Abstract

Inverse Heat Conduction Problems (IHCPs) have been widely used in engineering fields in recent decades. IHCPs are not the same as direct heat conduction problems which are "well-posed". IHCPs are made more difficult since they are inherently "ill-posed"; that is, a small error perturbation will lead to a large error in the solution reconstructed. Prediction of an unknown in an IHCP is not an easy event. An IHCP also handles the desired information from measurements containing noise. A stable and accurate reliable inversion solver shall be studied. This dissertation is split into four parts. The first part describes space boundary IHCPs, and attempts to utilize noisy measurement data to predict unknown surface temperatures or heat fluxes. A new algorithm, using a Kalman Filter to filter the measurement noise combined with an implicit time-marching finite difference scheme, solves a space boundary IHCP. In the second part, errors in reconstruction of the temperature at each boundary of a one-dimensional IHCP can be presented by a simple relation. Each relation contains an unknown coefficient, which can be determined by using one simulation through the inversion solver of a pair of specified sensor locations. This relation can then be used to estimate the other recovery errors at the boundary without using the inverse solver. In the third part, an experimental study of temperature drop between two rough surfaces is conducted. The experimental data are analyzed by utilizing an inversion solver developed in this dissertation. In the fourth part, an IHCP with a melting process using the measured temperature and heat flux at one surface is solved by a new geometry inversion solver with a heat flux limiter to reconstruct the melting front location and the temperature history inside the test domain.