Study on the prediction of inner wall surface geometry of a two-layer-wall furnace by an inverse process combined with grey theory

Abstract

Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.In this work the inner wall surface geometry of a two-layer­-wall furnace system is estimated using inverse process method combined with grey prediction model. In estimating process a virtual area extended from the inner surface of furnace wall is used fur analysis. The heat conduction equation and the boundary condition are first discretized by finite diffierence method to form a linear matrix equation; the inverse model is then optimized by linear least-squares error method and the temperatures of virtual boundary are obtained from a few of measured temperatures in furnace wall using the linear inverse model; and finally the temperature distribution of system is got by direct process and the inner surface geometry of furnace wall can be estimated accordingly. The result shows that using inverse process combined with grey prediction model the geometry can be exactly estimated from relatively small number of measured temperatures. Moreover, the effects of measurement error, location and number of measured points on the estimation for inner surface geometry of furnace wall are discussed in detail.