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Heating Humid AirCalculating enthalpy change and temperature rise when heating moist and humid airwithout adding moisture

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The process of sensible heating - heating without adding moisture - of air can be expressed in the Mollier diagramas:

Heating of air moves the air condition from A to B along a constant specific humidity - x - line. The supplied heat -dH - can be read in the diagram as shown.

The heating process of air expressed can also be expressed in the psychrometric chart as:

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Heating Humid Air http://www.engineeringtoolbox.com/heating-humid-air-d_693.html

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oF

Length

m km in ft yards miles nautical

miles

Volume

m3

liters in3

ft3

us gal

Velocity

m/s km/h ft/min ft/s mph knots

Pressure

Pa (N/m2) bar mm H2O

Note! When heating air the specific moisture remains constant and the relative humidity decreases.

Calculating EnthalpyThe enthalpy of moist air can be expressed as:

h = cpa t + x [cpw t + hwe] (1)

where

h = specific enthalpy of moist air (kJ/kg)

cpa = 1.01 - specific heat capacity of air at constant pressure (kJ/kgoC, kWs/kgK)

t = air temperature (oC)

x = humidity ratio (kg/kg)

cpw = 1.84 - specific heat capacity of water vapor at constant pressure (kJ/kg.oC, kWs/kg.K)

hwe = 2502 - evaporation heat of water at 0oC (kJ/kg)

(1) can be modified as:

h = 1.01 (kJ/kg.oC) t + x [1.84 (kJ/kg.oC) t + 2502 (kJ/kg)] (1b)

The Enthalpy DifferenceThe enthalpy difference when heating air without changing moisture content can be expressed as:


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kg/cm2

psi inches H2O

Flow

m3/s m3/h US gpm cfm

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dhA-B = cpa tB + x [cpw tB + hwe] - cpa tA + x [cpw tA + hwe]

= cpa(tB - tA) + x cpw (tB - tA) (2)

Example - Enthalpy Difference Heating Air

The specific humidity of air at 25oC and relative moisture 50% is 0.0115 kg/kg - check the Mollier diagram. Thechange in enthalpy when heating the air to 35oC can be calculated as:

dhA-B = (1.01 kJ/kgoC)(35oC - 25oC) + (0.0115 kg/kg) (1.84 kJ/kgoC) (35oC - 25oC)

= (10.1 kJ/kg) + (0.2 kJ/kg)

= 10.3 (kJ/kg)

Note! The contribution from the water vapor is relatively small and for practical purposes it may often be neglected.(2) can then be modified to:

dhA-B = cpa( tB - tA) (2b)

Increase in Temperature when Heating AirIf heat is added to humid air the increase air temperature can be calculated by modifying (2b) [(2) to be moreexact]:

tB - tA = dhA-B / cpa (2b)

Example - Heating Air and Temperature RiseIf 10.1 kJ is added to 1 kg air, the temperature rise can be calculated as:

tB - tA = (10.1 kJ/kg) / (1.01 kJ/kgoC)

= 10 (oC)

Heat Flow in a Heating CoilThe total heat flow rate through a heating coil can be calculated as:

q = m (hB - hA) (3)

where

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

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


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The total heat flow can also be expressed as:

qs = v ρ (hB - hA) (3a)

where

v = volume flow (m3/s)

ρ = density of air (kg/m3)

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

It's common to express the sensible heat flow rate as:

q = m cpa (tB - tA) (3b)

or alternatively:

q = v ρ cpa (tB - tA) (3c)

Heating Coil EffectivenessFor a limited heating coil surface the average surface temperature will always be higher than the outlet airtemperature. The effectiveness of a heating coil can be expressed as:

μ = (tB - tA) / (tHC - tA) (4)

where

μ = heating coil effectiveness

tHC = mean surface temperature of the heating coil (oC)

Example - Heating Air1 m3/s of air at 15oC and relative humidity 60% (A) is heated to 30oC (B). The surface temperature of the heatingcoil is 80oC. The density of air at 20oC is 1.205 kg/m3.

From the Mollier diagram the enthalpy in (A) is 31 kJ/kg and in (B) 46 kJ/kg.

The heating coil effectiveness can be calculated as:

μ = (30oC - 15oC) / (80oC - 15oC)

= 0.23


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The heat flow can be calculated as:

q = (1 m3/s) (1.205 kg/m3) ((46 kJ/kg) - (31 kJ/kg))

= 18 (kJ/s, kW)

As an alternative, as one of the most common methods:

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

= 18.3 (kJ/s, kW)

Note! Due to inaccuracy when working diagrams there is a small difference between the total heat flow and the sumof the latent and sensible heat. This inaccuracy is in general within acceptable limits.

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Related Topics

Air Psychrometrics - The study of moist and humid air - air condition - psychrometric charts, Mollierdiagrams, air temperature, absolute and relative humidity, moisture content and more

Related Documents

Heat-Recovery - Ventilation and heat-recovery calculations, sensible and latent heat - online calculators -imperial units

Changing Air Condition by Heating, Cooling, Mixing, Humidifying or Dehumidifying Processes -Basic air condition processes - heating, cooling, mixing, humidifying and dehumidifying by adding steamor water - psychometric diagrams and the Mollier charts

Cooling and Dehumidifying Air - Cooling and dehumidifying processes of moist and humid air - sensibleand latent cooling

Drying Force of Air - The Drying Force of air may be expressed as the moisture holding capacity of theair and the evaporation capacity from a water surface to the air

Air Heating Systems - Using air to heat buildings - temperature rise diagram

Heat Removed in Cooling Air - Heat removed in cooling air to storage room conditions

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