Nonlinear estimation applied to the nonlinear inverse heat conduction problem

Abstract

The estimation of the surface temperature or heat flux density utilizing a measured temperature history inside a heat-conducting solid is called the inverse heat conduction problem. This problem becomes nonlinear if the thermal properties are temperature-dependent. A new finite-difference method is given. It is based in part upon the concepts of a general technique for solving inverse problems called nonlinear estimation. The method (or family of methods) estimates the components of the heat flux one at a time and thus, may be considered an on-line method. Another method is outlined for which all of the components of the heat flux are found simultaneously. As suggested by the developments in nonlinear estimation, the sensitivity coefficients can be utilized to gain insight into these methods. The sensitivity coefficients help indicate that the on-line method requires “future” temperatures when small time steps are to be used. Several examples of the use of the on-line method are given. These examples are for cases with non-exact data. The results demonstrate a method that is rather remarkable in its ability to extract information about the surface condition from experimental measurements that lag and are damped compared to the surface condition.