A Finite Element Approach for Multidimensional Inverse Heat Conduction

Abstract : An efficient technique for mapping thermal boundary conditions is described and demonstrated. The technique is based on a piece-wise polynomial approximation where the Laplacian derivatives in space are constrained using the heat equation. Measured values for the Laplacian are obtained from temperature rate measurements from sensors embedded within a body. The technique has been implemented in a digital signal processor and is able to provide real-time data on thermal boundary conditions over a surface. The technique is adaptable to complex geometry. In this paper the technique will be applied to a study of the injector-wall interactions in a laboratory scale liquid rocket engine.