Estimation of Boundary Conditions in Nonlinear Inverse Heat Conduction Problems

摘要

A sequential method is proposed to estimate boundary conditions for nonlinear heat conduction problems. An inverse solution is deduced from a finite element method, the concept of the future time, and a modified Newton-Raphson method. The undetermined boundary condition at each time step is denoted as the unknown variable in 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 is needed to represent the undetermined function in advance. Two examples are used to demonstrate the characteristics of the proposed method. The close agreement between the exact values and the estimated results confirms the validity and accuracy of the proposed method. The results show that the proposed method is an accurate, stable, and efficient method to determine the boundary conditions in two-dimensional nonlinear inverse heat conduction problems.