Geometry estimation for the inner surface in a furnace wall made of functionally graded materials

The aim of this study is to solve an inverse geometry heat conduction problem (shape identification problem) to estimate the unknown geometry of the inner surface in a furnace wall which is made of functionally graded materials (FGMs). The inner surface geometry is estimated from the temperatures of measured points within the furnace wall. The inverse algorithm used in the study is based on the conjugate gradient method (CGM) and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples are discussed. Results show that the unknown geometry of the inner wall surface can be predicted precisely by using the present approach.