Trend analysis in the 1D solution of the inverse heat conduction problem by the sequential function specification technique

Abstract

Inverse heat conduction problems are categorized by the solution technique or algorithm (Function Specification, Regularization, Laplace Transform, Conjugate Gradient, Mollification), by the solution method (Duhamel's Theorem, Difference Method Finite, Finite Element Method), and by the time domain (Stoltz Method, Sequential Method, and Complete Domain). In the direct approach, the unique solution of an effect due to a cause is obtained. From the cause-effect view, inverse problems are characterized by not meeting the existing criteria and the uniqueness of determining the cause when analyzing an effect. However, this has promoted the implementation of robust methods to optimize the stability of a solution. In this work, the study system consists of a long solid cylinder at an elevated temperature that is cooled. The implemented methodology allowed the creation of data trends through linear extrapolation to improve estimation accuracy for abrupt changes in the function (boundary condition). The results show an acceptable increase in punctual precision in the estimation, and it is a consequence of the solution that the calculated thermal histories already contain an implicit degree of error.