A non-iterative finite element method for inverse heat conduction problems

A non-iterative, nite element-based inverse method for estimating surface heat ux histories on thermally conducting bodies is developed. The technique, which accommodates both linear and non-linear problems, and which sequentially minimizes the least squares error norm between corresponding sets of measured and computed temperatures, takes advantage of the linearity between computed temperatures and the instantaneous surface heat ux distribution. Explicit minimization of the instantaneous error norm thus leads to a linear system, i.e. a matrix normal equation, in the current set of nodal surface uxes. The technique is rst validated against a simple analytical quenching model. Simulated low-noise measurements, generated using the analytical model, lead to heat transfer coe cient estimates that are within 1% of actual values. Simulated high-noise measurements lead to h estimates that oscillate about the low-noise solution. Extensions of the present method, designed to smooth oscillatory solutions, and based on future time steps or regularization, are brie y described. The method’s ability to resolve highly transient, early-time heat transfer is also examined; it is found that time resolution decreases linearly with distance to the nearest subsurface measurement site. Once validated, the technique is used to investigate surface heat transfer during experimental quenching of cylinders. Comparison with an earlier inverse analysis of a similar experiment shows that the present method provides solutions that are fully consistent with the earlier results. Although the technique is illustrated using a simple one-dimensional example, the method can be readily extended to multidimensional problems