The quenching of steels by water is one of the important problems in engineering for the applications of heat treatment or continuous casting process, but the fundamental researches by the theoretical approaches have not been satisfactorily improved yet. The very rapid cooling problems by the thermal conduction including the latent heat of phase transformation in steel and the transient boiling heat transfer of water on the surface of the steel covering from $850^{circ}C$ to $20^{circ}C$ are the key problems of heat treatment. The present quenching experiments are performed for the cylindrical specimens of carbon steel, S45C of diameters (12-30). Nonlinear transient heat conduction and transient boiling heat transfer problem of water on the surface of specimens is analyzed by the numerical method of inverse heat conduction problem. The conditions for the calculation are that the initial temperature of specimens is $820^{circ}C$ and the cooling water in bath are $20^{circ}C$,$40^{circ}C$,$60^{circ}C$,$80^{circ}C$,$95^{circ}C$ with no agitation.