A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity

• Published in: International journal of heat and mass transfer Vol. 53; no. 21; pp. 4876 - 4884
• Main Author: Liu, Chein-Shan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.10.2010; Elsevier
• Subjects: Acceptable noise levels; Analytical and numerical techniques; Conduction; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Inverse problem; Inverse problems; Mass transfer; Mathematical analysis; Mathematical models; Parameter identification; Physics; Shooting; Thermal diffusivity; Time-dependent thermal diffusivity; Two-stage Lie-group shooting method; Time-dependent thermal diffusivity; Two-stage Lie-group shooting method; Parameter identification; Inverse problem; Temperature measurement; Time dependence; Parameter estimation; Inverse problems; Digital simulation; Lie groups; Boundary conditions; Thermal diffusivity; Modelling; Shooting method; Thermal conduction
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2010.06.005

We consider an inverse problem for identifying a time-dependent thermal diffusivity α( t) in a heat conduction equation T t ( x, t) = α( t) T xx ( x, t), with the aid of an extra measurement of temperature at an internal point of a rod. Because the data are acquired at an inner point we require to develop a two-stage Lie-group shooting method (TSLGSM) to solve this inverse problem. The present approach is novel and is examined through some numerical tests. By comparing the calculated results with exact ones we can assure that the TSLGSM is an accurate and efficient method, whose estimation error is small even for the identification of a discontinuous and oscillatory thermal diffusivity. Under noise, the identified solutions are also acceptable.