Computer Solution of Heat-Transfer Problems

Many practical problems in heat transfer are solved with computer techniques. In the chapters which follow, many examples will be presented to illustrate setups for computer solutions, and many end-of-chapter problems will pose interesting questions to be answered by the reader. But this is not to play down analysis or appreciation of the fundamental principles of the subject. These principles are even more important in computer work because the engineer must be extra careful about input variables and have a notion of the correct magnitude of the output from the computer. 

The reader may note the absence of specific computer programs throughout the text. There are many ways to approach a solution and the assumption is made that the reader is computer literate and can handle the solution once a basic algorithm is laid out. Thus, our general approach to computer-related problems is to  

We may summarize our introductory remarks very simply. Heat transfer may take place by one or more of three modes conduction, convection, and radiation. It has been noted that the physical mechanism of convection is related to the heat conduction through the thin layer of fluid adjacent to the heat-transfer surface. In both conduction and convection Fourier s law is applicable, although fluid mechanics must be brought into play in the convection problem in order to establish the temperature gradient. 

Radiation heat transfer involves a different physical mechanism—that of propagation of electromagnetic energy. To study this type of energy transfer we introduce the concept of an ideal radiator, or blackbody, which radiates energy at a rate proportional to its absolute temperature to the fourth power. 

It is easy to envision cases in which all three modes of heat transfer are present, as in Fig. 1-9. In this case the heat conducted through the plate is removed from the plate surface by a combination of convection and radiation. An energy balance would give 

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