Convective instability of a liquid layer in a magnetic field for finite thickness and finite thermal conductivity of the walls

Vu Zuy Quang

Abstract
A study is made of the convective instability of a horizontal layer of an electrically conducting liquid generated by dc Joule heating when the liquid is in a transverse dc magnetic field. The study takes into account the finite thickness and the finite thermal conductivity of the walls bounding the layer. The external surfaces of the walls are taken to be at various but constant temperatures. Equations for the small monotonic perturbations of the equilibrium are solved using a variation of the Bubnov-Galerkin method. In this case, approximations with four base functions are used. The range of values of the parameters for which the finite thickness and finite thermal conductivity of the walls have a substantial effect on the critical Rayleigh numbers was found. It is noted that the critical Rayleigh number could be negative because of the Joule heating and associated thermal boundary conditions.