Influence of Prandtl number on mixed convective flow in a vertical pipe filled with porous medium: A linear stability analysis

Abstract

The stably stratified flow in a linearly heated vertical pipe filled with a fluid-saturated porous medium is studied. We have emphasized the impact of permeability (via Darcy number, Da) as well as Prandtl number (Pr) on the stability of basic flow at the different azimuthal modes of disturbances (n = 0, 1). The stability of basic flow is examined for a wide range (0.01, 100) of Pr, which comprises different types of fluids (i.e., mercury, gas, liquid, and heavy oils). The extensive numerical results indicate that the least stable mode is either n = 0 (axisymmetric disturbance) or n = 1 (non-axisymmetric disturbance), which depends on the value of Pr as well as Da. At the least stable mode, the basic flow gets destabilized rapidly in the entire range of Pr for Da=10−1. There exists a very small range of Pr in the neighborhood of Pr = 0.3 in which the destabilizing characteristics of Pr changes into stabilizing characteristic for Da=10−2, 10−3, and 10−4 owing to the change of instability mechanism from thermal-shear to thermal-buoyant. The basic flow stabilizes on reducing the media permeability by varying Da from 10−1 to 10−4 for the considered values of Pr. The magnitudes of disturbance radial and circumferential velocities are found to be less than the disturbance axial velocity due to the forced flow in the axial direction. The multi-cellular structure of circumferential and axial velocities is converted into bi-cellular for a relatively large value of Pr.