Inverse Determination of Eroded Smelter Wall Thickness Variation Using an Elastic Membrane Concept

A novel algorithm has been developed for the nondestructive determination of the shape of the interface between a melt and a refractory material wall in smelter furnaces. This method uses measurements of temperature and heat flux at a number of points on the outer surface of the furnace, and assumes that the inner (guessed) surface of the furnace wall is isothermal. The temperature field is then predicted in the entire furnace wall material by numerically solving a steady state heat conduction equation subject to the measured temperature values on the external surface and the isothermal melt material solidus temperature on the inner surface of the wall. The byproduct of this analysis is the computed heat flux on the external surface. The difference between the measured and the computed heat fluxes on the outer surface of the furnace is then used as a forcing function in an elastic membrane motion concept to determine perturbations to the inner (melt-refractory) surface motion. The inverse determination of the melt-refractory interface shape can be achieved by utilizing this algorithm and any available analysis software for the temperature field in the refractory wall. The initial guess of the inner shape of the wall can be significantly different from the final (unknown) wall shape. The entire wall shape determination procedure requires typically 5–15 temperature field analyses in the furnace wall material.