  The (1+1)-dimensional nonlinear boundary value problem, modeling the process
of melting and evaporation of metals, is studied by means of the classical Lie
symmetry method. All possible Lie operators of the nonlinear heat equation,
which allow us to reduce the problem to the boundary value problem for the
system of ordinary differential equations, are found. The forms of heat
conductivity coefficients are established when the given problem can be
analytically solved in an explicit form.
