Eur. Phys. J. B (2012) 85: 201
https://doi.org/10.1140/epjb/e2012-30048-8

Regular Article

Role of uniform horizontal magnetic field on convective flow

¹ Department of Mathematics, National Institute of Technology, 713209 Durgapur, India
² Department of Physics and Meteorology, Indian Institute of Technology, 721302 Kharagpur, India

^a e-mail: pinaki.math@gmail.com

Received: 18 January 2012
Received in final form: 13 April 2012
Published online: 20 June 2012

Abstract

The effect of uniform magnetic field applied along a fixed horizontal direction in Rayleigh-Bénard convection in low-Prandtl-number fluids has been studied using a low dimensional model. The model shows the onset of convection (primary instability) in the form of two dimensional stationary rolls in the absence of magnetic field, when the Rayleigh number R is raised above a critical value R_c. The flow becomes three dimensional at slightly higher values of Rayleigh number via wavy instability. These wavy rolls become chaotic for slightly higher values of R in low-Prandtl-number (P_r) fluids. A uniform magnetic field along horizontal plane strongly affects all kinds of convective flows observed at higher values of R in its absence. As the magnetic field is raised above certain value, it orients the convective rolls in its own direction. Although the horizontal magnetic field does not change the threshold for the primary instability, it affects the threshold for secondary (wavy) instability. It inhibits the onset of wavy instability. The critical Rayleigh number R_o(Q,P_r) at the onset of wavy instability, which depends on Chandrasekhar’s number Q and P_r, increases monotonically with Q for a fixed value of P_r. The dimensionless number R_o(Q,P_r) / (R_cQP_r) scales with Q as Q^-1. A stronger magnetic field suppresses chaos and makes the flow two dimensional with roll pattern aligned along its direction.