Analytic solutions of inverse heat conduction problems

A direct analytic approach is systematically developed for solving inverse heat conduction problems in multi-dimensional finite regions. The inverse problems involve the determination of the surface conditions from the knowledge of the time variation of the temperature at an interior point in the region. In the present approach, the unknown surface temperature is represented by a polynominal in time and a splitting-up procedure is employed to develop a rapidly converging inverse solution. The least square technique is then utilized to estimate the unknown parameters associated with the solution. The method is developed first for the analysis of one-dimensional cases, and then it is generalized to handle two- and three-dimensional situations. It provides an efficient, stable and systematic approach for inverse heat condition problems. The stability and accuracy of the current method of analysis are demonstrated by several numerical examples chosen to provide a very strict test.