Modeling and Approximation in Heat Transfer

Introduction: Goals of this Book

In many situations faced by the product designer or researcher, the initial step – how to formulate the problem – is unclear, and the presence of multiple thermal phenomena complicate this initial step further. The central challenge is often to make a simplified model of the system or process and to obtain some first-order approximations for the magnitude of the key variables. This textbook presents an introduction to methods of thermal modeling and associated approximation tools. Abroad rang of techniques is discussed. Some will give only order of magnitude estimates, while others may provide very close approximations, often without laborious calculations. We will generally approach these tools and methods as means of evaluating new, initially complicated heat transfer problems, identifying the governing physical phenomena and establishing their magnitude. Our hope is to provide readers with a much greater facility to deal with these challenges.

In this chapter, we review the engineering approach for defining a problem and exploring possible solutions. Several broad tools are considered, ranging from examination of the very general context of the problem to specific steps used to begin an initial estimate of the performance. The application to complex real-world problems is contrasted with the more controlled approach used in simplified academic exercises.

The first step in proper modeling is to make a careful definition of the goals of the project. The important factors to be considered in identifying goals are discussed next. The balance of the first chapter is devoted to an introduction to modeling techniques that can be employed in the start-up phase of the new concept or design. These same techniques are illustrated in the succeeding chapters, where we will develop modeling approximations for a number of different heat transfer processes.

The Art of Engineering: What Textbooks Don't Cover

Traditional textbooks in heat transfer and other thermal sciences concentrate on the development of fundamental principles and their corollaries, usually through the analysis of well-defined situations with relatively simple geometries. In many cases, a closed-form solution results. Emphasis is placed on obtaining very accurate solutions to very well defined problems. Although this may be a satisfactory way to initiate students into a new field, it leaves many ill prepared to deal with challenges that arise in engineering practice.