Finite Element Formulation of the Two-Dimensional Nonlinear Inverse Heat Conduction Problem

摘要

The calculation of the surface temperature and surface heat flux from measured temperature transients at one or more interior points of a body is identified in the literature as the inverse heat conduction problem. Heretofore, analytical and computational methods of treating this problem have been limited to one-dimensional nonlinear or two-dimensional linear material models. An inverse solution technique applicable to the two-dimensional nonlinear model with temperature-dependent thermophysical properties is presented. This utilizes a finite element heat conduction model and a generalization of Beck's one-dimensional nonlinear estimation procedure. The formulation is applied to the cross section of a composite cylinder with temperature-dependent material properties. Results are presented to demonstrate that the inverse formulation is capable of successfully treating experimental data. An important feature of the method is that small time steps are permitted while avoiding severe oscillations or numerical instabilities due to experimental errors in measured data. (ERA citation 06:001208)