Inverse Heat Conduction in a Finite Slab with Measured Back Surface Temperature and Heat Flux

Abstract

In High-Energy Laser (HEL) heating of target, the temperature and heat flux at the heated surface is not directly measurable, but can be estimated by solving an inverse heat conduction problem (IHCP) based on measured temperature or/and heat flux at the accessible (back) surface. In this study, the one-dimensional (1-D) IHCP in a finite slab is solved by the conjugate gradient method (CGM) using measured temperature and heat flux at the accessible (back) surface. Simulated measurement data are generated by solving a direct problem where 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 showed that the latter choice, i.e., choosing back surface heat flux as the unknown function, can give better estimation accuracy in the IHCP solution. The front surface temperature can be computed with a high precision as a byproduct of the IHCP algorithm. The robustness of this IHCP formulation is tested by different measurement errors and frequencies of the input periodic heating flux.