Abstract
In many industrial applications, such as in the steel industry, it is important to monitor the surface temperature, and also heating or cooling rates, during an industrial process. However, often the surface may be inaccessible for direct measurements. Instead we are restricted to using interior measurements to estimate the surface temperature, by solving an inverse heat conduction problem. The problem is well-known and has been studied by many authors.In this paper a novel algorithm is proposed, which allows the use of multiple measurements taken inside the material. The procedure is based on formulating the problem as an operator equation and stability is achieved by Tikhonov regularization. By an iterative procedure, we can deal with non-linear problems where the material properties depend on the temperature.Numerical experiments show that the method works well. We also apply the proposed method to a real industrial problem with measured data taken during an steel heating experiment.