Thermoconvective instability of a ferrofluid in a strong magnetic field

Abstract

Finlayson has analyzed convective instability in a horizontal layer of magnetic fluid heated from below in the presence of a uniform vertical magnetic field. His analysis for determining critical temperature gradients required to induce hydrodynamic convection under gravity-free and terrestrial conditions is extended here to allow for the dependence of the effective shear viscosity on colloid concentration and on temperature in the presence of a strong magnetic field. A more rapidly converging Galerkin formalism is introduced and explicit predictions of critical temperature gradients are presented for the first time for the first time for ferrofluids with well defined physical properties. For aqueous ferrofluid layers about 1–2 mm thick we predict that an applied magnetic field leads to experimentally significant reductions in the critical temperature gradient and that these reductions are reinforced by the temperature dependence of the viscosity. Under gravity-free conditions the critical temperature gradients are determined by a single dimensionless number for N 0 c , provided that the temperature dependence of the shear viscosity is negligible. We obtain a value for N 0 c which is very close to that reported by Finlayson. For dilute magnetic fluids the temperature gradients necessary for convection in the absence of gravity are much larger than those required when gravity is present.