Reynolds number (100-2000), Grashof number (0 – 106) and Hartmann number (0-2000). The magnitude of the velocity is determined by the balance of the centrifugal, buoyancy and electromagnetic forces.

Highlights

MHD flows involve the motion of an electrically conducting fluid under the effect of an external strong magnetic field and are met in many practical applications such as fusion reactors, electromagnetic pumping and other engineering applications
The 3D contour plot of Fig. 2 clearly represents the effect of the magnetic field on the axial velocity distribution, for various Hartmann numbers and for Re=2000, Gr=0 and κ=0.2. As it can be observed as the Hartmann number increases side velocity jets are formulated in the left and right regions of the ring-shaped cross section, in a direction parallel to the external magnetic field and the magnitude of the axial velocity w is strongly suppressed at the regions of the Hartmann layers (θ=90° and 270°)
These results indicate that as the external magnetic field increases, the liquid metal tends to move mainly by the side regions parallel to the direction of the external magnetic field and tends to be nonmoving at the top and bottom wall regions normal to the external magnetic field

Summary

Introduction

MHD flows involve the motion of an electrically conducting fluid under the effect of an external strong magnetic field and are met in many practical applications such as fusion reactors, electromagnetic pumping and other engineering applications. One of the most important issues in the study of the MHD flow is the accurate determination of the induced magnetic field in order the divergence free condition to be satisfied with the highest accuracy. The divergence of the induced magnetic field was checked to be very small without corrections [14], or it was improved occasionally using numerical or mathematical technicalities [15], without to produce a method for the systematic improvement of the accuracy of the calculation of the induced magnetic field These problems are related with the fact that the divergence free condition is a first order partial differential equation which cannot incorporates the set of the required boundary conditions in closed space regions. The local Nusselt numbers are given for each wall by the following (15) reactions

Computational Methodology

Result & Discussion

Conclusions