Prediction of the inner wall shape of an eroded furnace by the nonlinear inverse heat conduction technique

Abstract

A new technique of estimating the unknown inner wall shape of eroded furnaces handling molten materials from the measured temperatures at the outside surface is developed. The inverse heat conduction problem using the conjugate gradient algorithm is extended to the case of nonlinear heat conduction, and is formulated in the general coordinate system. Instead of treating the unknown boundary directly, the heat flux distribution on a virtual boundary is estimated, and the real eroded surface is sought by a proper thermal condition for the surface. Smooth erosion with shallow depths can be estimated well by a single analysis with a flat virtual surface, but deep erosions or sharp changes as in triangular erosions cannot be well predicted by the single analysis with the flat virtual surface. When the virtual surface is modified iteratively, arbitrary shape with sharp changes and deep erosions could be predicted excellently even with temperature-dependent thermal conductivity.