The problem of phase change from liquid to solid in the inviscid plane-stagnation flow is theoretically investigated. The solution at the initial stage of freezing is obtained by expanding it in powers of time, and the final equilibrium state is determined from the steady-state governing equations. The transient solution is dependent on the three dimensionless parameters, but the equilibrium state is determined by one parameter of (temperature ratio/conductivity ratio). The effect of the fluid flow on the growth rate of the solid in the pure conduction problem can be clearly seen from the solution of the initial stage and the final equilibrium state. The characteristics of the transient heat transfer at the surface of the solid and the liquid side of the solid-liquid interface for all the dimensionless parameters are elucidated