ABSTRACT: Exact analytical solutions of engineering problems continue to be important in the computer age because of the continued need for benchmarking of fully-numeric solutions, and for direct solvers applied to inverse problems and to indirect measurements. Although many analytical solutions are available in classic books and in the archival literature, the authors of this material usually assume that the mathematical expression is all the reader needs. However for engineering applications, considerable additional work can be required in order to obtain numerical values. For this reason analytical solutions have something in common with imported furniture packed flat in a box – they should come with instructions and tools needed to assemble them into a usable form. The EXACT internet database contains solutions of the heat conduction equation which have been repackaged, by adding information and computer codes, to make them more useful to engineers and scientists.
The first half of the presentation will include a brief introduction to heat conduction and the method of Green’s functions, which has been used to obtain many of the solutions available on the EXACT database. Some examples from the EXACT database will be given.
The second half of the presentation is devoted to recent engineering projects for which an exact solution has been a key component. The projects include: measurement of a thermal protective coating in jet-engine tail pipes; a reaction-diffusion problem with application to fuel cells; and, a moving-heat-source problem with application to welding and additive manufacturing.