Effects of Magnetic Field and Non-uniform Basic Temperature Gradient on the Onset of Rayleigh-Benard Convection in a Micropolar Fluid

Abstract

The effects of magnetic field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard convection in an electrically conducting micro polar fluid are studied using the Garlerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classically electrically conducting fluid without suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.