Rayleigh-Bénard convection with magnetic field

Abstract

We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The magnetic field stabilizes, due to the Lorentz force, more or less Rayleigh-B?nard convective cellular motion. The solution of the eigenvalue problem shows that the critical Rayleigh number increases with increasing Hartmann number while the corresponding wave length decreases. Interesting analogies to solar granulation and black spots phenomena are obvious. The influence of a horizontal field is stronger than that of a vertical field. It is easy to understand this by discussing the influence of the Lorentz force on the Rayleigh-B?nard convection. This result corrects earlier calculations in the literature.Diskutuje se resenje jednacina sa malom perturbacijom za horizontalni fluidni sloj zagrevan odozdo sa magnetnim poljem u vertikalnom ili horizontalnom pravcu. Magnetsko polje je stabilizovalo, zbog Lorentz-ove sile, manje ili vise Rayleigh-B?nard-ovo konvektivno celularno kretanje. Resenje problema sopstvenih vrednosti pokazuje da kriticni Rayleigh-jev broj raste sa porastom Hartmann-ovog broja dok odgovarajuca talasna duzina opada. Interesantne analogije sa fenomenima solarne granulacije i crnih mrlja su ocigledne. Uticaj horizontalnog polja je jaci od uticaja vertikalnog polja. Ovo je lako je razumeti pomocu diskusije uticaja Lorentz-ove sile na Rayleigh-B?nard-ovu konvekciju. Ovaj rezultat ispravlja ranija izracunavanja raspoloziva u literaturi.