Mixed velocity and thermal boundary effects on the onset of LTNE anisotropic Darcy–Bénard convection

Abstract This study investigates the interplay of mixed velocity and thermal boundary conditions on the onset of local thermal non-equilibrium (LTNE) Darcy–Bénard convection in an anisotropic porous layer. Four distinct combinations of boundary permeability—impermeable/impermeable, porous/porous, porous/impermeable, and impermeable/porous are considered, with a constant heat flux lower surface and an isothermal upper surface. Anisotropies in permeability and thermal conductivities of the fluid and solid phases are incorporated, assuming horizontal isotropy. Linear stability of the steady basic state is examined using a normal-mode analysis of the governing perturbation equations. It is established that the principle of exchange of stabilities holds for all the velocity boundary conditions examined, and the corresponding eigenvalue problem is solved numerically by the shooting method. The system is most stable for impermeable–impermeable boundaries and least stable for porous–porous boundaries, with mixed configurations showing intermediate behavior. Increased mechanical anisotropy and reduced thermal anisotropy, inter-phase heat transfer, and porosity-modified conductivity ratios destabilize the flow, while a lower isoflux–upper isothermal configuration requires a smaller temperature difference to trigger convection compared to the isothermal–isothermal case.