Engineering Transactions, 60, 4, pp. 355–370, 2012

A Characterization of the Rivlin-Ericksen Viscoelastic Fluid in the Presence of a Magnetic Field and Rotation

Ajaib S. BANYAL
Department of Mathematics, Govt. College Nadaun, Hamirpur

A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence
of an uniform vertical magnetic field and rotation. Following the linearized stability theory and
normal mode analysis, this paper mathematically establishes the condition for characterizing
oscillatory motion, which may be neutral or unstable, for rigid boundaries at the top and
bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in
the configurations, are necessarily non-oscillatory in the regime
TAF
2 +
TA
4 +
Qp2
2
1;
where TA is the Taylor number, Q is the Chandrasekhar number, p2 is the magnetic Prandtl
number, and F is the viscoelasticity parameter. This result is important, since it holds for all
wave numbers for rigid boundaries of infinite horizontal extension at the top and bottom of the
fluid, and the exact solutions of the problem investigated in closed form are not obtainable.
Keywords: thermal convection, Rivlin-Ericksen fluid, rotation, magnetic field PES, Rayleigh number, Chandrasekhar number, Taylor number.
Full Text: PDF


Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland