Application of the Finite-Element Method to the Inverse Heat Conduction Problem

The surface heat flux at one boundary of a one-dimensional system is computed by using a transient finite-element analysis, given the initial temperature history at on interior node. A technique based on a difference of squares of temperatures is used to determine incremental changes in the surface heat flux. Specifically, two cases are treated. The first case involves an imposed step change in the surface heat flux, and the second involves an imposed surface heat flux that oscillates periodically in the form of a square wave. Comparison of the predicted heat flux with the imposed heat flux provides an evaluation of the inverse technique.