Stability of Vertical Throughow of a Power Law Fluid in Double Diffusive Convection in a Porous Channel

The instability of non-Newtonian power law fluid in double diffusive convection in a porous medium with vertical throughflow is investigated. The lower and upper boundaries are taken to be permeable, isothermal and isosolutal. For vertical throughflow the linear stability of flow is determined by the power law index (n), non-Newtonian Rayleigh number (Ra), Buoyancy ratio (N), Péclet number (Pe) and Lewis number (Le). The eigenvalue problem is solved by two-term Galerkin approximation to obtain the critical value of Rayleigh number and neutral stability curves. It is observed that the neutral stability curves, as well as the critical wave number and Rayleigh number, are affected by the parameters such as Péclet number, buoyancy ratio and Lewis number. The neutral stability curves indicate that power law index n has destabilizing nature when it takes values for dilatant fluid at low Péclet numbers while for the pseudoplastic fluids it shows stabilizing effect. In the absence of buoyancy ratio and vertical throughflow, the present numerical results coincide with the solution of standard Horton-Rogers-Lapwood Problem. The numerical analysis of linear stability for the limiting case of absolute pseudoplasticity is also done by using Galerkin method.