Simulation of the onset of convection in a porous medium layer saturated by a couple-stress nanofluid

Linear and nonlinear stability analyses for the onset of time-dependent convection in a horizontal layer porous medium saturated by couple-stress non-Newtonian nanofluid, intercalated between two thermally insulated plates, are presented. Brinkman Maxwell–Garnett formulations adopted nanoscale effects. A modified Darcy formulation that includes time derivative term is used momentum equation. The nanofluid assumed to be dilute this enables treated as weakly heterogeneous with variation thermal conductivity viscosity, vertical direction. general transport equations solved Galerkin-type weighted residuals method. perturbation method deployed linear analysis Runge–Kutta–Gill quadrature scheme analysis. critical Rayleigh number, wave numbers stationary oscillatory modes, frequency oscillations obtained analytically using theory, executed minimal representation truncated Fourier series involving only terms. effect various parameters on behavior visualized. parameter convections also shown graphically. It found has stabilizing both convections. Transient Nusselt number Sherwood exhibit an nature when small. However, at very large values time, approach their steady-state values. study relevant dynamics biopolymers solution microfluidic devices rheological nanoparticle methods petroleum recovery.