What is the most suitable fixed grid solidification method for handling time-varying inverse Stefan problems in high temperature industrial furnaces?

This paper presents a simple inverse heat transfer method for predicting the time-varying bank thickness of the phase change protective layer inside a high temperature furnace. The direct problem is handled with the single phase method which is neglecting the latent heat. The inverse method rests on the Adjoint Problem and the Conjugate Gradient Method. It is shown that the iterative inverse procedure based on the single phase method predicts a virtual incident heat flux in the liquid zone that yields accurate time-varying bank predictions. Results also indicate that the benefits of the virtual iterative approach are twofold: the CPU time required for solving the inverse problem is reduced and the lagging effect inherent to the inversion is diminished for non isothermal phase change processes. For typical melting furnace operating conditions, it is shown that the virtual approach doubles the allowable diagnostic frequency for predicting the time-varying bank thickness.