A Lie—Group Shooting Method For The Inverse Problems Of Coupled Radiation And Conduction Heat Transfer

Combined conduction-radiation heat transfer is applied widely in industry,found to involve in many thermodynamic processes and engineering applications.Accurate measurement of the conductive and radiative properties of semi-transparent materials is of great significance because it's the basis of control and optimization for heat transfer.However,the properties of materials can not be measured directly in most cases.Accurate measurement of physical properties usually requires inversion for the reason that it is often the equivalent property,rather than the physical property of the material,that is obtained by traditional methods of measurement.Therefore,it is of great significance in theory and practice to retrieve the physical properties of the medium by the photothermal information represented by the process of heat transfer.As a novel method for inverse problems,Lie-group shooting method(LGSM)is mainly used to estimate the thermal conductivity,heat source and initial conditions in heat conduction.In this paper,LGSM was introduced to the field of inverse problem of combined conduction-radiation heat transfer for the first time.The main work of this thesis includes the following aspects:1.The theoretic foundation of LGSM was deeply studied and compared with the existing methods,after which the feasibility of introducing the method into the inverse problem of combined conduction-radiation heat transfer was analyzed.2.The discrete ordinates method(DOM)was used to solve the radiative transfer equation and then the conduction-radiation energy equation was decoupled by the radiative source term.On the basis of this equation,an Lie-group shooting methed was used to estimate the inhomogeneous thermal conductivity and absorption coefficient of different distributions in a uniform refractive index medium independently.Then the reconstruction for the refractive index of graded index medium was also accomplished.3.In this paper,the applicability of Rosseland diffusion equation was analyzed under different physical parameters for semitransparent media with large optical thickness.4.On the basis of Rosseland diffusion equation,independent and simultaneous inversion was accomplished for the inhomogeneous thermal conductivity and extinction coefficient of different distributions in semitransparent media with large optical thickness by the means of LGSM.Then temperature-dependent thermal conductivity and extinction coefficient were esimated using this methed.