Analytical Solution and Inverse Analysis of Heat Conduction Problems with Time-Dependent Boundary Conditions

  • 黃 聰文

Student thesis: Doctoral Thesis


This paper discusses the analytical solution and inverse analysis of heat conduction problems with time-dependent boundary conditions First the non-uniform medium heat conduction problem is studied A new analytic solution method is developed without integral transform to find the exact solution for the transient heat conduction in non-uniform medium with general time-dependent boundary conditions By introducing suitable shifting functions the governing second-order differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions If the physic properties of the medium are in polynomial forms the exact solution of the system can be developed Then examples are given to illustrate the analysis Limiting cases are studied and compared with those in the existing literature The influence of physic parameters on the temperature distribution of the system is revealed Secondly a hybrid inverse scheme involving the shifting functions eigenfunction expansion and least-square methods in conjunction with experimental data inside the test material without integral transform is proposed to estimate the unknown surface conditions for the linear inverse heat conduction problems with uniform medium The functional form of the surface conditions is unknown a priori We can analyze the whole time domain or divide it into several sub-time intervals for analysis and then estimates the unknown surface conditions on each sub-time interval In order to show the accuracy and reliability of the present inverse scheme comparisons among the present estimates exact solution previous results and experimental data are made The effects of the measurement locations on the estimated results are also investigated The results show that good estimation of the surface conditions can be obtained
Date of Award2014 Feb 6
Original languageEnglish
SupervisorSen-Yung Lee (Supervisor)

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