Boundary conditions identification from internal temperature measurement at selected points

This work discusses the solution of two-dimensional inverse heat conduction problems by a derivative method. The solution is presented in terms of temperature data and their time derivatives. A Gram orthogonal polynomial method is proposed for smoothing noisy data spatially and along the time and to approximate the time derivatives of temperature data. The presented method is easy to use and can handle noisy data. The surface temperatures are estimated with a good accuracy for the different Biot numbers, time step and measurement errors. In the case of estimating the heat flux there is a certain limitation for the time step. The results are unstable when the time step is too small. Other advantages of the solution method are that the method does not need any information about the initial temperature distribution and the data at few nodes are needed to estimate the surface conditions.