Numerical analysis of magnetoconvection in square enclosures with differentially thermally active vertical walls

Abstract

Magnetoconvection in cavities received a great deal of attention because of its multi-faceted applications in geo-physics, astro-physics, bio-medical problems, in the study of structure of stars and planets, magneto hydrodynamic generators, space science, nuclear reactors etc. In this thesis, unsteady natural convection in square enclosres with differentially thermally active vertical walls in the presence of a uniform magnetic field is studied numerically. This research focuses on the flow variables such as stream lines, isotherms and heat transfer coefficient for various values of the parameters under the effect of magnetic field. The objectives of the present research work are to study the effect of Grashof number, Hartmann number on the heat transfer coefficient, namely the average Nusselt number. In order to check the accuracy of the present numerical code developed in Digital Fortran, the values obtained are compared with available literature and are found to be in good agreement. The detailed flow structure and the associated flow characteristics inside the cavity are presented in the form of isotherms, streamlines and velocity profiles. The fluid motion inside the cavity comprises of either single or multiple counter rotating cells. The flow characteristics inside the cavity, dominated by the buoyancy flow, are completely dampened by the influence of magnetic field. The average Nusselt number is found to increase with increase in Grashof number and decrease with increase in Hartmann number. When the magnetic field is strong, the velocities are suppressed and the convective heat transfer rate is reduced. The average Nusselt number behaves in a non-linear fashion with increase in angle of inclination. Thus, the overall heat transfer rate in the cavity can be significantly reduced by applying a magnetic field parallel to gravity with appropriate choice of the boundary conditions. newline