The effect of vertical throughflow in Rivlin–Ericksen elastico-viscous nanofluid in a non-Darcy porous medium

The instability of convection in a Rivlin–Ericksen elastico-viscous nanofluid with vertical throughflow is investigated using the linear stability theory. A modified Brinkman model is employed and single-term Galerkin method is used to solve the conservation equations. Nine dominating parameters are extracted from the analysis. Due to the combined effect of vertical throughflow, Brownaian motion, and thermophoresis, the Rayleigh number is reduced by a substantial amount. It is found that through flow delays the convection while other nanofluid parameter enhance the convection. The thermal capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern stationary convection. Using the convective component of nanoparticle flux, the critical wave number is a function of nanofluid parameters as well as throughflow parameter. Major trends are investigated briefly by plotting the graphs.