Free Electrothermo-Convective Instability in a Dielectric Oldroydian Nanofluid Layer in a Porous Medium

For the last few years, thermal instability of non-Newtonian nanofluids becomes a prominent field of research because it has various applications in automotive industries, energy-saving, nuclear reactors, transportation, electronics etc. and suspensions of nanoparticles are being developed in medical applications including cancer therapy. In this paper, a free electrothermo-convective instability in a dielectric nanofluid layer in a porous medium is studied. An Oldroyd’s constitutive equation is used to describe the behaviour of nanofluid and for porous medium, the Darcy model is employed. The equation of conservation of momentum of fluid is stimulated due to the presence of an AC electric field, stress-relaxation parameter and strain-retardation parameter. The stability of the system is discussed in stationary and oscillatory convections for free–free boundaries. For the case stationary convection, it is found that the Oldroydian Nanofluid behaves like an ordinary nanofluid as the stationary Rayleigh number is independent of the stress-relaxation parameter, the strain-retardation parameter and Vadasz number. The effect of stress-relaxation-time parameter, strain-retardation-time parameter, Vadasz number, nanoparticles Rayleigh number, modified diffusivity ratio, medium porosity, Lewis number and electric Rayleigh number examined numerically and graphs have been plotted to analyse the stability of the system. It is observed that the electrical Rayleigh number has destabilizing influence whereas nanoparticles Rayleigh number, porosity and modified diffusivity ratio have stabilizing effect on the system. The oscillatory convection is possible for the values of the stress-relaxation parameter less than the strain-retardation parameter for both top-heavy/bottom-heavy distributions of nanoparticles.