A method for determining thermal boundary conditions on surfaces of thermally conducting solids where such quantities were unknown has been developed and demonstrated. The method uses a non-iterative or direct approach in solving steady inverse heat conduction problems. Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on any portion of the surface, the temperature field within the object and any unknown thermal boundary conditions will be computed on surfaces where thermal boundary values are unavailable. A steady-state non-linear heat conduction BEM algorithm has been developed in two and three dimensions and was tested on several simple geometries where the analytic solutions are known. The accuracy and reliability of this technique is very good but tends to deteriorate when the known surface conditions are only slightly over-specified and far from the inaccessible surface. In addition, the algorithm was found not to be overly sensitive to measurement errors in the boundary values.
