| Many processes require that two thermal conditions be imposed on some of the boundaries of the system, the design surfaces. Thermal design consists of finding the conditions on the unconstrained elements of the system such that the two specifications are attained.; The conventional or forward design technique relies on the specification of one condition on each element of the system, so that the problem can be formulated by a stable system of equations containing the same number of unknowns and equations. However, forward design can only deal with problems in which two specifications are imposed on the design surfaces by means of a trial-and-error solution, which is limiting for a number of reasons.; Inverse design aims at finding the conditions in the unconstrained elements of the system directly from the two specifications on the design surface, avoiding the trial-and-error procedure of the forward technique. Inverse mathematical models allow some boundaries to have two imposed conditions, as well as some elements to have no prescribed condition. This is known to be an ill-posed problem, which is very unstable and cannot be satisfactorily solved unless the system of equations is regularized. Two regularization schemes are applied in this work: truncated singular value decomposition (TSVD), a direct method, and conjugate gradient (CG), an iterative method.; The major contribution of this dissertation is the extension of previous inverse design analysis of systems where the heat transfer was governed solely by radiation to include heat transfer combining radiation, convection and conduction mechanisms. In this case, the problem is formulated by an ill-conditioned system of non-linear equations. This work demonstrates various techniques for successfully obtaining inverse solution to highly non-linear problems.; Three inverse designs are investigated: the first considers the inverse heat source design in a purely radiative enclosure; the second problem extends the analysis to radiation-conduction combined mode heat transfer; and the last problem takes into account inverse boundary design combining radiation, convection and conduction mechanisms. In all cases, two-dimensional geometries are considered.; This research finds applicability in a number of important thermal processes, including gas-fired furnaces, drying systems, semiconductor wafer manufacturing, and infrared ovens. |
