Linear instability analysis of Rayleigh–Bénard convection in a cylinder with traveling magnetic field

•In low aspect ratio cylinder (A=1,2), the flow is stabilized by weak TMF force.•In high aspect ratio cylinder (A=3,4), the weak TMF force would stabilize the flow.•The flow under strong TMF force tends to be oscillatory unstable (except A=1).•The critical Rayleigh number gradually decreases to 0 under strong TMF.

Rayleigh–Bénard convection under a low frequency traveling magnetic field (TMF) in a vertical cylinder is investigated by linear stability analysis. The cylinder with a adiabatic vertical wall is heated from below and cooled from above. The effects of traveling magnetic field on flow instability are studied for four aspect ratios (height/radius) A=1, 2, 3, 4 and three Prandtl numbers Pr=0.001, 0.02, 0.1. The critical Rayleigh number and corresponding critical frequency are evaluated as a function of TMF force Ft, and diversity profiles of stability curves are obtained under different control parameters. Moreover, stability properties for different Prandtl numbers are compared at fixed aspect ratios. The results obtained show that the magnetic force is able to either stabilize or destabilize the flow, which is determined by the effects of combination of the strength of the force, the aspect ratio and the Prandtl number.