Investigation of sensitivity of the inverse method applied to determination of the thermal conductivity of steels

In this paper the analysis of the inverse method of thermal conductivity es timation of solid body is presented. A finite element method (FEM) has been applied to study the problem. When inverse problems are involved in determ ination of coefficient of thermal conduction, it is necessary to measure te mperature in some points of the solution domain. The proposed method has be en verified by comparison of the numerical results to those obtained from t he analytical solution of heat transfer equation for one-dimensional, trans ient heat conduction in semi-finite cylinder insulated on the circumferenti al surface when both boundary and initial conditions and thermal properties of the cylinder were known. Therefore, experimental data have been replace d by the temperature distribution coming from analytical formulation of the problem. Additionally it was assumed that the function of thermal conducti vity dependence on the temperature belongs to class of quadractic or linear polynomials. It was found out that the method gives good and stable result s in a wide range of input parameters. The set of a few temperature measure ment points has been used in numerical solution. Estimation results are clo se to the analytical solution for varying measurement simulation times. In a domain of parameters variability neither the number nor the location of m easuring points influence significantly the accuracy of thermal conductivit y estimation. It has been found out that the presented method is not sensit ive to the initial value of thermal conductivity used as a starting point i n the model.