A SEQUENTIAL ONE-DIMENSIONAL SOLUTION FOR THE SIDEWAYS HEAT EQUATION IN A SEMI-INFINITE, FINITE, AND MULTILAYER SLAB

The sideways heat equation concerns an inverse problem where an unknown and inaccessible surface temperature is estimated using sensor data gathered from an interior point of a slab. The article presents how the ill-posed problem is solved using a finite-difference technique, where the space variable is continuous and the time variable is discrete. The inverse procedure is based on a recursive deconvolution algorithm, derived from the direct solution. Regularization is completed with digital filters. The test runs give promising results. However, due to the time derivative approximation and disturbances, abrupt changes in the estimated signal cannot be perfectly reproduced.