Find the Heat Flow of a Dehumidifier

Calculate the heat flow of an ideal dehumidifier using psychrometric charts

First calculate the humidity ratio, the ratio between the water content in the air to the mass of the air without that moisture, in a room with a temperature of 20 degrees Celsius and a humidity of 60%:

In[1]:=

oWater=PsychrometricPropertyData["DryBulbTemperature"

°C

,"RelativeHumidity"

,"HumidityRatio"]

Out[1]=

0.0088

lb/lb

Next assume that we use sensible cooling, without altering the moisture content, to reduce the temperature down to the dew point. Calculate the dew point temperature from the original temperature and relative humidity:

In[2]:=

dew=PsychrometricPropertyData["DryBulbTemperature"

°C

,"RelativeHumidity"

,"DewPointTemperature"]

Out[2]=

°F

Then the dehumidifier uses latent cooling to reduce the temperature further to 2 degrees Celsius, condensing moisture out of the air. Calculate the new humidity ratio at 2 degrees Celsius and 100% relative humidity:

In[3]:=

fWater=PsychrometricPropertyData["DryBulbTemperature"

°C

,"RelativeHumidity"

100

,"HumidityRatio"]

Out[3]=

0.0044

lb/lb

Thus half of the water content has been removed from the air:

In[4]:=

oWater-fWater

Out[4]=

0.0044

lb/lb

Assume that we were running this dehumidifier in an airtight room without any source of additional moisture and calculate the total water collected by the dehumidifier:

In[5]:=

airmass=

dry air

CHEMICAL



density

*

;

In[6]:=

removedwater=airmass*(oWater-fWater)

Out[6]=

127.126

This is roughly half a cup:

In[7]:=

UnitConvertremovedwater

water

CHEMICAL



density

,"Cups"

Out[7]=

0.538921

Returning to the dehumidifier, we now must heat the air back up to 20 degrees Celsius, using sensible heating, to keep the temperature constant. Once this is completed, calculate the new relative humidity using the new humidity ratio:

In[8]:=

PsychrometricPropertyData["DryBulbTemperature"

°C

,"HumidityRatio"fWater,"RelativeHumidity"]

Out[8]=

Estimate heat flow by examining the enthalpy of the condensing and heating process. Calculate the enthalpy at the original temperature and humidity, the final condensation point, and the final temperature and humidity:

In[9]:=

originalEnthalpy=PsychrometricPropertyData["DryBulbTemperature"

°C

,"RelativeHumidity"

,"SpecificEnthalpy"];condensationEnthalpy=PsychrometricPropertyData["DryBulbTemperature"

°C

,"RelativeHumidity"

100

,"SpecificEnthalpy"];finalEnthalpy=PsychrometricPropertyData["DryBulbTemperature"

°C

,"HumidityRatio"fWater,"SpecificEnthalpy"];{originalEnthalpy,condensationEnthalpy,finalEnthalpy}

Out[9]=

{

4.58

Cal/lb

1.39

Cal/lb

3.38

Cal/lb

}

Take the difference between the start and end points of the condensation process and multiply by the air mass flow to find the heat flow for this process. Assume a standard density for the air and an air flow rate of 1 cubic meter per second:

In[10]:=

coolingHeatFlow=(originalEnthalpy-condensationEnthalpy)*

dry air

CHEMICAL



density

*

Out[10]=

8.9701

Cal/s

In[11]:=

UnitConvert[%,"Kilowatts"]

Out[11]=

37.5309

We can apply the same idea to the heating process, though this time the heat is flowing into the system as opposed to being extracted:

In[12]:=

heatingHeatFlow=(finalEnthalpy-condensationEnthalpy)*

dry air

CHEMICAL



density

*

Out[12]=

5.58844

Cal/s

In[13]:=

UnitConvert[%,"Kilowatts"]

Out[13]=

23.382

Calculate the time to heat or cool the room at 1 cubic meter per second:

In[14]:=

time=N





Out[14]=

22.6535

Apply this time to the heating and cooling heat flows that we just determined to find the total energy used:

In[15]:=

(coolingHeatFlow+heatingHeatFlow)*time

Out[15]=

329.802

Cal

In[16]:=

UnitConvert[%,"Joules"]

Out[16]=

1.37989×

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Find the Heat Flow of a Dehumidifier

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Find the Heat Flow of a Dehumidifier

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