Perspectives on local thermal non-equilibrium (LTNE) Darcy–Bénard convection: Variable permeability and viscosity effects

The interplay between variations in permeability and viscosity on the onset of local thermal non-equilibrium in Darcy–Bénard convection has been investigated. Specifically, permeability is modeled as decreasing linearly with depth, while viscosity decreases exponentially. The validity of the principle of exchange of stabilities is confirmed. A linear instability analysis of the quiescent state is conducted through normal mode decomposition of disturbances, with threshold values for instability onset computed numerically using the Galerkin method. The individual and combined effects of increasing the variable permeability and viscosity parameters on the instability characteristics of the system are examined in detail, highlighting both commonalities and distinctions. It is observed that increasing each parameter individually hastens the onset of convection. However, their combined influence produces both stabilizing and destabilizing effects under certain parametric conditions. In all scenarios, an increase in the scaled interphase heat transfer coefficient consistently delays the onset of convection, whereas a higher ratio of porosity-modified conductivities has the opposite effect. Furthermore, the size of the convection cells remains unchanged at the extreme values of the scaled interphase heat transfer coefficient.