Simulations of thermo-magnetic convection in an annulus between two concentric cylinders

Abstract

In this paper the thermo-magnetic convection of a magnetic fluid held between two vertical concentric cylinders is studied. Three-dimensional computer simulations of thermo-magnetic convection have been conducted under an azimuthal magnetic field, when the inner cylinder is kept at a higher temperature than the peripheral one. Simulations have been carried out both in the absence and in the presence of gravity. In the absence of gravity, the problem will be analogous to the classical Rayleigh-Bernard instability in a radial gravitation field. The objective of this study is to investigate the combined effects of magnetic and buoyancy driven convection. In the absence of gravity the simulations revealed the expected flow pattern consisting of counter rotating convection cells with diameter equal to the thickness of the fluid layer. When the gravity is introduced, the case may become unsteady consisting of cells drifting upward. For small gravitational Rayleigh numbers introduction of magnetic field gradient may stabilize the flow. The onset of instability depends on the magnetic and the gravitational Rayleigh numbers and their ratio, radius and aspect ratios of the cylinders as well as on the fluid properties.