Determination of boundary conditions from the solution of the inverse heat conduction problem in the gas nitriding process

Abstract

Two non-linear unsteady methods for solving the inverse heat conduction problem are discussed and compared in this paper. The first method is based on the finite element method, uses the variational calculus and the BFGS (Broyden-Fletcher–Goldfarb–Shanno) optimization algorithm. The second is an analytical and numerical method based on the approximation of the solution in the form of a linear combination of Chebyshev polynomials. In numerical tests, the stability of the temperature, heat flux density, and heat transfer coefficient obtained from both methods was analyzed. On the basis of experimental data, oscillations of the measured gas temperature and temperature in the component were analyzed. Oscillations of the gas temperature obtained from the experiment were taken into consideration during tests. The first method to solve the inverse problem was used to determine the boundary conditions for the entire gas nitriding process. As a result, stable values of temperature, heat flux density, and the heat transfer coefficient on the surface of the component under treatment in a real gas nitriding process, so far unpublished, were obtained.