Common heat transfer problems are associated with a physical cause-effect behaviour which can be described by mathematical models constituting of differential equations. In a thermal process, causes are typically referred to as input variables (e.g. a boundary heat flux), while effects are referred to as output variables or observations (e.g. a temperature field in the body). During the past decades, the theory and application of so-called inverse heat transfer problems (IHTP), which rely on measurements for the estimation of unknown thermal quantities, have attained enormous research interest because of their practical significance as well as the mathematical difficulties and the bottleneck of available computational techniques.

In this talk, a brief summary of our recent developments in the efficient solution of the 3D IHCP which accomplishes different computational tasks arising from practice is given. The proposed solution method incorporates an iterative regularization based on a conjugate gradient method for the normal equations (CGNE) and a multi level adaptive computational strategy. According to our knowledge, the proposed solution technique is an original contribution to the field of IHCP. It is designed to cope with realistic 3D geometries and with non-uniformly distributed configurations of point measurements, which has never been treated in prior research. The solution method has been successfully applied to a few practical examples, e.g. to the reconstruction of local instantaneous surface heat fluxes from experimental temperature data in pool boiling, the identification of heat flux densities at the internal surface of a guide tube,
etc. For the first time, the computational effort of such tasks reduces to the order of minutes on standard desktop computers. The numerical approach has already been coded in C++ and integrated with the NETGEN/NGSolve software package. This numerical kernel of the IHCP tool is augmented by a graphical user interface. In this way, the software can be easily operated on different types of industrial problems.