Benard Convection in a Non-Linear Magnetic Fluid

[摘要] Convective instabilities in the Benard problem have been examined for a magnetohydrodynamic fluid with a non-linear permeability, the model having been proposed by P. H. Roberts [45] in the context of neutron stars. This non-linearity is found to have no effect on the development of instabilities through the mechanism of stationary convection but influences the onset of overstable convection. The linear stability of the magnetic Benard problem is investigated via a generalized energy theory. The magnetic field is shown to have a stabilising effect using this generalized energy theory. In chapter (6), the Benard problem is investigated on the assumption that the magnetic field is in the direction of the vertical. The case of a non-vertical magnetic field is considered in chapter (7). The effect of both magnetic field and rotation is examined in chapter (8). In chapter (9) an energy analysis of the Benard problem is considered when the magnetic field is in the direction of the vertical. Chapters (2), (3) and (4) describe and illustrate the numerical methods which were used to solve the related eigenvalue problems. A constitutive analysis for a typical permeability is considered in chapter (5).

[发布机构] University:University of Glasgow

[关键词] Applied mathematics, Fluid mechanics