The free convective heat transfer to the power-law non-Newtonian flow from
a vertical plate in a porous medium saturated with nanofluid under laminar conditions is
investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical
model of power-law. The model used for the nanofluid incorporates the effects of Brownian
motion and thermophoresis. The partial differential system governing the problem is
transformed into an ordinary system via a usual similarity transformation. The numerical
solutions of the resulting ordinary system are obtained. These solutions depend on
the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion
number Nb, and thermophoresis number Nt. For various values of n and Le, the effects
of the influence parameters on the fluid behavior as well as the reduced Nusselt number
are presented and discussed