Scientific Research of the Institute of Mathematics and Computer Science IDENTIFICATION OF THERMAL CONDUCTIVITY BY MEANS OF THE GRADIENT METHOD AND THE BEM Ewa Majchrzak 1, 2 , Miroslaw Dziewoński 1 , Marek Jasiński 1 1 Department for Strength of Materials and Computational Mechanics Silesian University of Technology, Gliwice, Poland 2 Institute of Mathematics and Computer Science, Czestochowa University of Technology Czestochowa, Poland, email: ewa.majchrzak@polsl.pl Abstract. In the paper the application of the gradient method coupled with the boundary element method for numerical solution of the inverse parametric problem is presented. On the basis of the knowledge of temperature field in the domain considered the tempera- ture dependent thermal conductivity is identified. The non-steady state is considered and 1D problem is discussed. In the final part of the paper the results of computations are shown. 1. Direct problem The following boundary initial problem is considered ( ( 29 ( ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 , , 0 : , 0: , , : , 0 0: , b T xt T xt x L c T t x x T xt x qxt T q x T xt x L qxt T x t T xt T ∂  ∂  ∂ < < = λ   ∂ ∂ ∂   ∂ = = -λ = ∂ ∂ = = -λ = ∂ = = (1) where c is the volumetric specific heat, λ(T ) is the thermal conductivity, T, x, t denote temperature, spatial co-ordinate and time, q b is the boundary heat flux and T 0 is the initial temperature. In order to solve the problem (1) by means of the boundary element method the Kirchhoff transformation is introduced [1, 2] ( 29 ( 29 0 d T UT = λμ μ ∫ (2)