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 sys-tem.In order to study the conditions and physical properties of its generation,this paper es-tablishes a fluid model,derives the characteristic equations satisfied by physical quantities un-der fixed boundary conditions from the basic set of control equations,uses an important di-mensionless number,the Rayleigh number Ra,to characterize whether convection occurs or not,and deduces a critical value of convection from the static mutation to the stable convection Rc1=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 Rc2 can be solved by substituting the parameter,and under the assumption of the present paper,Rc2=46177.Accordingly,the conditions for the generation of Benard convection are Rc1<Ra<Rc2.
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