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Thermomechanics


Thermomechanics


“All Engineers should study Thermodynamics”

 

This was a response I gave at a recent IMechE meeting, as a rejoinder to historical perspectives on the accreditation requirements of the IMechE.  I was then asked to amplify the statement, so here goes!

At the present time we are at what may become to be seen as an historic divide.  Students are very unprepared for traditional HE in both maths and physics, and as in my view mechanical engineering is “approximate physics for profit”, then you have to get the physics right before you can make a profit!  This is a challenge and, at the risk of sounding like a Management Consultant (ugh!), both a problem and an opportunity.  It is a problem in that we have got to change the teaching of engineering and science at universities, and an opportunity in that the students coming in know so little we can teach them from scratch, and get it right first time!  We actually have a double opportunity, as we are simultaneously changing both our response to changing input standards, and the revision of the professional competencies for professional engineers.  In my view all engineers should be “Registered”, and some may choose to go on to be “Chartered”, but the route to chartered engineer should be available to all.  I believe people should expect to be registered engineers 3-5 years after graduation.  As the future is most likely to be under the Bologna Declaration, then the BEng will become the “mobility degree”, and should satisfy the educational base for a registered engineer.  Chartered engineers would then have additional requirements such as a two year Masters degree.  These views are a logical extension of the new EC(UK) SPEC, if Bologna proceeds as I expect.
 

With massification, broadening syllabuses, and changes at school level, university is now a “seventh form college” for approaching 50% of the population. This will in my view lead to a BEng being a “generalist degree”, with much common material across the whole of engineering in the first two years, and specialist study in later years.  This is how it used to be done, and is still done in a number of highly regarded higher education establishments – so is it “back to the future”?  We need to go back to basics, we should be teaching students how to solve problems, not the solutions to various problems.  Therefore, in a generalist environment, all engineers should study thermodynamics, but the question is what type of thermodynamics?


Within engineering perceptions of “thermodynamics” within the UK are generally coloured by the 19th century view of reversible thermodynamics embodied in “Heat Engines”, which is almost universally disliked by students.  Students should be taught modern thermodynamics, or as it is now being known “Thermomechanics”.  Thermomechanics is a burgeoning field of research, and is the 20/21st century thermodynamics of irreversible processes, as all processes in the real world are irreversible.  The growing understanding of the nature of irreversibility is even changing fundamental concepts such as time.


Mechanical engineering students, in my experience, have rarely/never understood the fundamentals of physics, and because of their changed school background they now know even less.  We need to go back to the absolute basics - the conservation laws (energy and momentum) and the Principle of Stationary Action [PSA].  PSA is only a manifestation of the fact that energy is conserved, and is synonymous with the stationary value of the total potential energy.  Potential energy in this context is not the very restricted version that most engineers think of, which is actually the gravitational potential, but the wider concept of “potential” meaning the ability to do work, and the total potential energy includes all forms of energy i.e. gravitational, motion, electrical and chemical (dark?) etc.
 

The concept of “free energy” needs to be introduced, and again it is very simply explained as a consequence of the stationary value of the total potential energy linked to the work-energy relationship, and leads directly to Entropy.  This almost universally hated and misunderstood concept, can again be simply shown to be a natural consequence of the conservation of energy and hence directly relevant to real life.  The most powerful techniques stem from the rate formulation of the second law, posed in terms of free energies, known as the Clausius-Duhem inequality.  This expression is truly remarkable in its capacity for prediction. If you tell it it is a solid you will derive Newton’s Laws, if you tell it it is a liquid you derive Navier-Stokes, if you tell it it is an electrical medium you derive Maxwell’s equation etc.  Ultimately this approach leads to “Extended Irreversible Thermodynamics” where the rate effects are important, but this is a fiercesomely mathematical field.


For dynamics, if we start with “Action” (the Lagrangian) then the Principle of Stationary Action (PSA) can be taught with only elementary calculus of a single variable, and it can be generalised later in the course when the students have better mathematical capabilities.  Then Newton’s Laws can be derived as a consequence of PSA, this gives the student the background and the understanding that far deeper issues are involved than just F = m.a , for instance the overiding importance of the Third Law in free Body analysis Energy scales at all scales, force does not.  The fundamental concept is energy (pity we don’t know what it is!), forces are different depending what energy conversion is being undertaken, and at what scale i.e. mechanical forces are different to electrical forces, sub-atomic forces are different to real world forces etc. – but energy is always the same.  If again, entropy production is zero this gives conservative systems, and conventional dynamics then follow.


For “Statics” if the work/energy relationship and virtual work is the starting point, then equilibrium (both translational and rotational) can be derived, so giving a better understanding of the deeper significance than just stating that equilibrium happens (see Feyman).  This then naturally leads to elastic structural design. Moving on to deformable bodies, the quantity to be extremised (minimised) is the Helmholtz free energy, this is entirely analogous to PSA if the gravitational and motion potentials do not vary.  This leads naturally to the concept of the maximum rate of entropy production, which minimises the potentials at the greatest rate, and they can be then used for continuum damage mechanics, injury biomechanics and fracture. Energy methods, as they have always been called, can then be used to show what instabilities such as buckling are all about.


Classical thermodynamics can now be introduced from the total potential energy as systems where entropy production is zero, and the state variables i.e. pressure etc. are constant across the control volume.  This then leads on to what is conventionally taught, but it is put into a global framework.  Analysis of fluid flow uses all the same concepts, and the maximum rate of entropy production is becoming the favoured approach for turbulent flow, mixing, climatology,  and even extra-terrestrial climatology (see Gaia). Following on from the more traditional elements the subject can then be generalised to information theory, complexity and evolution.  The best models of life are now thermodynamic models, and the second law of thermodynamics and concepts such as the maximum rate of entropy production are now considered the most likely candidates for the fundamental drivers of evolution, and the direction and development of the universe on all scales from the quantum (Plank) scales to cosmology.
 

In conclusion, returning to the title, what I really meant to say was that as Universities are becoming seven'th form colleges, and with the changing output from schools, then first degrees should be generalist and everyone should have a grounding in Thermomechanics because, with due acknowledgement to Douglas Adams - it is the story of life, the universe, and everything!!



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