Читать книгу Heat Transfer 1 - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 12

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 the nature of the propagation of thermal flows by impacts.

Let us suppose that the great majority of the brawlers come from a ship with a white uniform. Let us suppose that another boat in the port has uniforms that are red. The red ones are initially all united. We will then quickly see that the red mariners, as they receive and return blows, spread out across the room. We have just shown the mechanism of diffusion of matter, of a component within a mixture.

We will have a better qualitative understanding that the fundamental law of conduction (Fourier Law) is formally identical to the law for the diffusion of mass (Fick Law).

Let us put our agitated sailors in the compartments of a flatcar train, where they continue to fight. And let us start the train moving. The kinetic energy that they contain is transported from one point to another.

We have just invented thermal convection.

We can go further.

Let us imagine a series of flatcar trains on a set of parallel tracks. The train furthest to the side is fixed to a platform. All of these trains are full of sailors. Let us suppose that our train follows the outside, parallel rail tracks. No brakes will prevent these trains from moving. Only the last train, at the platform, is stuck.

For a reason we do not need to analyze (cinema allows all kinds of fantasy), “clusters” of fighting sailors jump from one wagon to the next. These “clusters” contain a component of speed that is parallel to the train, which will communicate information about the quantity of movement to the adjacent train. These trains will then start to move, more quickly the closer they are to the outside train. And the same occurs up to the train at the platform. This train will not move, but a force will be applied to its brakes.

We have just discovered the mechanism of dynamic viscosity. At the same time, the parallel trains in relative movement give us a picture of the notion of boundary layers.

At the same time, these agitated clusters carry their disordered kinetic energy, “thermal” agitation. We have just seen the mechanism of the thermal boundary layer.

Finally, let us include a few red mariners in the crowd of white. They will be carried with the clusters, and we have just invented the limit layer of diffusion of a species.

We are in a fantasy, and let us benefit from it as far as we can. To finish, let us suppose that this is carnival day; each sailor has a belt equipped with bells.

All the individuals have a different speed, and the impacts are random, all the bells start to jingle, each with a different frequency. The distribution of frequencies will depend on the statistical distribution of speeds (Boltzmann statistics), and the intensity of noise produced will depend on the total agitation energy of the sailors.

We have just understood the basic mechanism of radiation. We have just realized why the theory of radiation needed to use the concepts of statistics derived from the work of Boltzmann – a brilliant pupil of Planck – to produce the emissions spectrum of a black body, for example.

NOTE.– the model is certainly simplistic. The emission comes from quantum transitions in the gas atoms.

Here, we have already deviated from the pure substance of the book, but we could go even further.

Let us suppose that our agitated sailors are in a room with one mobile wall (a nightmare scenario frequently seen on the silver screen).

The incessant impacts of the fighters on this wall create a force that pushes it. This force, reduced to a surface unit, explains the notion of pressure.

By pushing against this wall, our crowd applies work that is greater than the resistance.

Here we see an equivalence spring up between work and heat that, at a fundamental level, are simply two mechanical energies: one ordered and the other disordered. The first principle of thermodynamics is illustrated by this.

We can see that the incidence of an average blow on the wall is rarely normal.

Therefore, an average fighter will have a trajectory that will be reflected off the wall. And only the normal component of its speed will be able to push (or transfer work to) the wall.

Thus, we see that it will be impossible for the crowd (taken to mean a gas) to give all its energy to a mobile wall.

The fundamental mechanism that leads to the second principle of thermodynamics has just been demonstrated.

These “light-hearted” images, which will perhaps not please everyone, were an oral support for the presentation of different transport phenomena by one of the authors. We hope that the reader, once they have studied this book, will want to return to this text. They will then have understood, we hope, the images that lead to the development of thermodynamics.

And if this text has a moral, it would be: Writing down thermodynamics, just like thermal science, is based on continuous equations. The fundamentals of physics that determine these phenomena arise from the field of the discontinuous: discontinuity of matter, divided into particles; discontinuity of light, divided into photons.