We focus on a problem of a binary alloy growing over a horizontal, cooled planar substrate pulled at a constant speed in horizontal direction. From the practical point of view, such experimental configuration is motivated by the applications in material engineering. From the theoretical point of view, the main task is the study of a non-trivial flow in the liquid region ahead of the mushy layer and its interaction with the mushy layer. The pulled substrate is the source of a boundary-layer flow in the liquid phase ahead of the mush/liquid interface. The self-similar solutions of the governing boundary-layer equations are found and analysed via the asymptotic methods. The main goal of the thesis is to determine how the boundary-layer flow influences the physical characteristics of the solidifying system.