Available online at www.pelagiaresearchlibrary.com Pelagia Research Library Advances in Applied Science Research, 2014, 5(5):106-118 ISSN: 0976-8610 CODEN (USA): AASRFC 106 Pelagia Research Library Double-diffusive rotatory convection coupled with cross-diffusions in viscoelastic fluid Hari Mohan and Sada Ram Department of Mathematics, ICDEOL, Himachal Pradesh University, Summer Hill, Shimla, India ______________________________________________________________________________________________ ABSTRACT The present paper investigates the effect of a uniform vertical rotation on the physical problem of double-diffusive convection coupled with cross-diffusions in viscoelastic fluid. Some general qualitative results concerning the stability of oscillatory motions and limitations on the oscillatory motions of growing amplitude are derived. The results for the double- diffusive convection problems with or without the individual consideration of Dufour and Soret effects follow as a consequence. Keywords: Double-diffusive convection, Dufour-Soret effects, Rivlin-Ericksen viscoelastic fluid, Rayleigh numbers, Prandtl number, Taylor number MSC 2000 No: 76E99, 76E06 ______________________________________________________________________________________________ INTRODUCTION Thermosolutal convection or more generally double-diffusive convection, like its classical counterpart, namely, single –diffusive convection, has carved a niche for itself in the domain of hydrodynamic stability on account of its interesting complexities as a double- diffusive phenomenon as well as its direct relevance in the fields of Oceanography, Astrophysics, Geophysics, Limnology and Chemical engineering etc. can be seen from the review articles by Turner [1] and Brandt and Fernando [2]. An interesting early experimental study is that of Caldwell [3]. The problem is more complex than that of a single - diffusive fluid because the gradient in the relative concentration of two components can contribute to a density gradient just as effectively as can a temperature gradient. Further, the presence of two diffusive modes allows either stationary or overstable flow states at the onset of convection depending on the magnitude of the fluid parameters, the boundary conditions and the competition between thermal expansion and the thermal diffusion. More complicated double- diffusive phenomenon appears if the destabilizing thermal/concentration gradient is opposed by the effect of a magnetic field or rotation. In the domain of linear stability theory the double- diffusive convection problems can be described by a set of linear ordinary differential equations with constant coefficient and homogeneous boundary conditions. The task of finding the explicit analytical solutions of these equations ( especially when boundaries are rigid) and thereby characterizing the critical conditions at the threshold of instability are not entirely trivial since prohibitive amount of numerical work is required to affirm oscillatory or non- oscillatory motions as the eigen value equation involves all the parameters of the problem implicitly. The stability properties of binary fluids are quite different from pure fluids because of Soret and Dufour effects [4], [5]. An externally imposed temperature gradient produces a chemical potential gradient and the phenomenon known as the Soret effect, arises when the mass flux contains a term that depends upon the temperature gradient. The analogous effect that arises from a concentration gradient dependent term in the heat flux is called the Dufour effect.