Structured Multiblock Grid Solution of Two-Dimensional Transient Inverse Heat Conduction Problems in Cartesian Coordinate System

ABSTRACT

In this study a structured multiblock grid is used to solve two-dimensional transient inverse heat conduction problems. The multiblock method is implemented for geometric decomposition of the physical domain into regions with blocked interfaces. The finite-element method is employed for direct solution of the transient heat conduction equation in a Cartesian coordinate system. Inverse algorithms used in this research are iterative Levenberg-Marquardt and adjoint conjugate gradient techniques for parameter and function estimations. The measured transient temperature data needed in the inverse solution are given by exact or noisy data. Simultaneous estimation of unknown linear/nonlinear time-varying strengths of two heat sources in two joined surfaces with equal and different heights is obtained for the solution of the inverse problems, and the results of the present study for unknown heat source functions are compared to those of exact functions. This study is an attempt to challenge the goal of combining a multiblock technique with inverse analysis methods. In fact, the structured multiblock grid is capable of providing accurate solutions of inverse heat conduction problems (IHCPs) in industrial configurations, including composite structures. In addition, the multiblock IHCP solver is suitable to estimate unknown parameters and functions in these structures.

The authors would like to acknowledge the partial financial support received from the Centre of Excellence in Energy Conversion (CEEC), Sharif University of Technology, and Engineering and Process Development Division, Research Institute of Petroleum Industry (RIPI), Iran.

Notes

^a Root mean square.

^b Adjoint conjugate gradient.

^a Root mean square.

^b Adjoint conjugate gradient.