Thermal convection instability with throughflow in an Oldroyd-B fluid saturated bidispersive porous layer

Abstract

This research explores the thermal convection instability with throughflow in a bidispersive porous layer saturated with Oldroyd-B fluid, using a modified Darcy-Oldroyd model. The study identifies both stationary and oscillatory modes through linear stability analysis. The eigenspectrums of eigenvalues demonstrate that two modes of instability are present in the Oldroyd-B fluid model, whereas only the stationary mode is observed in the Newtonian fluid model. Furthermore, the throughflow significantly influences the instability modes. When Péclet number Pe is less than 2, instability manifests in two modes: stationary and oscillatory. However, as Pe exceeds 2, only the oscillatory mode is observed. Moreover, this critical value remains unaffected by variations in other parameters. The neutral stability curve reveals that instability is suppressed as the throughflow increases. When both the oscillatory and stationary modes occur simultaneously (Pe < 2), the neutral stability curve exhibits two minima, each corresponding to one of the modes. Additionally, an increase in relaxation time magnifies instability, whereas an increment in the permeability ratio (K_r) suppresses instability.