Now that we know a lot more about boundary layer behaviour
and heat transfer, we can see why the wing panel radiators were
ineffective.
To transfer heat to air (an insulator) you need very
thin boundary layers. Very thin boundary layers occur on and near the
front of sharp leading edges, like those you see in your oil cooler and auto
radiator.
As the boundary layer grows thicker (as it moves
downstream from the leading edge), the thermal gradient between hot surface and
colder flow drops dramatically, and the rate of heat transfer drops quickly.
So to get excellent heat transfer, you need lots of knife edges facing forward,
and after the flow passes a short distance (fractions of an inch) you then
terminate the surface (the fin) and start a new one with a new leading edge to
start a new, very thin boundary layer. The resulting heat transfer
coefficients near sharp edges facing forward are many times greater than for a well developed boundary
layer that has passed over inches or feet of fuselage or wing surface.
For fluids like air that have a Prandtl number near
one (0.7 for air) the thermal boundary layer and velocity/momentum boundary
layer (the one we worry about for drag, stall and such) are nearly the same
shape and thickness. (The Prandtl number is essentially a ratio of the
ability of a fluid to transfer momentum via viscosity compared to the ability to
transfer heat via thermal conductivity and specific heat.) So if you know
one boundary layer, you more or less know the other.
On a flat plate oriented parallel to the flow at the
speeds we fly at, the boundary layer thickness is roughly 1% of the distance
from the leading edge (gross over simplification, but communicates the
idea). So two feet back from a leading edge, the boundary layer is about
a quarter of an inch thick. That does not help heat transfer very much.
If you take a magnifying glass and look into the
passages of a modern radiator, you will see that the fins which are themselves
not very long are now themselves punched with tiny louvers to create still more
leading edges to get those thin boundary layers. The key is to balance
heat transfer and friction loss. Large truck radiators have gone far in
this direction since the cooling loads on a 600 HP diesel full throttle on a
summer day climbing the Rockies
can be significant drag on fuel economy.
Wing panel radiators have two other fundamental
problems. First, they get hot and cold, and thus they grow and
shrink. It makes mechanical design a bit of a nightmare especially when
the panel is many square feet in size. Second,
heat addition to boundary layers is destabilizing, causing premature transition
from laminar to turbulent flow which then increases drag.
Behold the humble modern radiator. It
accomplishes so much in so little space.
Fred
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The Macchi-Castoldi can be seen
at an Italian air museum on Lago di Bracciano near Rome.
An interesting detour for aviation nuts.
According to description in the museum, the wing radiators were sufficient for
speed run, but not for the Schneider Trophy. Probably to due to hydraulic
flow questions. In any case the idea was not used again.
Yakjock wrote:
With the discussion on speed and heat drag I thought I'd remind folks of the
Macchi-Castoldi MC-72…