Estimation of Boundary Conditions in Nonlinear Inverse Heat Conduction Problems

Abstract

A sequential method is proposed to estimate boundary conditions for nonlinear heat conduction problems. An inverse solution is deduced from a e nite element method, the concept of the future time, and a modie ed Newton‐ Raphson method. The undetermined boundary condition at each timestep is denoted as theunknown variablein a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of nonlinear equations. No selected function isneeded to represent the undetermined function in advance. Two examples are used to demonstrate the characteristics of the proposed method. Thecloseagreementbetween theexactvaluesand theestimated resultscone rmsthevalidity and accuracy of the proposed method. The results show that the proposed method is an accurate, stable, and efe cient method to determine the boundary conditions in two-dimensional nonlinear inverse heat conduction problems.