ABSTRACT
This chapter discusses the modeling of thermal systems. Because of the complexity of typical thermal systems, it is necessary to simplify the analysis so that the inputs needed for design can be obtained with the desired accuracy and without spending exorbitant time and effort on computations or experiments. Several types of models are considered, including analog, mathematical, physical, and numerical models. This chapter considers mathematical and physical modeling in detail. In mathematical modeling, both theoretical models, derived on the basis of the underlying physical phenomena, and empirical models, which simply curve fit available data, are considered. Conservation laws are used to derive the applicable equations. Physical modeling refers to the process of developing a model that is similar in shape and geometry to the given component or system. Dimensional analysis is employed to obtain the important dimensionless groups that determine the behavior of the given system and to reduce the experimental effort. The results from experiments and mathematical modeling are often obtained at discrete values of the variables. These data can be obtained in a more useful form by curve fitting, which yields mathematical equations that represent the data. Both exact and best fit to the data are presented. A best fit is appropriate for large data sets with significant error in the results and is of particular interest. Different methods for curve fitting are presented. Modeling is one of the most crucial elements in the design and optimization of thermal systems and this chapter presents the essential elements in detail, along with several examples.
