Onset of triply diffusive convection in a power-law fluid saturated porous layer

The linear instability of triply diffusive power-law fluid saturated porous layer is investigated. The modified Darcy's law and the Oberbeck-Boussinesq approximation are adopted for modeling the buoyant flow. The governing equations studied at varous pahycial parameters of power-law fluid. It is found that for minimal values of Peclet number, the pseudoplastic fluids are more stable than the Newtonian fluids, while the dilatant fluids are less stable. An opposite behavior is observed at large values of Peclet number. The asymptotic cases in the regime of small wave number and small Peclet number are discussed in detail. In these regimes, an analytical expression is obtained for the marginal stability condition.