Thermoconvection in magnetized ferrofluids: the influence of boundaries with finite heat conductivity

Abstract

Realistic boundaries of finite heat conductivity Realistic boundaries of finite heat conductivity for thermoconvection in a Rayleigh-B\'enard setup with magnetized ferrofluids are investigated. A linear stability analysis of the conductive state is performed with a shooting method. It shows that the critical wave number is for any magnetic field stronly influenced by the conductivity of the boundaries. Linear as well as nonlinear coefficients of a Ginzburg Landau amplitude equation for convection shortly above the onset are evaluated as functions of the magnetic Rayleigh number, the boundary conductivities, and the fluid Prandtl number.