Linear stability analysis of the magnetic fluid in a rotating cylindrical annulus by using solenoidal galerkin method

In this study, onset of convection motion of a electrically conducting fluid in an annular space, which rotates with a certain angular velocity Omega and has a temperature difference between the inner and outer surface of the annulus, is numerically simulated under a homogeneous magnetic field B. The rigid boundary conditions are considered to provide both the inner and outersurfaces of annulus. The numerical technique is based on solenoidal basis functions satisfying the boundary conditions for both velocity and induced magnetic field. Theexpansion bases for the thermal field are also constructed to satisfy the boundary conditions.The governing partial differential equations are reduced to a system of ordinary differentialequations governing the time evolution of the expansion coefficients under Galerkin projectiononto the subspace spanned by the dual bases. In the process, the pressure term in themomentum equation is eliminated. This system is used in various numerical experiments in the linear flow regime to test the solenoidal basis and reflect the procedure.