Analysis of non-uniform temperature profiles on Bénard convection in micropolar fluids

摘要

The qualitative effect of non-uniform temperature profile on the linear stability analysis of the Bénard convection in micropolar fluids is examined. The Rayleigh numbers are obtained for free–free, rigid–rigid, rigid–free velocity boundary combinations with adiabatic temperature on the micro-rotation free boundaries. The influence of various micropolar fluid parameters on the onset of stationary convection is analyzed. Three types of temperature profiles viz., linear, parabolic and inverted parabolic are considered and their comparative effect on the onset of convection is discussed. It is observed that the Rayleigh number obtained is less than that of the corresponding Newtonian problem.