USING RAYLEIGH NUMBER THEORY TO STUDY THE CONDITIONS OF BÉNARD CONVECTION

Bénard Convection is a natural convection phenomenon in the plane horizontal layer of fluid heated from below. The study of this phenomenon is of great significance to deeply understand the physical image of dissipative structure and the motion of fluid in chaotic system. In order to study the conditions and physical properties of its generation, this paper establishes a fluid model, derives the characteristic equations satisfied by physical quantities under fixed boundary conditions from the basic set of control equations, uses an important dimensionless number, the Rayleigh number R_a, to characterize whether convection occurs or not, and deduces a critical value of convection from the static mutation to the stable convection R_cl=1708. The theoretical value is obtained and simulated using COMSOL Multiphysics^® to verify that it meets the theoretical prediction and the motion characteristics of the liquid are further analyzed by deriving motion animations, In order to investigate the second instability of convection when the temperature gradient is large, Lorentz equations theory is introduced, and the second critical value R_c2 can be solved by substituting the parameter, and under the assumption of the present paper, R_c2=46177. Accordingly, the conditions for the generation of Benard convection are R_c1＜R_a＜R_c2.