Thermosolutal stability analysis of Brinkman porous layer under local thermal non-equilibrium situation in the presence of viscous dissipation

Accurately predicting local thermal non-equilibrium (LTNE) behavior between fluid and solid phases in weakly conducting, highly viscous flows is essential for numerous engineering applications, including electronic cooling and thermochemical energy storage systems. Motivated by these considerations, we investigate the instability mechanisms of double-diffusive convection influenced by viscous dissipation within a horizontal porous layer under LTNE conditions. A mathematical model is formulated wherein the momentum equation incorporates the Brinkman extension of Darcy's law to account for viscous effects. The thermal boundary conditions assume an adiabatic lower surface and a constant temperature upper surface. A linear stability analysis is conducted by introducing normal mode perturbations to the base state, resulting in an eigenvalue problem that is solved numerically. The study accounts for arbitrarily oriented oblique roll disturbances and reveals that the primary instability mode corresponds to longitudinal rolls (P=0 or δ=π/2), where the roll axis aligns with the primary flow direction. The onset of convection is characterized by determining the critical solutal Rayleigh number (Rc) and associated wavenumber (ac) for both longitudinal and oblique rolls. These results are illustrated graphically for varying values of the interphase heat transfer coefficient (H) and viscous dissipation parameter (ξ). It has been observed that the viscous dissipation parameter and the porosity-modified conductivity ratio exert a destabilizing influence, whereas the interphase heat transfer coefficient contributes to system stabilization over a certain intermediate range.