Unsteady 2D natural convection/phase change of a non-Newtonian liquid inside a square container caused by external mixed convection of a Newtonian fluid with various cavity configurations has been studied numerically. Air was chosen as external cooling fluid and modified non-Newtonian water as the internal solidifying fluid. Conjugate convective fluid and heat transport, described in terms of nonlinear coupled continuity, momentum, and energy equations, were solved by using the finite volume method with the SIMPLE algorithm. Effects of four external fluid inlet/outlet locations and four non-Newtonian rheological models were studied. Results for the time evolution of streamlines, isotherms and freezing curves are analyzed. The effect of the cavity inlet/outlet configuration on streamlines of the external fluid is remarkable, near the region close to the non-Newtonian liquid filled container. (C) 2011 Elsevier Ltd. All rights reserved.