| Inverse theory is an emerging field of study with application to a diverse range of problems. Inverse thermal problems are the focus of this dissertation; specifically, the parameter estimation problem and inverse heat conduction problem (IHCP) are investigated. Although one-dimensional inverse thermal problems have been widely investigated, multi-dimensional problems are beginning to receive an increasing amount of attention. One- and two-dimensional cases are addressed for both the noted inverse problems, including an experimental application.;A sequential-in-time implementation is proposed for a conjugate gradient method, utilizing an adjoint equation approach, to solve the IHCP. Because the IHCP is generally ill-posed, Tikhonov regularization is included to stabilize the solution. The proposed sequential method benefits from the efficiency and on-line capabilities of a sequential implementation, without requiring a priori information about the (unknown) surface heat flux. Aspects of the sequential gradient method are discussed and examined. Several promising features of the sequential gradient method are noted. Simulated one- and two-dimensional test cases are presented to study the sequential implementation. Numerical solutions are obtained using a finite difference procedure. Results indicate the sequential implementation has accuracy comparable to a standard whole domain solution, but in certain cases requires significantly more computational time. Methods to improve the computational requirements, which make the method competitive, are presented.;Parameter estimation techniques are applied to estimate the thermal properties of a carbon-carbon composite from transient experiments. Properties are determined as a function of temperature and direction relative to the fiber orientation. The thermal conductivity is assumed to be orthotropic, varying in the direction normal and parallel to the fibers; the volumetric heat capacity is assumed isotropic. Thermal properties from room temperature up to 500C are obtained. The thermal conductivity normal to the fiber is found to be less than one-tenth of the thermal conductivity parallel to the fiber. Agreement within 7% is demonstrated between independent one- and two-dimensional results. |
