Wow, a challenge from My Little Ponytail!

And I’d love to hear Ludwig explain in his own words why we use Prantl numbers and Nussult numbers, and what those have to do with heat transfer

OK… Are you reading?

In the field of fluid mechanics, there are many other nondemsional numbers that have been developed to characterize fluid flows. The Prandtl number and the Nusselt number are two of them. The Prandtl number is used to characterize heat flows, and is the ratio of the viscous diffusion rate to the thermal diffusion rate.

Pr = “nu”/”alpha, where “alpha” = kf/”rho” cp

Here, “nu” is the viscosity, “alpha” is the thermal diffusion rate, cp is the specific heat, and kf is the thermal conductivity, with units of W/mK, and is not to be confused with the Boltzman constant. When one remembers that the effect of viscosity is to bleed off energy from fluid motion, one sees that a small Prandtl number means that heat diffuses very quickly compared to loss of energy due to viscosity. Air, at one atmosphere, has a small Prandtl number of around 0.7. We note in passing, that the Peclet number is the mass transfer analogue of the Prandtl number.

The Nusselt number, Nu, is the ratio of conductive heat transfer to convective heat transfer.

Nu = hl/kf

Here h, is the convective heat transfer, l, is the characteristic length (as in the definition of the Reynolds number) and is the thermal conductivity of the fluid.

So how does a gimp like my little ponytail know about fluids?