David Combs wrote:

For those of us who's most recent engineering, physics, thermo, fluids,
etc courses were a LONG time ago (early 60's for me)

Me too.

please expand your very-interesting text with perhaps a few definitions,
therefores, etc...

OK.

wrote:
Edwin Pawlowski wrote:

Ceiling fans just circulate the hot air already in the room...
You have to blow hot air out and draw cooler air in.

And make sure the cool air scrubs the heat out of the room surfaces, vs
just passing through rooms with still air near the surfaces

Still air is a poor heat conductor, about R5 per inch. A square foot of
still air 1" thick is like a 5 ohm resistor, for heatflow through the 1"
thickness. DEFINITION: Ohm's law for heatflow is just like Ohm's law for
electricity with different units, thermal resistances vs ohms, Btu/h vs
amps, and Fahrenheit temperature differences instead of voltage diffs.
For example, 4 Btu/h flows in this circuit, viewed in a fixed font:

3
-------www-------
| ----- |
| 12 4 |
--- |
- |
| |
| |
--- ---
- -

(including people surfaces, which feel cooler in moving air.)

THEREFORE, if a person generates 300 Btu/h at 100 F internally with a 91 F
skin temp (measured with a $50 Raytek IR thermometer), we have something
like this, with an internal resistance Ri and a skin surface resistance Ra
in 70 F slow-moving air:

91 F
Ri | Ra
---------www-------------www-------
| -------------------- |
| I = 300 Btu/h |
| 100 F | 70 F
--- ---
- -
| |
| |
--- ---
- -

300Ri = (100-91) makes Ri = 0.03 and 300Ra = (91-70) makes Ra = 0.07, no?

If the slow moving air has a film conductance Ua = 2 Btu/h-F-ft^2 and
Ra = 1/(UaAs) = 0.07, the person might have As = 1/(RaUa) = 7 ft^2 of
exposed skin, out of 20 ft^2 of total average Dubois skin surface.

Now if the room temp rises to 85 F and everything else is the same, the skin
temp rises to 85+300Ra = 106 F, very uncomfortable. What to do? Rest vs work,
eg a siesta to lower heat generation, which can vary by 10:1, depending on
activity, or lose weight, since heat output increases with body mass, or
decrease Ri (some people in Arizona adapt to heat with more blood flow near
the skin and higher skin temps), or evaporate sweat, or stand in a bucket
of water, or increase the airspeed near the skin, and/or remove clothing.

To be equally comfortable with a 91 F skin temp, we might reduce Ra until
300Ra = (91-85), ie Ra = 0.02 or Ga = 1/Ra = 50 = AsUa. Increasing airspeed
to 6 mph (enough to blow papers off desks) makes Ua = 2+6/2 = 5 Btu/h-F-ft^2
and As = 10 ft^2, with more exposed skin, and so on.

Ceiling fans can help whole house fans. Picture surface thermal mass
in series with an airfilm conductance Ua that increases with air velocity
(Ua = 2+V/2 Btu/h-F-ft^2, with V in mph, approximately) in series with
a conductance to outdoor air cfm Btu/h-F, approximately),

DEFINITION: fans are thermal conductors. A 1000 cfm airstream with a dT (F)
temperature difference moves about 1000dT Btu/h, ie it has a conductance of
about 1000 Btu/h-F.

like this, viewed in a fixed font:

1/cfm 1/(AUa)
Tout ---www------www----------- Tsurf
|
|
--- Csurf = 0.5A Btu/F/ft^2
---
| for A ft^2 of 1/2" drywall.
|
-

And 1 ft^2 of 1/2" drywall is like a 0.5 farad capacitor...

A 10'x20' room with 880 ft^2 of drywall might have Csurf = 440 Btu/F.
With a 1000 cfm window fan and a ceiling fan that raises the airspeed
near the surface to V = 2 mph, it might have a natural time constant
RC = Csurf(1/cfm+1/(A(2+V/2)) = 440(1/1000+1/(880(2+2/2)) = 0.6 hours.

DEFINITION: an RC time constant is a measure of how fast a circuit
reacts to change.

In 2 hours with Tout = 70 F, a Tsurf = 80 F room would would cool to
70+(80-70)e^-(2/0.6) = 70.4 F.

The wall starts at Tsurf = Ti and becomes T(t) = Tout + (Ti-Tout)e^(-t/RC)
t hours after the fan starts. Initially, T(t) = Tout + (Ti-Tout)e^(-0/RC)
= Ti. After a very long time, T(t) = Tout + (Ti-Tout)e^(-oo/RC) = Tout.
Nice, huh? Most of this happens in 3 or 4 time constants. In between,
the exponential function e^(-t/RC) gradually squashes the initial temp diff
(Ti-Tout) to 0 over time.

With a 500 cfm window fan and no ceiling fan, RC = 1.1 hours...

Adding resistors in series, RC = (1/500+1/(2x880))440 = 1.13 hours.

it might only cool to 70+(80-70)e^-(2/1.1) = 71.7, or more, if the bulk
of the air near the surface stays warm, hardly moving at all.

With R20 walls, after 8 hours with Tout = 90 F with the window fan off
and no internal heat gains and RC = 10 hours...

RC = 20ft^2-F-h/Btux0.5Btu/F-ft^2 = 10 hours.

the 70.4 F drywall temp would climb to 90+(70.4-90)e^-(8/10) = 81.2

.... as before, with a final temp and a negative initial temp diff that
gets stomped down to 0 over time by the cruel but patient exponential.

or less, with 2 layers of drywall with RC = 20 hours and
90+(70.4-90)e^-(8/20) = 76.9.

Same old stuff, with slower stomping.

We might have a lot more mass and a lower temp if we cooled a basement
at night and circulated house air through the basement during the day.

Basements have lots of thermal mass. If we don't live in them, we can cool
them below the comfort temp, but we have to be careful to avoid blowing
moist outdoor air through a basement, with condensation.

THANKS!

You are welcome.

Nick