Inverse resolution of the heat-transfer equation with internal heat source: Application to the quenching of steels with phase transformations

A method is described for calculating the time dependence of the temperature and heat flux (on heating and fooling) at the surface of a solid body, For a given ambient temperature and a known time-temperature function of an interior point, the surface hear flux is computed through an inverse conduction algorithm taking into account the nonlinear nature of the problem, Moreover, this algorithm includes the enthalpy of phase transformations. The influence of space and time steps on inverse calculations (precision, stability) is investigated, The method is then applied to thermal cases involving different transformations in steels.