Solution of the inverse heat conduction problem with a time-variable number of future temperatures

The one-dimensional linear inverse heat conduction problem (IHCP) is considered here. In this problem, the accuracy in the determination of the surface heat flux is not only affected by noise occurring in the remote measurement but is also influenced by the bias introduced by the method itself. A modified function specification algorithm is proposed that automatically balances the sensitivity to measurement error and the bias, for each time step. This algorithm uses a time-variable number of future temperatures. The new method is compared with the classic Beck's function specification method, i.e., with a constant number of future temperatures. Using a clear definition of the different errors, the comparison shows that, in many cases, the modified method significantly improves the IHCP resolution.