Inverse Heat Conduction Using Measured Back Surface Temperature and Heat Flux

Abstract

In the high-energy laser heating of a target, the temperature and heat flux at the heated surface are not directly measurable, but they can be estimated by solving an inverse heat conduction problem based on the measured temperature and/or the heat flux at the accessible (back) surface. In this study, the one-dimensional inverse heat conduction problem in a finite slab is solved by the conjugate gradient method, using measured temperature and heat flux at the accessible (back) surface. Simulated measurement data are generated by solving a direct problem, in which the front surface of the slab is subjected to high-intensity periodic heating. Two cases are simulated and compared, with the temperature or heat flux at the heated front surface chosen as the unknown function to be recovered. The results show that the latter choice (i.e., choosing back surface heat flux as the unknown function) can give better estimation accuracy in the inverse heat conduction problem solution. The front surface temperature can be computed with high precision as a by-product of the inverse heat conduction problem algorithm. The robustness of this inverse heat conduction problem formulation is tested by different measurement errors and frequencies of the input periodic heating flux.