Numerical-Analytical Solution of the Nonlinear Coefficient Inverse Heat Conduction Problem

An approach to identification of thermophysical characteristics on the basis of numerical-analytical solution of a nonlinear coefficient inverse heat conduction problem is considered. The proposed approach is based on reduction of the differential heat conduction equation, which models measuring operations, to the corresponding integro-functional equation with the use of the method of integral transformation and on its numerical solution by iteration method. To raise the stability of numerical solution and eliminate the noises in the measuring apparatuses that distort the measured values of the temperature field, an approximation by the least square method and preliminary smoothing of experimental temperature data by spline-functions are made. The results of numerical experiments carried out on model problems are given, from which it follows that as to the accuracy of calculation the indicated approach is superior to the well-known numerical methods, retaining the possibility of constructing identifiable characteristics as arbitrary functions of temperature.