treatment) to conduction, will be of interest primarily to readers who are looking for “simple” prediction methods.
After the generalities outlined in Chapter 1, Chapter 2 presents the physical laws of conduction, describing the Fourier law and setting out the heat equation. We then pinpoint the fundamental content of the problems found in conduction and their approach. At this point, we will need to distinguish between stationary (we also refer to permanent regimes) and non-stationary problems.
Chapter 3 deals with conduction in a stationary regime. Emphasis is logically placed on plane and cylindrical geometries. Importance is placed on the concept of thermal resistance, an essential tool for thermal scientists, in both of these geometries. This chapter provides many examples of application of this concept.
Chapter 4 presents the notion of a quasi-stationary regime; this method, although approximate, does in fact have undeniable practical scope. Valid for relatively slow transfers – presuming the temperature environment is homogeneous – instantaneous balances can be obtained, in addition to the laws of thermal evolution that allow valid approximations to the problems that, in principle, relate to the variable regime. Again, in this context, this chapter deals with the plane and cylindrical problems.
Chapter 5 deals with variable conduction regimes. The most classic monodimensional problems are tackled: fixed temperature at the interface at the instant t = 0, non-stationary conduction at constant flow density, temperature with sinusoidal variation fixed at the interface and the problem of two adjoining walls.
Many examples are provided to illustrate this important aspect of conductive transfers.
Chapter 6 presents the notion of fin theory, which is associated with a few simple examples.
Within the Appendices, there are tables of error functions and their offshoots: erf, erfc, ierfc, as well as reminders that are often essential for hyperbolic functions. They also provide information on the notion of treating certain non-stationary problems using Laplace transformations. Again, many examples are given to illustrate another important aspect of conductive transfers.
November 2020
Introduction
I.1. Preamble
Thermal energy was probably first perceived (if not identified) by humanity, through the Sun. The themes of night and day are found at the center of most ancient myths. Humanity’s greatest fear was probably that the Sun would not return again in the morning. Fire became controlled in approximately 400,000 BP. Thermal transfer was therefore a companion of Homo ergaster, long before Homo sapiens sapiens.
However, it took a few hundred thousand years before so-called “modern” science was born. Newtonian mechanics dates from three centuries ago. Paradoxically, another century and a half passed by before energy was correctly perceived by scientists, in terms of the new field of thermodynamics. Furthermore, a systematic study of heat transfer mechanisms was carried out at the end of the 19th century, and even later for the study of limit layers, the basis of convection.
Heating, lighting and operating the steam engines of the 19th century were all very prosaic concerns. Yet this is where revolutions in the history of physics began: the explosion of statistical thermodynamics driven by Boltzmann’s genius, and quantum mechanics erupted with Planck, again with Boltzmann’s invovlement.
Advances in radiation science, particularly in sensor technology, have enabled us to push back our “vision” of the universe by a considerable number of light years. To these advances we owe, in particular, the renewed interest in general relativity that quantum mechanics had slightly eclipsed, through demonstration of black holes, the physics of which may still hold further surprises for us.
Closer to home, fundamental thermal science, whether it is conduction, convection or radiation, contributes to the improvement of our daily lives. This is particularly true in the field of housing where it contributes, under pressure from environmental questions, to the evolution of new concepts such as the active house.
The physics that we describe in this way, and to which we will perhaps introduce some readers, is therefore related both to the pinnacles of knowledge and the banality of our daily lives. Modestly, we will place our ambition in this latter area.
There are numerous heat transfer textbooks in different formats: “handbooks” attempting to be exhaustive are an irreplaceable collection of correlations. High-level courses, at universities or engineering schools, are also quite exhaustive, but they remain demanding for the listener or the reader. Specialist, more empirical thematic manuals are still focused on specialists in spite of all this.
So why do we need another book?
The authors have taught at university level and in prestigious French engineering schools, and have been involved in the training of engineers on block-release courses. This last method of teaching, which has been gaining popularity in recent years, particularly in Europe, incorporates a distinctive feature from an educational point of view. Its practice has, in part, inspired this book.
The aim is to help learners who have not had high-level mathematical training in their first years following the French Baccalaureate (therefore accessible to apprentices), and pupils with more traditional profiles. At the same time, we would like to show this broad audience the very new possibilities in the field of digital processing of complex problems.
When a miner wants to detach a block of coal or precious mineral from a wall, they pick up a pneumatic drill. If we want to construct a tunnel, we must use dynamite. The same is true for physicists.
Whether they are researchers, engineers or simply teachers, scientists have two tools in their hands: a calculator and a computer (with very variable power). Since both authors are teacher researchers, they know they owe everything to the invention of the computer. From the point of view of teaching, however, each one of the two authors has remained specialist, one holding out for the calculator and “back-of-the-napkin” calculations, and the other one using digital calculations.
The revolution that digital tools has generated in the world of “science” and “technical” fields, aside from the context of our daily lives, no longer needs to be proved. We are a “has been” nowadays if we do not talk about Industry 4.0. The “digital divide” is bigger than the social divide, unless it is part of it.…
Indeed, the memory of this revolution is now fading. Have students today ever had a “slide rule” in their hands? Do they even know what it is? Yet, all the physicists behind the laws of thermal science had only this tool in hand, giving three significant figures (four with good visibility and tenacity), leaving the user to find the power of ten of the result. It goes without saying that a simple calculation of a reversible adiabatic expansion became an ordeal, which played a part in degrading the already negative image of thermodynamics held by the average student.
This reminder will seem useless to some; slide rules are at best sleeping in drawers. But there is a moral to this story: no matter what type of keyboard we type on, a calculator or a computer, our head must have control over our fingers. This book has been written on the basis of this moral.
A good physicist must have a perfect understanding of the idea of an “order of magnitude”. For this, the tool is a calculator. We always do a rough sizing of a project before moving on to detailed modeling and
