Stability Analysis of Natural Convection with Variable Physical Coefficients Using Linear Stability Theory

In this research, the effects of variation of physical transport coefficient of fluid, such as kinematic viscosity and thermal diffusivity coefficient, on the primary instability of natural convection has been investigated. Accordingly, the governing equations are calculated for the onset of free convective flow by using the perturbation theory on the variation of temperature and velocity. Using the theory of linear stability and the wave function, it can be defined the minimum Rayleigh number as critical Rayleigh number in assumed eigenvalue problem. It is assumed that the flow variables, such as the thermal diffusivity coefficient and kinematic viscosity, change exponentially relative to the location. The simulation results show that the critical-wave number function is a even function. Also, the dependence of the amplitude and frequency of oscillation of temperature and velocity disturbances on effective parameters on properties changes was evaluated and the results were analyzed. It can be said that critical Rayleigh number behavior is completely inverse in relation to the thermal emission and kinematic viscosity coefficients, and therefore their simultaneous effect in solving the equations will lead to a decrease in the critical interval of the oscillation.