Department of mathematics, Indian Institute of Technology Kharagpur, India
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.