Estimation for inner surface geometry of a two-layer-wall furnace with inner wall made of functionally graded materials

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse heat conduction problem in estimating the unknown inner wall surface geometry of a two-layer-wall furnace whose inner wall is made of functionally graded materials (FGMs). The unknown geometry is estimated from the temperature measurements taken within the furnace wall. The inverse solutions will be justified based on the numerical experiments in which two different geometry of inner surface are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors and measurement locations on the precision of the estimated results is also investigated. Results show that the unknown geometry of the inner wall surface can be predicted precisely by using the present approach for the test cases considered in this study.