Inverse Analysis Of Thermal Conductivities In Non-homogeneous Heat Conductions Using Boundary Element Method

Inverse heat conduction problem is of great significance in various fields. Numerical studies of heat transfer problems are much earlier in the study of boundary element method。 There are many commercial softwares to study the heat conduction problem based on the finite difference method and finite element method. But there are no a universal software dearling with the ill-conditioned inverse heat conduction problem.Boundary element method is an effective numerical method. It quickly becames a new and effective tool for engineering analysis because of many advantages such as the dimension reduction, high precision and high speed of convergence.Lyness and Moler originated the ingenious idea of Complex Variable Differentiation Method (CVDM) in1967. In the method, the partial derivative is calculated by transforming into calculation of function value in the complex domain, and this makes the method have high accuracy of the corresponding partial derivative calculation. It has extensive application prospect in the calculation of optimization in aeronautics and astronautics and other fields because it’s high sensitivity in dealing with problems.It is first appeared in the1970s to study the heat conduction problem based on boundary element method. There are no researches to study the inverse heat conduction problem with the development of the boundary element method combined with least square method and minimum energy method until1980s.This paper presents a new inverse analysis approach for sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to the function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. A Fortran program has been written for general solution of the inverse problem of heat conductions based on this theory. The program has the advantages of easy calculation and applicability. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.