Dehumidifying Moist Air - Latent Cooling
If the temperature on a cold surface is lower than the dew point temperature - tDP - of the humid air, vapor in the air condensates on the surface. Latent heat - vapor - is removed from the humid air.
This process can be expressed in the Mollier diagram as below. The air cools in the direction of point C, which is the intersection point of the cold surface temperature (the cooling surface dew point temperature or the apparatus dew-point - tADP) and the saturation line.
With a cold surface of unlimited size and a very small amount of air, it would be possible to reach point C. In the real world a limited surface is never 100% effective and the final state of the cooled and dehumidified air will be somewhere on the straight line between point A and C - point B.
The amount of condensated vapor will be the difference xA - xB.
Contact Factor - β
The efficiency of a cooling coil is commonly expressed with the Contact Factor - β - and can be expressed as
β = (xA - xB) / (xA - xC)
= (hA - hB) / (hA - hC)
≈ (tA - tB) / (tA - tC) (1)
β = Contact Factor
x = specific humidity (kg/kg)
h = enthalpy (kJ/kg)
t = temperature (oC)
Bypass Factor - BPF
The Bypass Factor - BPF - (or BF) is commonly used to express a cooling coils efficiency:
BPF = (hB - hC) / (hA - hC)
= (tB - tC) / (tA - tC)
= (xB - xC) / (xA - xC) (2)
BPF = Bypass Factor (BF)
The relationship between the Contact Factor and the Bypass Factor can be expressed as:
BPF = 1 - β (3)
Heat Flow in a Cooling Coil
The total heat flow rate through the cooling coil can be calculated as:
q = m (hA - hB) (4)
q = heat flow rate (kJ/s, kW)
m = mass flow rate of air (kg/s)
The total heat flow can also be expressed as:
qs = v ρ (hA - hB) (4a)
v = volume flow (m3/s)
ρ = density of air (kg/m3)
Note! The density of air varies with temperature. At 0oC the density is 1.293 kg/m3. At 80oC the density is 1.0 kg/m3.
The total heat flow rate can be split into sensible and latent heat. The sensible heat flow rate can be expressed as:
qs = m cp (tA - tB) (4b)
cp = 1.01 - specific heat capacity of air (kJ/kg.oC)
The latent heat can be expressed as:
qs = m hwe (xA - xB) (4c)
hwe = 2502 (kJ/kg)
Example - Cooling and Dehumidifying Air
1 m3/s of air at 30oC and relative humidity 60% (A) is cooled down to 15oC (B). The surface temperature of the cooling coil is 0oC (C). The density of air at 20oC is 1.205 kg/m3.
Using the Mollier diagram the state of the cooled air (B) is in the intersection between the straight line between (A) and (C) and the 15oC temperature line.
From the Mollier diagram the enthalpy in (A) is 70 kJ/kg, in (B) 38.5 kJ/kg and in (C) 8.5 kJ/kg.
The Contact Factor can be calculated as:
β = ((70 kJ/kg) - (38.5 kJ/kg)) / ((70 kJ/kg) - (8.5 kJ/kg))
The total heat flow can be calculated as:
q = (1 m3/s) (1.205 kg/m3) ((70 kJ/kg) - (38.5 kJ/kg))
= 38 (kJ/s, kW)
The sensible heat flow can be calculated as:
qs = (1 m3/s) (1.205 kg/m3) (1.01 kJ/kg.oC) (30oC - 15oC)
= 18.3 (kW)
According to the Mollier diagram the specific humidity in (A) is 0.016 kg/kg and in (B) 0.0096 kg/kg and the latent heat flow can be calculated as:
qs = (1 m3/s) (1.205 kg/m3) (2,502 kJ/kg) ((0.016 kg/kg) - (0.0096 kg/kg))
= 19.3 (kW)
Note! Due to inaccuracy when working with graphical diagrams there is a small difference between the total heat flow and the sum of the latent and sensible heat. The inaccuracies are in general within acceptable limits.