Evaporative Cooling – A Mechanism Enhanced by Mass Transport

Jesse Hamilton ME547

How Hot Is Hot?• Have you ever been to Phoenix?• How about New Orleans?

• Both are hot, but you experience two different types of hot depending on where you are!

Where would you expect to encounter this?

Where would you traditionally experience this type of heat?

Contrast your experiences in a humid climate (New Orleans) vs. an arid climate (Phoenix).

Closer to HomeAverage Conditions in August

Portland: 81 F, 65% HumidityElectricity costs (KWh): $0.1072

Phoenix: 104 F, 36% HumidityElectricity costs (KWh): $0.1196

Pause and ask – what is an Engineer’s purpose? Solve problems and answer questions.

• The questions I present.– 1. How can I stay cool?– 2. How much will it cost?

– Assumptions: For energy calculations, 20 hours of operation per day to maintain a comfortable temperature and average temperature/humidity numbers for 31 days (August).

Door #1: The A/C

5 ton unit operating at 14 SEER would cost:

• $317.80 in Phoenix• $284.85 in Portland

Door #2: The EAC

5000 CFM unit operating would cost:

• $85.27 in Phoenix• $76.43 in Portland

Decision Made?

That's it . . . I'm done . . . I've got my solution that saves $$$ . . . but wait, why are we talking

about A/C and EAC?

Well, not so fast . . .

• A/C and EAC work differently• A/C is a closed system with a compressor• EAC is an open system that uses water to cool

the air

What's the rub?

• A/C is a closed system – As such, its effectiveness is not subject to the

variation of atmospheric conditions – A/C works in most any climate

On the Other Hand

• EAC works by cooling air with water. • Specifically, the vaporization of water is a

phase change and requires significantly more energy (than conductive heat transfer alone).– Specific Heat of water = 4.186 kJ/kg– Energy of Vaporization = 2,257 kJ/kg

• By nature, this is dependent up the atmospheric conditions . . . especially humidity.

Analytical Solutions

• Things get complex very quickly It's spherical . . . take a look.

An Interesting Fact

• One Gallon of Water– Water at 50F and poured on a sidewalk at 90F

generates 9000 BTU of cooling– Water at 90Fpoured on a side walk at 90F

generates 8700 BTU of cooling

Clearly, there's more going on here . . .

Mass Transfer Impacts

To accurately describe this system, it requires the equations of motion, energy, and continuity for species to describe the impact of convection and mass transfer on the energy change.

Equations of Motion, Energy, and Species

Simplified Model (A. Fouda, Z. Melikyan)

• Even Simplified, this looks complex. Convective, energy, mass transfer all together.– is a mass transfer constant, is humidity of saturated air, is the air humidity, is

specific enthalpy of saturated air at wet bulb temp., is the specific enthalpy of moist air.

A. Fouda, Z. Melikyan, A Simplified Model for Analysis of Heat and Mass Transfer in a Direct Evaporative Cooler, Applied Thermal Engineering 31(2011): 932–936.

𝜌(𝜕𝑢𝜕𝑡 +𝜌𝑢𝜕𝑢𝜕 𝑥 )=𝜇𝜕

2𝑢𝜕𝑥2

−𝑢 (𝑘𝑎 (𝑑𝑠−𝑑) ) 𝜌𝜕𝑢𝜕 𝑥

=𝑘𝑎 (𝑑𝑠−𝑑 )

𝜌𝐶𝑝 (𝜕𝑇𝜕𝑡 +𝑢𝜕𝑇𝜕𝑥 )=𝑘 𝜕

2𝑇𝜕𝑥

−𝑘𝑎 (h𝑠−h )

Solution?

• Yeah Right Function . . . Companion of the Error Function and Gamma Function

(I made this up . . . )

• Not really, but the likelihood of producing an analytical solution is remote with 3 complex PDEs

Other Options

• There is significant experimental data • A popular presentation of experimental data is

graphical• Enter the Pyschrometric Chart. . .

What I've Learned and Observed

• EAC is functional in hot and dry climates like Phoenix.– Phoenix . . . 104 F and 36% humidity.

• EAC is not functional in more humid climates like Portland.– Portland . . . 81 F and 65% humidity.

What To Choose?

• When temperatures are lower, humidity needs to be lower for an EAC to be effective. For example, to be effective at average Portland temperatures, the humidity would need to be below 20%.

EAC Viability

• Temperatures are high (around 95F) • Humidity low (around 30%)• Electrical operation costs are less than 27% an

A/C.

• With lower temperatures (<85F) and higher humidity (>40%), comfort is consistently produce only with an A/C.

Questions???