Solution Of The System Of Differential Equations Related To Marangoni Convections In One ∞uid Layer

Abstract

A linear stability analysis applied to a system consisting of a horizontal layers which contains conducting fluid, affected by uniform vertical magnetic field and solute, the fluid with uniform heating from below. The flow in a fluid layer is assumed to be governed by the Navier-Stokes equation. Numerical solutions were obtained for stationary convection case using the method of expansion of Chebyshev polynomials (the spec- tral method). We conclude that the presence of the magnetic field always has a stabilizing effect on the flow, and that the increasing of the solute Marangoni number leads to the increasing of instability in the fluid