Application of Inverse Methods to the Estimation of Boundary Conditions and Properties

Inverse methods can be used in solidification and related processes for the estimation of boundary conditions or physical properties of materials. For heat flow problems, these methods are based upon a minimisation of the errors between calculated and measured temperatures at given locations and times of the space-time domain, the calculated values being obtained from a numerical solution of the heat flow equation. In the present case, a maximum a posteriori technique has been implemented into a finite element code. This method is then applied to several situations for the determination of : i) the time-dependent heat-transfer coefficient at the surface of a steel rod which has been water-cooled after induction heating (non-stationary situation) ; ii) the space-dependent heat flow at the surface of a direct chill cast aluminium slab (stationary situation) ; and iii) the temperature-dependent thermal conductivity of aluminium-silicon alloys. In this latter case, the influence of the silicon concentration on the thermal conductivity is clearly revealed.