Stability analysis of thermosolutal convection in a Brinkman porous layer in the presence of viscous dissipation

Since weakly conducting and highly viscous fluid flows are very common in petroleum and polymer chemical engineering processes, in this article, the significance of the Darcy number on the breakdown of a double-diffusive convection is investigated inside a long horizontal porous channel with the effects of viscous dissipation. It is assumed that the bottom wall of the channel is adiabatic, and the top wall is isothermal. The Brinkman-extended Darcy model is used in the momentum equation of the governing flow through the porous layer. In the stability analysis, arbitrarily oriented oblique roll disturbances are encountered. It is shown that the most significant instability is in the longitudinal rolls (when P=0 or δ=π/2), with the axis parallel to the main flow direction. The obtained eigenvalue problems for both the rolls have been solved by the bvp4c technique in MATLAB. The impacts of the viscous dissipation parameter (ξ) and the Darcy number (Da) on the instability mechanism are examined in addition to the controlling parameter, the solutal Rayleigh number R. Furthermore, the contribution of the Brinkman model is also discussed on the onset of convection for several values of the viscous dissipation parameter and the flow conditions close to the limiting situation of a clear fluid. It is observed that the Darcy number has a stabilizing effect, whereas the viscous dissipation destabilizes the flow.