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# Learn fluid mechanics or thermodynamics ?

I am graduate student from solid mechanics and need to learn 1 course from fluids and thermal group which includes fluid mechanics or thermodynamics+heat transfer. I am unsure which one would be better to learn, especially which would be helpful in future for solid mechanics. My work is related to solid mechanics. Can you share your views? By the way, I will just learn 1 course.

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## Depends on what you are about

Depends on what you are about to follow next as a specific field of expertise. Solid mechanics are present both in fluid-structure interaction and in thermoelastic problems where fluid mechanics and thermodynamics correspondigly play an important role. Both fields are essential in engineering.

## Go for fluid mechanics

IMO, go for fluid mechanics.

Fluid mechanics has NS equations. They involve nonlinearity, their formulation involves tensor products, and, one of them is precisely on the conservation of energy flows in continua (i.e. the same energy as in thermo, and the same conduction and convection as in heat transfer). They involve time-rates of quantities analogous to those in solid mechanics, and necessarily involve ``large deformations'' over time. They involve both Lagrangian and Eulerian perspectives explicitly. The presence of such topics/aspects

shouldhelp ``solidify'' your understanding of solid mechanics (which, at least initially, tends to be only linear, only small deformation, only isothermal cases, only in the Eulerian frame, etc.). Further, an advanced course on FM will involve, or at least help you prepare better, to possibly look into their numerical studies in future. Now, numerical techniques for the NS equations tend to involve techniques that are simpler (FDM, FVM), which means, it will not only add depth to your understanding of time-marching, but also provide close familiarity with the two simplest cases of the variational techniques of FEM (which are routinely used in solid mechanics), but in a nontrivial context (of nonlinearity).Of course, with this choice, you will lose on thermodynamics. Two points here: (1) If it is a combined thermo + heat transfer course, what you lose on won't be much. The character of equations in used in thermo and heat transfer courses at the PG level does not change radically from those in the UG level courses, and so, if required in future, you could pick it up on your own. But at the UG level, even though NS

areintroduced, only simplest cases are dealt with in them. Studying NS to fuller depth could make you appreciate many areas as above. (2) If you are inclined more towards engg. applications than fundamental theory of abstract states, then subjects involving the transient aspects (FM, heat transfer) are more in line to your interests.Finally, there is a

$1 millionprize for a problem on NS equations (see the Clay Maths Institute's Millenium problems), butnonefor thermodynamics and heat transfer. Think of yourcurrentstipend/earnings, and compare it tothatnumber! ... Just think, what happens only if you crack that problem---what you will do with that money. (Make sure to devote at least half a day to this one aspect alone, before you firm up your decision.)Hope this helps.

Best,

--Ajit

## Further on why FM. And correcting my parenthetical remark

I made a mistake of sorts. In my reply above, in a parenthetical remark, I said ``only in the Eulerian frame'', but there, it should have been ``Lagrangian.'' In the small deformation theory the two do lose distinction, but I was trying to point out the easiest route to conceptually relate the analytical solutions approaches in FM to those in the XII grade mechanics of particles (which does get taught only in the Eulerian framework), and thus happened to say ``Eulerian.''

However, come to think of even just the analytical solution approaches in FM, taking the example of the inviscid Burger's equation, guess it is easier using this equation in the Lagrangian form. Further, in FEM, for small but non-infinitesimal deformations, i.e., whenever you need to remesh, you are basically following the Lagrangian approach. So, even though in linear elasticity both are identical, the parenthetical remark still should have said: Lagrangian. ... Was writing in a (too much) hurry. Sorry about that.

Two further points: A second course on FM also helps deepen the two topics of (i) dimensional analysis (so frequently used also in heat transfer) in a more systematic manner, and (ii) turbulence (the idea of energy cascades across scales, i.e. essentially, the idea of multi-scaling; also, the idea of chaos as a nonlinear phenomenon) gets neatly exposed in FM, but not in thermo.

Depends on the specific contents of the FM course and the treatment followed for it, as also the student's own personal inclinations and objectives, but speaking overall, if it must be only one course, guess, going in for FM should be the better choice.

Bye for now, and best,

--Ajit