Impact of Media Permeability on Poiseuille Flow in Fluid Overlying Porous Domain: Effect of Low and High Prandtl Number

The present study is dedicated towards the stability analysis of non-isothermal plane Poiseuille flow in a fluid domain that overlies a porous domain. The Navier Stokes equations are implemented to govern the flow of the incompressible Newtonian fluid in the fluid domain whereas Darcy model is used in the porous domain since the value of porosity considered in the present study is 0.3. The flow of gases and heavy oil is analysed by changing the Prandtl number of the fluid since the Prandtl number helps to determine the type of fluid. The effect of depth ratio and media permeability in terms of Darcy number on the stability of the superposed system is analysed. This is accomplished using the neutral stability curves produced by the linear stability analysis. The stability curves illustrate bimodal (both fluid and porous mode) behaviour according to the considered variation under effect. It is observed that decreasing depth ratio while increasing Darcy number instigates the porous dominant instability. Also, for low Prandtl number, the porous mode dominates for a very small range of wavenumber as compared to those for Prandtl number.