Inverse estimation for temperatures of outer surface and geometry of inner surface of furnace with two layer walls

This study provides an inverse analysis to estimate the boundary thermal behavior of a furnace with two layer walls. The unknown temperature distribution of the outer surface and the geometry of the inner surface were estimated from the temperatures of a small number of measured points within the furnace wall. The present approach rearranged the matrix forms of the governing differential equations and then combined the reversed matrix method, the linear least squares error method and the concept of virtual area to determine the unknown boundary conditions of the furnace system. The dimensionless temperature data obtained from the direct problem were used to simulate the temperature measurements. The influence of temperature measurement errors upon the precision of the estimated results was also investigated. The advantage of this approach is that the unknown condition can be directly solved by only one calculation process without initially guessed temperatures, and the iteration process of the traditional method can be avoided in the analysis of the heat transfer. Therefore, the calculation in this work is more rapid and exact than the traditional method. The result showed that the estimation error of the geometry increased with increasing distance between measured points and inner surface and in preset error, and with decreasing number of measured points. However, the geometry of the furnace inner surface could be successfully estimated by only the temperatures of a small number of measured points within and near the outer surface under reasonable preset error.