Its fairly clear
that air flow and core area are two of the most significant factors as
together they determine the basic Mass flow possible through the
cooler. If that is not sufficient to carry away the heat you are
trying to reject then all else is moot.
In K&W there
are two coefficients they focus on, Kh the heat transfer
coefficient which is dependent on the characteristics of the core,
Kp the pressure drop
coefficient - again based on core characteristics. They end up with a
combined coefficient that rates how well the core transfers heat based on
the pressure drop this is Kv = Kh/Kp.
These coefficients are dependent on such things as the openness ratio, the
hydraulic diameter of the individual passage in the core and the thickenss
of the core. Both Kh and
Kp
are also weakly dependent on the Reynolds number
of the air flow throught the core. I say weakly because they relate to
the inverse fourth power of the Reynolds number or
1/(Re)^(1/4).
Interestingly enough because it is an inverse relationship the heat transfer
is better to the air with lower velocity through the core. Not quite
certain that I fully understand why, except it appears to do with the shear
force and friction between the air flow in the core passage and the the
passage walls. However, while heat is apparently passed from the core
walls to the air better at the lower Reynolds numbers, the downside is that
low Reynold number also means lower air velocity throught the core which in
turn means Low mass flow which is not good for
cooling.
So from the
equations in K&W that there is an optimum balance between the heat
transfer due to the lower Reynolds effect and the heat removed due to higher
mass flow through the core. Too much of one and not enough of the other and
your cooling is suboptimal.
FWIW
The Reynolds
number (a dimensionless parameter) includes “characteristic length” of the
channel, so although the heat transfer coefficient is increasing with
increased velocity, the “residence time” of the air is decreasing, meaning
less time for the air to heat up. But the ¼ power of the Re in the
demoninator is only one piece of the equation (isn’t it?). Somewhere
in the numerator is the mass flow (velocity) which wins out every
time. For a given core, higher velocity removes more heat. But
of course, there are other limits on velocity.
Or am I missing
something. It’s been a long time since I worked on details of
convective heat transfer.
Al
According to
K&W the heat-transfer coefficient Kh and pressure-drop
coefficient Kp both decrease with
increase in air velocity through the core. However,
even though these coefficients decrease,
the overall heat removal may increase (up to a point) due
to the higher mass flow through the core because of the higher air velocity.
So as I understand it lower velocity throught the core increases the
coefficients, but decrease the mass flow while higher velocity decreases the
coefficients but increase the mass flow. So from what I think I
understand it appears that there is a theoretical optimum balance between
keeping the value of these important coefficients sufficient high by
limiting the velocity through the core, but keeping the mass flow
sufficiently high by sizing the area of the core so that you removed the
desired quantity of heat. Again, a lot of
compromise.
The equation
given for Kp= (1/s)*(L/D)*(0.316/(Re)^(1/4))
and Kh = 1/2*(L/D)*(0.316/(Re)^(1/4)).
With Re = VcD/sv with s being the openness ratio, L (thickness of
Core) and D the Hydraulic Diameter, Vc being velocity at the face of the
core. So as you mention the pressure drop coefficent goes up with
increased thickenss (L) but down as the diameter (D) of the
passage is increase and also down as the velocity increases (Re
increases). Also the more open (s
=larger), the less pressure drop.
The equation
given for heat transfer (the thing we are really interested in)
Q
= pVcAcCp(Tw-Ti)(1 - e^(-Kh). Which has the
all important mass flow factor pVcAc, the temp difference
between wall and air and the anitlog of heat transference coefficience
Kh.
Makes my head
hurt.
Ed
.