Onset of double-diffusive convection of a sparsely packed micropolar fluid in a porous medium layer saturated with a nanofluid

The onset of convection of a sparsely packed micropolar fluid in a porous medium layer saturated by a nanofluid is examined by using a linear and nonlinear stability analyses. The Darcy-Brinkman-Forchheimer model is employed for the porous medium layer. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The critical Rayleigh number, wave number for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory, and the nonlinear analysis is made with minimal representation of the truncated Fourier series analysis involving only two terms. The effect of various parameters on the stationary and oscillatory convections is shown pictorially. The dependence of stationary or oscillatory convection on the porous parameter and parameters involved in micropolar fluids is also discussed. We also study the effect of time on transient Nusselt number and Sherwood number which are found to be oscillatory when time is small. However, when time becomes very large, both the transient Nusselt value and Sherwood value approach to their steady-state values.