Monday, February 27, 2006

Nondimensional Nightmares

Non dimensionalization has been the heart of Fluid Mechanics / Heat Transfer for more than a century. Elegant generalizations have been made by Fluid Mechanists, ranging from Osborne Reynolds, Prandtl, Nusselt to Stefan. Non dimensionalization has been man's most elegant attempt at trying to grasp one of Nature's most confunding yet awe inspiring phenomena: the behaviour of fluids.

Non dimesnionalization is a trademark of any Fluid Mechanics text book: rather than talk of velocity, diameter and viscosity seperately, their cumulative effect is described by a simple parameter. The Reynolds Number. Similarly, the Nusselt and the Biot Numbers. These numbers have been tested by experiment and by theory. They play an incredible role in today's experimental work: humongous dams can be simulated in the laboratory for dynamic similitude; aircraft wings can be brought to minute airfoil dimensions, again with dynamic similitude.

But, of course, Non Dimensionalization comes with a price. No doubt, you do generalize if you non-dimensionalize properly. But everybody isn't Einstien. There are those who - think of an effect - say radiation in a pipe. They realize that Radiation would play a significant role in improving the heat transfer within a pipe at high temperatures. Say 3000K. Now, if you show me a pipe that can carry water at 3000K - then I will show you the abominable snowman playing chess.

Of course, our man (the 3000K guy) decides to do some "numerical" modeling. He writes a finite difference code, solves the problem, optimizes it (perhaps optimizes the flow rate of water?). He is also aware that "3000K" will get him rejected from any peer reviewed Journal. So, he does what Reynolds did: Non - dimensionalizes. He divides it by the speed of sound multipled by something else, divided by the surface area of the duct .... you get the drift. The utter irrelevance hides behind the cloak of "non-dimensionalization".

And viola: he has a Non Dimensional Number! He calls it G or something - the "Radiation Parameter" - and assigns it a deceptively low value of 0.002. He never mentions the 3000K in the paper. He mentions the 0.002 instead. No peer rejects this: all the reviewers think this is marvelous new work. This gets accepted and published.

And years later, some unsuspecting PhD student like me spends a lot of money in printing out this verbosity, reads the utter bilge, gets fiercely upset and blogs his discontent. The frustrated PhD student also vows to mention typical values of various dimensional parameters if non-dimensional results are ever presented in his publications.

No comments: