Effect of experimental uncertainty on the accuracy and stability of a new inverse method for heat transfer in solidification

A robust new method for the solution of the inverse heat conduction problem for a one-dimensional body undergoing a change of phase has been developed. Inverse heat conduction problems arise when it is desired to calculate boundary conditions from interior temperature measurements. The calculation of these boundary conditions is necessary if phase change problems are to be properly simulated. The new inverse method is accurate, and reasonably insensitive to noise in the measured data. It is also shown to be superior to other commonly used inverse methods (such as the Weber Method). The method is applied to the case of the solidification of aluminium alloys in ceramic moulds. The effects of uncertainty in experimental measurements on the calculation of interface boundary conditions are examined. The uncertainties include noise in the measured thermal data, bias of the mould thermocouple, accuracy of thermocouple location, accuracy of mould thickness measurement, and accuracy of thermal properties.