Rapid solidification as an irreversible process involves an excess enthalpy change, Delta H-ex, which is dissipated and stored at the solid-liquid interface, and implies an unreleased part of the latent heat of fusion; this Delta H-ex is not negligible on modeling the moving of the solid-liquid interface. In the present paper, the values of Delta H-0(ne), the enthalpy difference between rapidly solidified and annealed alloy, were estimated using a DSC measurement method in as-melt spun Al-Si and Al-Mn alloys. The value of Delta H-0(ne) was related to the excess enthalpy change, Delta H-ex. Taking this "thermal engine effect" and the interface kinetic attachment into account, a conceptual model of a "moving boundary problem (MBP)" was formulated to describe the crystal growth during rapid unidirectional solidification. The author attempts to emphasize that this modeling scheme differs from classical MBP, the so-called "Stenfen Problem" in the mathematical formulation and physical contents, due to consideration of the "thermal engine effect".