S. Aniss et al., THERMOCONVECTIVE INSTABILITY OF MAGNETIC FLUID IN HELE-SHAW CELL, Comptes rendus de l'Academie des sciences. Serie II. Mecanique, physique, chimie, astronomie, 321(4), 1995, pp. 133-138
This paper deals with a theoretical investigation of Rayleigh-Benard c
onvection in a magnetic liquid enclosed in a Hele-Shaw cell. The magne
tic liquid is submitted simultaneously to a gradient of magnetic field
and a gradient of temperature which are parallel to the gravity. It h
as been evidenced that the magnetic convection can accelerate or check
the onset of gravitational convection. During this study we show that
the Hele-Shaw approximation leads to two nonlinear problems; each one
depends on the order of magnitude of Prandtl number. Finally, we pres
ent the results of the linear and weakly nonlinear analysis of stabili
ty near the onset of convection.