Stability analysis of Poiseuille flow in a fluid overlying anisotropic and highly porous domain*

The present study is dedicated towards the instability of non-isothermal plane Poiseuille flow in a

fluid domain that overlies an anisotropic porous domain with very high value of porosity. The Navier

Stokes equations are implemented to govern the flow of the incompressible Newtonian fluid in the

fluid domain whereas Darcy-Brinkman model is employed to cope with the high porosity in the

underlying porous domain. The effect of depth ratio, permeability in terms of Darcy number and

anisotropy on the stability of the superposed system is examined with the help of the neutral stability

curves obtained via the linear stability analysis. The stability curves illustrate unimodal (porous

mode) or bimodal (both fluid and porous mode) behavior according to the considered variation under

effect. It is observed that decreasing depth ratio and anisotropy while increasing Darcy number

instigates the porous dominant instability.

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