THERMOCONVECTIVE INSTABILITY OF MAGNETIC FLUID IN HELE-SHAW CELL

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.