Determination of thermal diffusivity from experimental data

The solution of an inverse problem for a one-dimensional unsteady heat equation is examined. The problem consists of determining the temperature dependence of thermal diffusivity from thermocouple data obtained at several points in the bulk of the body. The unknown function is sought in the form of a polynomial. The problem is reduced to an extremal statement where the required parameters are selected on the basis of the discrepancy principle. The functional characterizing the degree of discrepancy is minimized by the method of steepest descents. An algorith for the solution of the problem is proposed and is applied to an example.