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1. Propagation of heat :
Jean-Pierre Van Dormael had the kindness tomake a very interesting article on this subject. It is essential to understand this process of heat transfer to design correctly a Stirling engine, to choose the good gas, to ensure our own security…
2. Basic principles of thermodynamics :
It is not question of making long talks about the principles of Carnot or other developments relating to thermodynamics. However, in this chapter some bases aregiven which are quite useful to understand how a Stirling engine runs, what are the performances that one can expect.
3. Kinematics of main Stirling engines:
When one wants to study a Stirling engine, it is necessary to have good bases of thermodynamics but also good bases of kinematics. Indeed, the kinematics will enable us to quantify, at any moment, volumes in the different parts of theengine.
4. Calculate your engine:
When one associates the principles of thermodynamics and the elements of kinematics, one can easily (?) calculate the engine of our own design.
1. Propagation of heat in the air.
We know that the sound travels in the air at about 340 m / sec. For a Stirling engine, this high speed allows to admit that, if we ignore the pressure loss in exchangers, the pressure isthe same throughout the engine, at any time. This assumption is often made in the methods of calculating Stirling engine.
The velocity of propagation heat in the air is much less known because the involved mechanisms are much more complicated. Let us try to see there a little more clearly.
1.1. Experimental principles.
The equation describing the propagation of heat in a substance can bededuced from three simple and almost obvious experimental observations.
The first observation is that in any point of a substance, the heat flows from hot to cold. The quantity of heat flowing per second (ie. its current) is proportional to two things: the thermal conductivity of the substance and the slope with which the temperature decreases at the observed point.
The second experimental observationis that the temperature of a volume containing a substance increases when a quantity of heat penetrates there. This increase in temperature is, of course, proportional to the quantity of heat received and inversely proportional to the volume, to the density of the substance which is there, and to its specific heat.
The third experimental observation is that no energy is created from nothing. Theresult is a principle of continuity: the heat which penetrates in an element of volume (according to the first observation) must necessarily correspond to that which makes increase its temperature (according to the second observation). In other words, in the absence of a source of heat in the volume, two afore-said heat quantities must be equal otherwise there would be creation of spontaneousheat, which is not possible.
1.2. The equations.
To express mathematically these physical realities, we will be satisfied with only one dimension of space. That is enough to describe what occurs in a wire or a long and fine tube filled with gas. One will indicate by T(x,t) that the temperature T is a function of the position x in the tube and of the time t of the observation.
We will make the...