Implementation of Geometrical Domain Decomposition Method for Solution of Axisymmetric Transient Inverse Heat Conduction Problems

Abstract

The objective of this article is to study the performance of iterative parameter and function estimation techniques to solve simultaneously two unknown functions (quadratic in time, and linear in time and space) using transient inverse heat conduction method in conjunction with a geometrical domain decomposition approach, in cylindrical coordinates. For geometrical decomposition of physical domain, a multi-block method has been used. The numerical scheme for the solution of the governing partial differential equations is the finite element method. The results of the present study for a configuration composed of two joined disks with different heights are compared to those of exact heat source and temperature boundary condition using inverse analysis. Good agreement between the estimated results and exact functions has been observed for parameter estimation techniques in contrast to those of function estimation approach. In summary, the results show that the function estimation technique is sensitive to the location of measurement points, but is useful to estimate unknown functions without a priori knowledge of the functions' spatial and/or temporal distributions. However, the function estimation technique suffers from a drawback: its implementation and data extraction are less straightforward than parameter estimation method. Finally, it is shown that the use of geometrical domain decomposition offers the possibility of developing a robust inverse analysis code for general purpose heat conduction problems.

ACKNOWLEDGMENT

The authors would like to acknowledge the Office of Vice-Chancellor for Research, Sharif University of Technology, Iran, for its partial financial support of this research and to express their sincere gratitude toward the reviewers of this article.

Notes

* for estimating the boundary condition using sensors located near the right boundary of block 2

^†for estimating the boundary condition using sensors located near the upper boundary of block 2

* Boundary condition.