Stability of non-isothermal Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous domain

A two-domain approach is used to investigate the thermal convection of Poiseuille flow in an anisotropic and inhomogeneous porous domain underlying a fluid domain. The Newtonian regulated by Darcy's law with implementation Beavers–Joseph condition at interface. impact medium anisotropy inhomogeneity inspected virtue linear stability analysis along other governing parameters such as depth ratio (ratio domain), Darcy number, Reynolds number Prandtl concerning fluid–porous system. neutral curves are found be bimodal unimodal nature leaving its imprint on parametric variation. An increase or decrease parameter follows modal change from (porous) (both fluid). Also, it has been identified that, irrespective considered variations inhomogeneity, least stable mode for ${<}0.05$ ${>}0.16$ fluid. Furthermore, energy budget carried out classify type instability validate mode. thermal–buoyant omission low numbers very values permeability horizontal vertical direction, where thermal–shear witnessed. Likewise, secondary patterns context streamfunction temperature contour analysed prevailing presented numerical results find good experimental support Chen & ( J. Fluid Mech. , vol. 207, 1989, pp. 311–321) limit natural isotropic homogeneous