Heat Transfer 2. Abdelkhalak El Hami
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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 numerical calculations.
The two authors belong to the world of engineering sciences, meaning most of their PhD students have entered the private sector. One of them, having moved into the aerospace sector, came back to see us very surprised by the recurrence of “back-of-the-napkin” calculations in his day-to-day work.
Fundamental or “basic physics” concepts are taken from a type of manual that is resolutely different from those dedicated to the numerical approach. In this case, the authors allow themselves to believe that it is no bad thing to collect them all together in a single book, for once. This is a significant difference that will surprise some and, without doubt, be criticized by others. Nevertheless, when reading this book, an “average” student will be initiated to a field that teaching models generally promised “for later on” (or never if he/she never goes beyond a certain level of education). It is also true that fully immersed in equations and complex calculations, specialist readers will be able to “be refreshed” when faced with the short exercises, which can sometimes surprise and encourage them – why not – to go back to their roots (assuming they had indeed been there).
Another significant difference is that this book is directed at a large scientific audience, which covers possibly the entire field: researchers, PhD students or those who have obtained Confirmation and are just starting out in the field, technicians, students or professionals, engineers. This last type of scientist is perhaps the main target of this book.
So, what is this book for?
Above all, it contains problems to be worked on, of which most are accessible to all, from the level of an apprentice technician upwards, either one or two years after the Baccalaureate. This book was written in France, where scientific teaching is structured around universities, engineering Grandes Écoles, engineering training through apprenticeships and two types of technician training sections at high schools or universities. In countries with simpler models, readers should also find it useful.
It seems necessary to surround these problems with strong reminders of past learning, so that the reader does not need to permanently refer back to their manuals. We see two advantages in this: a presentation of the scientific material focusing on the problems, and a second chance for readers to integrate notions that perhaps had not been well understood in the initial teaching.
Lastly, upon rereading, the authors also recommend this book as an introduction to the taught disciplines.
I.2. Introduction
Thermal science is to thermodynamics as decree means is to law. It answers the following question – which all good leaders must (or should) ask themselves whenever they have an “idea”: “How would this work in practice?”.
In a way, thermal science “implements” thermodynamics, of which it is a branch.
A thermodynamics specialist is a kind of energy economist. Applying the first principle, they create a “grocery store”. With the second principle, they talk about the quality of their products. I add or remove heat from a source or work from a system. And the temperature, among other things, defines the quality of the energy for me.
But by what means do I take or do I give? Even calculations of elementary reversible transformations do not tell us by what process heat passes from a source to a system.
Thermal science specifies how, but “evacuates” the work. If in a given problem related to, for example, a convector where electrical energy (therefore in the “work” category) appears, it is immediately dissipated into heat by the Joule effect.
Three heat transfer modes can be identified: conduction and radiation – which can be seen separately, although they are often paired up – and convection, which is by nature an interaction of fluid mechanics and conduction.
Dividing the study of thermal science into three volumes is the result of logic. Presenting this work in three volumes is somewhat arbitrary; in our opinion, however, this split was necessary in order to keep the volumes in the collection a reasonable size.
The first volume, entitled Heat Transfer 1, is dedicated to “classic” approaches (analytical treatment) to conduction, which will be of greater interest to readers who are looking for “simple” prediction methods.
The second volume, entitled Heat Transfer 2, is dedicated to “classic” approaches (analytical treatment) of radiation, and assembles digital approaches of these various transfer modes. It is aimed at engineers or researchers who want to resolve more complex problems.
The third volume, entitled Heat Transfer 3, is focused on convection transfers. As we have already pointed out, all of these transport operations are rarely pure and lead to problems that involve three inter-connecting transfer modes, conduction, convection and radiation.
Before our readers immerse themselves in a text that, despite our best efforts, remains intellectually demanding, we propose a short text that is a little lighter.
I.3. Interlude
Let us imagine, in a “B movie” context, a somber hostel in the gray fog of a port in the middle of nowhere. Sailors from a faraway marina come and drink away their troubles. And as always, the drink helping them along, they turn to fighting.
Let us entrust Ludwig Boltzmann to direct the film. Our B movie heroes are getting agitated, delivering blows to one another. Each one of them has moderate kinetic energy, distributed heterogeneously among them in the room. For some reason, they get involved in a general brawl. Their average kinetic energy becomes much greater.
In everyday language, we would say that things are hotting up.
This would bring us right into line with a fundamental concept of Boltzmann, who was the first to hypothesize that heat is made up of molecular agitation. The temperature in a gas is proportional to the average quadratic energy of the molecules that make it up:
Using this model, we will return to the physical basis for all transport phenomena.
On the way, we rarely escape from the explosion of a door or a window, giving in under the repeated beatings of the brawlers.
We have just modeled the pressure, due to the transfer of the quantity of movement on the surface, by the impact of molecules.
Let us now imagine that the altercation is initially located in the corner of the room: a smaller group starts fighting between themselves.
From kicks to punches, after multiple impacts within the group and its immediate neighbors, the agitation will spread: we have just seen the mechanism of heat propagation by transfer of impacts.
Let us place an imaginary separation (geometrically but immaterially defined) at the center of the room. Let us count the sailors that cross through it within a unit of time.
This wall is now crossed by kinetic energy: we have defined a flow of heat.
Let us put a metal ring with a surface area of S = 1m2 in the room. On both sides of this ring, the blows exchanged constitute a transfer of kinetic energy – we have just defined the heat flow density.
And we have just understood