Effect of non-uniform temperature gradient on magnetoconvection driven by surface tension and buoyancy

Abstract

The effect of non-uniform temperature gradient and a uniform magnetic field on the onset of magneto-convection driven by surface tension and buoyancy force in a horizonaal layer of Boussinesq fluid is studied by means of linear stability analysis. The upper boundary is assumed to be free and adiabatic and the lower boundary is rigid and adiabatic. A Galerkin method is used to obtain the eigenvalues. A mechanism for suppressing or augmenting convection is discussed in detail. It is found that as the magnetic field increases the coupling between the two agencies causing instability becomes weaker even in the presence of non-uniform temperature gradient and a discontinuous change in cell size occurs at a certain value of the Rayleigh number as a result of sudden change over from convection dominated by one of the two agencies to that dominated by the other. The results obtained here are compared with the existing ones and found that even a single term Galerkin expnnsion gives rensonable results with minimum of mathematics.