Linear stability of mixed convection in a differentially heated vertical channel filled with high permeable porous-medium

Abstract

Linear stability analysis is used to analyze the stability of parallel flow induced by an external pressure gradient and buoyancy force in a differentially heated vertical channel filled with a fluid-saturated high permeable porous medium. The non-Darcy model which gives rise to the volume averaged Navier-Stokes (VANS) equation is used except for some comparative study where Darcy model is also used. The investigation is made for a wide range of Prandtl numbers (Pr) that includes mercury, air, water and heavy oils. The spectral method has been adopted to solve the governing equations of the problem. In the entire considered range of Reynolds number (Re) the linear stability results show that the type of instability for mercury is thermal-shear (i.e., the instability is hydrodynamic in origin, resulting from an unstable velocity distribution, and obtains most of its kinetic energy (KE) through shear source), for water as well as heavy oil it is thermal-buoyant (i.e., most of the KE for this instability is obtained through work done by fluctuating buoyant force), whereas for air it is interactive (i.e., KE for this instability is obtained from both shear as well as buoyant sources). When Re is fixed at 1000, the appearance of point of inflection in the basic flow velocity for a fluid with Pr less than 30 acts as a necessary condition for instability for all considered values of Darcy number. Furthermore, the form drag stabilizes the fluid flow with Pr≥7, however, it acts other way up to a threshold value for fluid flow with Pr<1. Finally, scale analysis reveals that for thermal-shear or interactive instability the minimum critical ΔT for parallel mixed convection flow is less than the same for parallel natural convective flow and it is other way for thermal-buoyant instability. As an example of thermal-buoyant instability, when the channel is filled with a porous medium having permeability 2.5 ×10−6m2 and half-width 5 cm, the mixed convective flow of water remains stable up to a temperature difference of 13.3oC between the walls, whereas the natural convective flow of water remains stable up to a temperature difference of 8.58oC between the walls.