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 estimation of solid body is presented. A finite element method (FEM) has been applied to study the problem. When inverse problems are involved in determination of coefficient of thermal conduction, it is necessary to measure temperature in some points of the solution domain. The proposed method has been verified by comparison of the numerical results to those obtained from the analytical solution of heat transfer equation for one-dimensional, transient heat conduction in semi-finite cylinder insulated on the circumferential surface when both boundary and initial conditions and thermal properties of the cylinder were known. Therefore, experimental data have been replaced by the temperature distribution coming from analytical formulation of the problem. Additionally it was assumed that the function of thermal conductivity dependence on the temperature belongs to class of quadractic or linear polynomials. It was found out that the method gives good and stable results in a wide range of input parameters. The set of a few temperature measurement points has been used in numerical solution. Estimation results are close to the analytical solution for varying measurement simulation times. In a domain of parameters variability neither the number nor the location of measuring points influence significantly the accuracy of thermal conductivity estimation. It has been found out that the presented method is not sensitive to the initial value of thermal conductivity used as a starting point in the model.