An Iterative Approach to the Solution of Inverse Heat Conduction Problems

A method is presented for determining the transient surface temperature of a solid when the temperature response as a function of time at an interior point within the solid is known. The method employs approximate iterative techniques suitable for the solution of one-dimensional transient thermal conduction problems in homogeneous or composite solids with constant thermal properties. An example problem is solved using a linear technique and a least-squares approach. This iteration technique exhibits a high degree of accuracy, rapid convergence, and excellent stability. In addition, an analytical expression is developed that predicts the computed surface noise resulting from fluctuations in the input data.