Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection. 1. Introduction Bénard convection originated from the experimental works of Bénard [1] and theoretical analysis of Lord Rayleigh [2]. Lord Rayleigh studied the dynamic origins of convective cells and proposed his theory on the buoyancy driven convection. The detailed study of Bénard convection in Newtonian fluid in nonporous medium under varying assumptions of hydrodynamics and hydromagnetics had been given by Chandrasekhar [3]. Lapwood [4] had studied the stability of convective flow in hydromagnetics in a porous medium using Rayleigh’s procedure. The Rayleigh instability of a thermal boundary layer in flow through a porous medium had been considered by Wooding [5]. McDonnel [6] suggested the importance of porosity in the astrophysical context. Double-diffusive convection is referred to buoyancy-driven flows induced by combined temperature and concentration gradients. The onset of double diffusive convection in a fluid saturated in porous medium is regarded as a classical problem due to its wide range of applications in many engineering fields such as evaporative cooling of high temperature systems, agricultural product storage, soil sciences, enhanced oil recovery, packed-bed catalytic reactors, and the pollutant transport in underground. A detailed review of the literature concerning double diffusive convection in binary fluid in a porous medium was given by Nield and Bejan [7], Trevisan and Bejan [8], and Malashetty and Kollur [9]. Thermal convection in binary fluid driven by the Soret and Dufour effects had been investigated by Knobloch [10] and showed that the equations were identical to the thermosolutal problem except relation between the thermal and solutal Rayleigh numbers. The above literature dealt with Newtonian fluids. The study of natural convection of non-Newtonian fluids in a porous medium had gained much attention because of its engineering and