NUMERICAL STUDY OF THE EFFECT OF THE MAGNETIC FIELD ON MAGNETOCONVECTIVE FLOW OF A NEWTONIAN FLUID CONFINED BETWEEN TWO VERTICALLY OFFSET HEMISPHERES.

This work consists of numerically studying the effect of a uniform oblique magnetic field on the magnetoconvection of an electrically conductive Newtonian fluid.The system studied is a hemispherical cavity formed by two vertically eccentric hemispheres.The inner hemisphere is subjects to a constant density flow,while the outer hemisphere is maintained at a fixed temperature. The thermal and electrical boundary conditions of the system under study are combined to find the critical values of the parameters that indicate the onset of instability.The equations governing this fluid instability are first projected into a bispherical coordinate system and then discretized using the finite difference method. This made it possible to develop a computer code in FORTRAN.This code was used to determine the growth rates for different values of the Hartmann number. The eccentricity, Rayleigh number, radius ratio, and magnetic field inclination angle remain fixed in numerical simulations. The results show that the magnetic field has an effect on this transfer mode. If the Hartmann number is low, the magnetic field is weak and the transfer is more convective,leading to an extended and chaotic convection structure,thus increasing the Nusselt number. A weak magnetic field has very little effect on magnetoconvective isotherms and isocurrents. On the other hand, when the Hartmann number is high, the magnetic field inhibits convection,thereby reducing the Nusselt number.Magnetoconvective isotherms and isocurrents are strongly affected,with a decrease in the size of the vortex and magnetoconvective motion.The results obtained at the end of the study are consistent and agree with those found in the literature.