Solving an inverse heat conduction problem using a non-integer identified model

An inverse heat conduction problem in a system is solved using a non-integer identified model as the direct model for the estimation procedure. This method is efficient when some governing parameters of the heat transfer equations, such as thermal conductivity or thermal resistance, are not known precisely. Reliability of the inversion depends on the precision of the identified model. From considerations on the analytical solutions in simple cases and on the definition of non-integer (or fractional) derivative, the non-integer model appears to be the most adapted. However, some experiments do need to be carried out on the physical thermal system before it can be identified. An application that consists in estimating the heat flux in a turning tool insert during machining is presented. First, identification is performed using a specific apparatus that permits a simultaneous measurement of temperature and heat flux in the insert. Then, during machining, heat flux can be estimated from temperature using this identified model.