Stability by magnetic fields in the magnetic Bénard problem (Q2774482)

The magnetic Bénard problem on the infinite layer is considered. A conducting fluid is moving under the influence of a temperature gradient perpendicular to the layer and an impressed constant magnetic field \(H_0=(a,b,c)\) with \(c\neq 0\). It is shown that the magnetic field has a strictly retarding effect on the onset of instability which takes place if the Rayleigh parameter \(\lambda\) crosses a critical value \(\lambda^*\) from left to right. The main result says that \(\lambda^* > \lambda^\prime\), where \(\lambda^\prime\) is the critical value of the Rayleigh parameter asssociated with the ordinary Bénard problem which arises if \(H_0=0\).