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This paper presents basic concepts of inverse and optimization problems. Deterministic and stochastic minimization techniques in finite and infinite dimensional spaces are revised; advantages and disadvantages of each of them are discussed and a hybrid technique is introduced. Applications of the techniques discussed for inverse and optimization problems in heat transfer are presented

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Systematic methods for the solution of inverse problems have developed significantly during the past two decades and have become a powerful tool for analysis and design in engineering. Inverse analysis is nowadays a common practice in which teams involved with experiments and numerical simulation synergistically collaborate throughout the research work, in order to obtain the maximum of information regarding the physical problem under study. In this paper, we briefly review various approaches for the solution of inverse problems, including those based on classical regularization techniques and those based on the Bayesian statistics. Applications of inverse problems are then presented for cases of practical interest, such as the characterization of nonhomogeneous materials and the prediction of the temperature field in oil pipelines.

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This paper deals with the application of inverse concepts to the drying of bodies that undergo changes in their dimensions. Simultaneous estimation is performed of moisture diffusivity, together with the thermal conductivity, heat capacity, density, and phase conversion factor of a drying body, as well as the heat and mass transfer coefficients and the relative humidity of drying air. This was accomplished by using only temperature measurements. A mathematical model of the drying process of shrinking bodies has been developed where the moisture content and temperature fields in the drying body are expressed by a system of two coupled partial differential equations. The shrinkage effect was incorporated through the experimentally obtained changes of the specific volume of the drying body in an experimental convective dryer. The proposed method was applied to the process of drying potatoes. For the estimation of the unknown parameters, the transient readings of a single temperature sensor located in the midplane of the potato slice, exposed to convective drying, have been used. The Levenberg–Marquardt method and a hybrid optimization method of minimization of the least-squares norm are used to solve the present parameter estimation problem. Analyses of the sensitivity coefficients and of the determinant of the information matrix are presented as well.