The calculation of surface heat transfer coefficient during quenching process is one of the
inverse heat conduction problem,
and it is a nonlinear and bad-posed problem. A new method to calculate the temperature-dependent surface heat transfer coefficient during quenching process is presented, which applies
finite element method (FEM), advance-retreat method and golden section method to the
inverse heat conduction problem, and can calculate the surface heat transfer coefficient according to the temperature curve gained by experiments. In order to apply the advance-retreat method to inverse heat conduction problem during quenching process, the arithmetic is improved, so that the searching interval of optimization can be gained by the improved advance-retreat method. The optimum values of surface heat transfer coefficient can be easily obtained in the searching interval by golden section method. During the calculation process, the phase-transform volume and phase-transform latent heat of every element in every time interval can be calculated easily by FEM, the temperature and phase-transform volume of every element are calculated with the coupling calculation of phase-transform latent heat.