A combination air cooler and dehumidification unit receives...

A combination air cooler and dehumidification unit receives outside ambient air at $35^{\circ} \mathrm{C}, 100$ $\mathrm{kPa},$ and $90 \%$ relative humidity. The moist air is first cooled to a low temperature $T_{2}$ to condense the proper amount of water; assume all the liquid leaves at $T_{2}$. The moist air is then heated and leaves the unit at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, and $30 \%$ relative humidity with a volume flow rate of 0.01 $\mathrm{m}^{3} / \mathrm{s} .$ Find the temperature $T_{2},$ the mass of liquid per kilogram of dry air, and the overall heat transfer rate.

Key Concepts

Overall Heat Transfer

Overall heat transfer in such systems encompasses both the removal of sensible heat during cooling and the latent heat associated with condensing water vapor. This integrated approach is fundamental for calculating the efficiency, cooling capacity, and energy requirements of air conditioning units.

Energy and Mass Balances in HVAC Processes

In cooling and heating systems, the conservation of energy and mass principles are applied to determine system performance. Energy balances account for both the sensible heat (associated with temperature changes) and latent heat (associated with phase changes like condensation), while mass balances ensure that the mass flow of air and moisture is accurately tracked through the system.

Psychrometrics

Psychrometrics is the study of the thermodynamic properties of moist air and the relations among them. It includes concepts such as dry-bulb temperature, wet-bulb temperature, relative humidity, and dew point, which are essential for analyzing processes in HVAC systems, especially those involving cooling and dehumidification.

Air-Water Vapor Mixture

This concept involves treating air as a binary mixture of dry air and water vapor. The properties of this mixture and the interaction between the two components are crucial for understanding how moisture condenses during cooling and how the overall enthalpy of the air is affected during heating or cooling processes.

Condensation and Dehumidification

Condensation occurs when air is cooled to a point where it can no longer hold all of its water vapor, leading to the formation of liquid water. This process is central to dehumidification in HVAC systems, where controlling the moisture content of air is important for comfort, health, and process requirements.

Transcript

00:01 Hi, everybody.

00:01 So, we need to find the temperature of t2, the mass of liquid per kilogram of dry air, and the overall heat transfer rate.

00:13 So to do this, we just need to find the pv1, which is 5 times pg1 equals 0 .9 times 5 .6.

00:30 628 equals 5 .0625k pascels.

00:39 Okay.

00:41 And then we can find the absolute community of 1, 0 .622 times 5 .0625, 100 minus 5 .0625, which is 0 .03318 from the absolute community equation.

01:12 So then the property of water and salt water be three and state three for that one is going to be 0 .3 times 2 .3.

01:38 Equals 0 .7017 k pascels.

01:45 And at absolutely many of the third one is 0 .622 times 0 .7117, 100 minus 0 .717.

02:03 Equals 0 .0439.

02:07 This is also going to be absumany of two.

02:11 So now we need find the mass flow weight of air.

02:17 So from that we have 100 minus 0 .7017 times 0 .01 divided by 0 .287 times 0 .08, divided by 0 .287 times.

02:35 293 .15 and we get 0 .118 .02 kilograms per second.

02:49 Okay.

02:50 And now we can find the mass of the liquid, which is mv1 minus mv2, which equals ma of m1 of 1 minus w2, which equals ma of 1 minus w2.

03:08 Equals ma here of 0 .0333118, minus 0 .00439.

03:23 And so we put m and lma together, massive error, and we get 0 .02879.

03:34 And this is before we continue on to add.

03:38 So we'll just leave it like that, so don't worry.

03:41 So we need to attain temperature 2, and it's going to be 0 .01 plus 5 minus 0 .01 times 0 .7017 minus 0 .6113, divided by 0 .8721 minus 0 .6113...

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