Influence of a slight nonuniformity of the magnetic field on MHD convection

A. C. Neubrand¹ - J. P. Garandet¹ - R. Moreau² - T. Alboussiere²

¹ Commissariat a I Energie Atomique DTA/CEREM/SES, Centre d Etudes Nucleaires de Grenoble, 17, av. des Martyrs, 38054 Grenoble Cedex 9, France
² EPM MADYLAM, CNRS UPR A 9033, ENSHMG, BP 95, 38402 St. Martin d Heres Cedex, France

Abstract
In this paper, we examine the sensitivity of MHD convection to a slight nonuniformity of the magnetic field. Our work is an extension of the asymptotic analysis in the high Hartmann number range proposed in [1] in the case of a uniform steady vertical magnetic field. The magnetic field nonuniformity b is assumed much smaller than the zeroth-order uniform magnetic field Bo, l = b/Bo << 1. Supposing further that the resulting velocity disturbance is also small with respect to the uniform field solution, a first-order perturbation analysis is carried out. With perfectly electrically conducting walls, the velocity modification is found to be of the same order as the intensity of the magnetic field perturbation, l. But when the walls are electrically insulating, the existence of a slight magnetic field nonuniformity can entail a velocity disturbance of the order lHa. This result may have important consequences for applications; for instance, in the case of horizontal Bridgman growth, the requirement on the magnet size, design, and performance are much more severe than expected. Figs 6, Table 1, Refs 15.