  In this paper, an analytical solution of alloy solidification problem is
presented. We develop a special method to obtain an exact analytical solution
for mushy zone problem. The main key of this method is a requirement that
thermal diffusivity in the mushy zone to be constant. From such condition we
obtain an ordinary differential equation for liquid fraction function. Thus the
method can be examine as ''a model'' to achive analytical solution of some
unrealistic problems.
  An example of solutions is presented: the noneutectic titanium-based alloy
solidification. We provide the comparison of numerical simulation results with
obtained exact solutions. It shown that very simple apparent capacity-based
numerical scheme is provided a good agreement with exact positions of the
solidus and liquidus isoterms, and with temperature profiles also.
  Finally, some extensions of the method are outlined.
