Double diffusive convection in a porous medium layer saturated with an Oldroyd nanofluid

Abstract

The onset of double diffusive convection in a horizontal layer of a porous medium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy-Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values.