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Authors
Affiliations
1 Department of Mathematics, NSCBM GC Hamirpur, (HP) 177005, IN
2 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) 177033, IN
Source
Research Journal of Science and Technology, Vol 9, No 1 (2017), Pagination: 101-110
Abstract
Thermosolutal instability of Veronis type in Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field in a porous medium is considered. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth in the presence of uniform vertical magnetic field in a porous medium, are necessarily non-oscillatory, in the regime
Rs ≤ [27π4/4][1/E'P3]{[1/ε+F/P1]-[QP2/π2]},
where Rs is the Thermosolutal Rayliegh number, Q is the Chandrasekhar number, p2 is the magnetic Prandtl number, p3 is the thermosolutal Prandtl number, P1 is the medium permeability, ε is the porosity and F is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. A similar characterization theorem is also proved for Stern type of configuration.
Keywords
Thermosolutal Convection, Rivlin-Ericksen Fluid, Magnetic Field, PES, Rayleigh Number, Chandrasekhar Number.
