Cooling and Dehumidifying Air

The cooling and dehumidifying process of moist and humid air. Sensible and Latent Cooling

Cooling Moist Air - Sensible Cooling

If the temperature on the cooling surface - t_C - is above or equal to the dew point temperature - t_DP - of the humid air, the air will be cooled without any change in specific humidity. It is the Sensible Heat - the "temperature heat" - in the air that is removed.

The air will cool along a constant specific humidity - x - line as expressed in the Mollier diagram below:

The process is very similar to the sensible heating process and the heating formulas can be adapted for calculating changes in enthalpy and temperature.

Note! The specific humidity is constant but the relative humidity increase.

Dehumidifying Moist Air - Latent Cooling

If the temperature on the cold surface is lower than the dew point temperature - t_DP - of the humid air, vapor in the air will condensate on the surface. Latent heat - the vapor - is removed from the humid air.

The 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 - t_ADP) 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 x_A - x_B.

Note! This process decreases the specific humidity. The relative humidity increases.

Contact Factor - β

The efficiency of a cooling coil is commonly expressed with the Contact Factor expressed as:

β = (x_A - x_B) / (x_A - x_C) = (h_A - h_B) / (h_A - h_C) ≈ (t_A - t_B) / (t_A - t_C) (1)

where

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 also commonly used to express the cooling coils efficiency:

BPF = (h_B - h_C) / (h_A - h_C) = (t_B - t_C) / (t_A - t_C) = (x_B - x_C) / (x_A - x_C) (2)

where

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 (h_A - h_B) (4)

where

q = heat flow rate (kJ/s, kW)

m = mass flow rate of air (kg/s)

The total heat flow can also be expressed as:

q_s = v ρ (h_A - h_B) (4a)

where

v = volume flow (m³/s)

ρ = density of air (kg/m³)

Note! The density vary with temperature. At 0^oC the density is 1.293 kg/m³. At 80^oC the density is 1.0 kg/m³.

The total heat flow rate can be split in sensible and latent heat. The sensible heat flow rate can be expressed as:

q_s = m c_p (t_A - t_B) (4b)

where

c_p = 1.01 - specific heat capacity of air (kJ/kg.^oC)

The latent heat can be expressed as:

q_s = m h_we (x_A - x_B) (4c)

where

h_we = 2,502 (kJ/kg)

Example - Cooling and Dehumidifying Air

1 m³/s of air at 30^oC and relative humidity 60% (A) is cooled down to 15^oC (B). The surface temperature of the cooling coil is 0^oC (C). The density of air at 20^oC 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 15^oC 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))

= 0.51

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:

q_s = (1 m³/s) (1.205 kg/m³) (1.01 kJ/kg.^oC) (30^oC - 15^oC)

= 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:

q_s = (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 diagrams there is a small difference between the total heat flow and the sum of the latent and sensible heat. This inaccuracy is in general within acceptable limits.

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