Non-linear Rayleigh–Bénard magnetoconvection in temperature-sensitive Newtonian liquids with heat source

Abstract

The present paper aims at weak non-linear stability analysis followed by linear analysis of finite-amplitude Rayleigh–Benard magnetoconvection problem in an electrically conducting Newtonian liquid with heat source/sink. It is showed that the internal Rayleigh number, thermorheological parameter and Chandrasekhar number influence the onset of stationary convection and Nusselt number. The generalised Lorenz model derived for the problem is essentially the classical Lorenz model with its coefficients depending on the variable heat source (sink), viscosity and the applied magnetic field. The result of the parameters’ influence on the critical Rayleigh number explains their effect on the Nusselt number as well. The effect of increasing strength of the magnetic field in stabilising the system and diminishing heat transport is demonstrated. But the heat source and variable viscosity work together to make the system unstable, as their effect enhances heat transfer.