화학공학소재연구정보센터
International Journal of Heat and Mass Transfer, Vol.51, No.9-10, 2603-2613, 2008
An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature
Considering here is an inverse problem for estimating the unknown nonhomogeneous heat conductivity function alpha(X) in T-t(x,t) = partial derivative(alpha(x)T-x)/partial derivative x + h(x,t) with the aid of all extra measurement of temperatures at a final time, which may be disturbed by random noise. A Lie-group shooting method (LGSM) is developed from the one-step Lie-group elements obtained by a spatial-discretization of heat conduction equation and by using the central difference or forward difference for alpha'(x) in spatial domain. The heat conductivities are available by directly solving linear equations. The new methods have twofold advantages in that no a priori information of heat conductivity is required and no iterations in the calculation process are needed. The accuracy and robustness of present methods are confirmed by comparing estimated results With exact solutions. The LGSM is stable and accurate, although the estimations are carried out under a large measurement noise. (c) 2008 Elsevier Ltd. All rights reserved.