Magnetothermal Convection of Water with the Presence or Absence of a Magnetic Force Acting on the Susceptibility Gradient

Abstract

Heat transfer of magnetothermal convection with the presence or absence of the magnetic force acting on the susceptibility gradient ( f _sc) was examined by three-dimensional numerical computations. Thermal convection of water enclosed in a shallow cylindrical vessel (diameter over vessel height = 6.0) with the Rayleigh-Benard model was adopted as the model, under the conditions of Prandtl number 6.0 and Ra number 7000, respectively. The momentum equations of convection were nondimensionalized, which involved the term of f _sc and the term of magnetic force acting on the magnetic field gradient ( f _b). All the computations resulted in axisymmetric steady rolls. The values of the averaged Nu, the averaged velocity components U, V, and W, and the isothermal distributions and flow patterns were almost completely the same, regardless of the presence or absence of the term of f _sc. As a result, we found that the effect of f _sc was extremely small, although much previous research emphasized the effect with paramagnetic solutions under an unsteady state. The magnitude of f _sc depends not only on magnetic conditions (magnitudes of magnetic susceptibility and magnetic flux density), but also on the thermal properties of the solution (thermal conductivity, thermal diffusivity, and viscosity). Therefore the effect of f _b becomes dominant on the magnetothermal convection. Active control over the density gradient with temperature will be required to advance heat transfer with the effect of f _sc.