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Convective stability analysis of a micropolar fluid layer by variational method
Authors:Joginder S Dhiman  Praveen K Sharma  Gurdeep Singh
Institution:Department of Mathematics, Himachal Pradesh University, Shimla 171005, India
Abstract:This paper studies Rayleigh-Bénard convection of micropolar fluid layer heated from below with realistic boundary conditions. A specific approach for stability analysis of a convective problem based on variational principle is applied to characterize the Rayleigh number for quite general nature of bounding surfaces. The analysis consists of replacing the set of field equations by a variational principle and the expressions for Rayleigh number are then obtained by using trial function satisfying the essential boundary conditions. Further, the values of the Rayleigh number for particular cases of large and small values of the microrotation coefficient have been obtained. The effects of wave number and micropolar parameter on the Rayleigh numbers for onset of stationary instability for each possible combination of the bounding surfaces are discussed and illustrated graphically. The present analysis establishes that the nature of bounding surfaces combination and microrotation have significant effect on the onset of convection.
Keywords:critical Rayleigh number  Rayleigh-Bénard convection  micropolar fluid  eigenvalue problem  variational principle
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