Solidification as a heat transfer process accompanying a phase transition plays a major role in manufacturing processes and material evolution processes. However, the complex combinations of solidification mechanisms at interfacial boundaries prevent us from its full understanding. A statistical thermodynamic transport theory for heat transfer has been proposed. We here demonstrate the validity of the heat transfer theory for internal convection and external conduction by examining the solidification processes at the interface of two different phase materials. Three variable separation constants designate particle number constants and play the major roles in exploring the distinct solidification mechanisms. In solidification, the four regimes of convection, nucleation, transient, and film solidification are illustrated and their heat flux curves are explored as a function of temperature difference between electrode and saturation temperature. Three limiting heat fluxes and four activation temperatures are implemented as input parameters. The heat transfer theory pictures that the formation mechanism of dendrites takes place under the control of nucleation solidification, and the relevant parameters in the control mechanism are predicted. Theoretical heat flux profiles in solidification agree with experimental heat flux data, and the theory is capable of predicting the heat flux mechanisms in full temperature regimes of solidification as well as in the spatial and temporal regimes. (C) 2013 Elsevier Ltd. All rights reserved.