Distributed parameter thermal controllability: a numerical method for solving the inverse heat conduction problem

This paper addresses the inverse heat conduction problem encountered in thermal manufacturing processes. A numerical control algorithm is developed for distributed parameter conduction systems, based on Galerkin optimization of an energy index employing Green’s functions. Various temperature profiles of variable complexity are studied, using the proposed technique, in order to determine the surface heat input distribution necessary to generate the desired temperature field inside a solid body. Furthermore, the effect of altering the iterative time step and duration of processing time, on the convergence of the solution generated by the aforementioned method is investigated. It is proved that despite the variations in numerical processing, the iterative technique is able to solve the problem of inverse heat conduction in the thermal processing of materials