Analysis of Least Stable Mode of Buoyancy Assisted Mixed Convective Flow in Vertical Pipe Filled with Porous Medium

Least stable mode of convective flow, induced by external pressure gradient and buoyancy force in the vertical pipe filled with porous medium, is investigated. Non-Darcy Brinkman-extended model has been considered. To study least stable mode of the fully developed flow linear theory of stability analysis has been used for an wide range [0.01, 100] of Prandtl number (Pr). To this end, coupled ordinary differential equations obtained from linear theory of stability analysis, have been solved numerically using Spectral collocation method. Four different values 10(-1), 10(-2), 10(-3), and 10(-4) of Darcy number (Da) have been considered to study the impact of permeability of the medium on the flow stability. Present study on the least stable mode analysis discloses that when fluid is gas (Pr = 0.7) or water (Pr = 7.0), for relatively large values of Darcy number (i.e. Da = 10(-1) and 10(-2)), first azimuthal mode is the least stable mode of the basic flow in the entire range of Reynold's number (Re) considered in this manuscript. However, when Pr = 70, based on the values of Da, there exist a minimum value of Re beyond it the least stability of the fluid is achieved for zero azimuthal number. Further, it was found that for Da equal to 10(-3) or 10(-4) the instability boundary curves in the (Re, Ra)-plane, for all above three fluids, are almost equal.