Re: Naked Ape?

In article <1123115594.513678.271280@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Friar Broccoli <EliasRK@xxxxxxxxx> wrote:
>Robert Grumbine wrote:
>> Tim Tyler wrote:
>
>>>> IIRC laminar flow sets up a 'boundary layer' and turbulent flow breaks
>>>> up the boundary layer. You may have it exactly backwards.
>
>>> Except that I don't - think about what you are saying.
>
>> In laminar flow, heat is carried away from the wall (skin in this case)
>> by molecular diffusion. Molecular processes of heat transfer are very
>> slow (diffusivity on the order of 1e-5 m^2/s). The non-goosebump
>> condition of skin is relatively smooth, so, _a priori_ one might think
>> of laminar boundary layers.
>
>> In turbulent flow, heat is carried away from the wall by advection,
>> as eddies whirl past the wall, pulling hot air from the skin out to
>> the cooler air outside. Turbulent eddy diffusivities in such a case
>> can be easily 0.1 m^2/s, 1e4 times as large.
>
>> If you are trying to shed heat, goosebumps are a possible advantage
>> (if they induce turbulent breakdown of an otherwise laminar boundary
>> layer).
>
> I am much more than a bit confused here. So I have a
> question that I hope will clarify things:
>
> How does all this relate to the well known example of the
> golf ball (or shark skin in water)?

Those are two more examples of ways in which fluid mechanics
can be counterintuitive, in differennt ways from the above
and each other.

> The little valleys in a golf ball cause a boundary layer of
> air to adhere to the ball in flight, thereby reducing air
> friction and increasing maximum flight distance by 2 or 3
> times.

The golf ball effect is from a different breakdown point. If you
drive a sphere through a fluid and watch the drag force as a function
of Reynolds number, you see that the coefficient of drag declines
steadily, though increasingly slowly, out to about 100,000. At a
slightly higher Re, the coefficient of drag suddenly drops by a factor
of 2-3, and then starts increasing.

The dimpling is to increase the Re so as to take a golf ball
just over that breakdown, from its normal just under. Dimpling
doesn't work for, say, baseballs, cars, or airplanes at normal
(including same as golf ball) speeds because they're enough larger
that they are always above this breakdown point. Re = U*L/nu.

> Similarly shark skin, which feels like sand paper, causes a
> layer of water to remain next to the skin allowing almost
> frictionless movement in the water.

Almost frictionless is an overstatement. Significant reduction
in coefficient of drag in the right circumstances, yes. The
physics here is different again from onset of turbulence (the Reynolds
problem) and golf balls. (As it's also a much more recent
discovery and understanding than my non-geophysical fluid
dynamics work, I'll leave it at that.)

> It seems obvious to me that such boundary layers would also
> reduce heat transfer since they insure that the same air
> remains in contact with the surface. Such a fixed boundary
> layer would therefore act as an insulator, preventing heat
> loss.
>
> I have no idea whether I am describing turbulent or laminar
> flow (or something completely different), but it does seem
> to me that the standing hairs and the extra roughness of
> the skin caused by goose bumps could (at least in
> principle) cause a static boundary layer to form, thereby
> reducing heat loss.

Again, the heat transfer off human skin problem doesn't
accept the analogy becauuse the air impinging is already
turbulent. To whatever extent turbulence would be desirable,
it already is present regardless of whether the hair is up
or down.

Now, if humans were arbitrarily large, eventually a boundary
layer of our own would form. Rule of thumb is that it takes
a downstream distance of about 100 times the height of the
obstacle(s) for that to happen. For 3 mm height obstructions
(my eyeball estimate of my relaxed arm and leg hair height),
that's 30 cm, greater than the path length over the arm or leg.
Erecting the hair, say, doubles that height, making a number
larger than arm or leg width, even larger than arm or leg width.

Aside: hair also erects in sneezing, I was reminded while posting.

Back to an earlier comment of mine: If goosebumps are for heat
transfer control (prevention), someone will have to explain how it is
that the same response is done both for being cold, and for being
hot. Your body is definitely not trying to prevent heat transfer
when you are facing, potentially rapid, fatal heat levels, yet hair
is erected in overheating as well.

It should also be explained why hair isn't erected over the torso
as well. There are a fair number of square cm of torso, which
are definitely aids to heat transfer (or penalties against it, if
you're trying to avoid it), yet it is only the extremities which
engage in hair erection.


I started my previous note as a thinking out loud. I rather like
the idea of our bodies engaging in some sneaky use/control of fluid
dynamical processes. But from, at this point, several different
angles it doesn't seem to work as either fluid dynamics or
given other circumstances in which hair is erected.

Not everything is necessarily currently adaptive, much less adaptive
to the problem we might think.

--
Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences

.

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