Abstract: Based on the theories of the heat transfer, the principle of phase transformation and the theory of electric and magnetic field, the mathematical model of transient temperature field involving phase transformation during magnetic field quenching is established. The heat exchange equation including magnetic field is founded. The finite element equation is set up. The distributing of transient temperature on the coupling effects of heat and magnetism is obtained. With test and measurement, the results show that after magnetic field quenching, cooling velocity is decreased, cooling curve is flatten out, and the hardness is slightly raised.

Key words: magnetic field quenching, specific heat's abrupt change, non-linear heat conduction equation