A thermal non-equilibrium perspective on instability mechanism of non-isothermal Poiseuille flow in a vertical porous-medium channel

We examine the influence of local thermal non-equilibrium state (LTNE) on the instability mechanism of non-isothermal Poiseuille flow in a vertical channel filled with porous medium. The temperature field of the solid porous matrix and the saturating fluid are governed by separate, but coupled, energy equations supplemented with three dimensionless LTNE parameters: inter-phase heat transfer coefficient (H), porosity scaled conductivity ratio (γ) and diffusivity ratio (Γ). The linear stability results show that the critical Rayleigh number (Rac) increases (decreases) with H (γ), which indicates that the effect of H (γ) is to stabilize (destabilize) the flow. The stabilizing impact of H for fluid with low Prandtl number (Pr) becomes high when kinetic energy due to non-isothermal effect is lost to the basic flow. The energy loss to the basic flow increases on increasing (decreasing) H (γ). Depending on the magnitude of all the studied parameters, three types of instabilities, namely: shear, mixed and buoyant have been observed. For relatively low permeable medium buoyant instability becomes the most dominant instability in the range of Prandtl number considered in this study.