Effect of permeability on steady flow in a dendrite layer

We consider the problem of nonlinear steady convective flow in a horizontal dendrite layer during alloy solidification. We analyze the effect of permeability of the layer on the stationary modes of convection in the form of two-dimensional rolls and three-dimensional patterns. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the two- and three-dimensional solutions to the weakly nonlinear problem by using a perturbation technique, and the stability of these solutions are investigated with respect to arbitrary three-dimensional disturbances. ... [more]published or submitted for publicationis peer reviewe