Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Cooling and Heating Equations

Latent and sensible cooling and heating equations - imperial units.

Sponsored Links

Sensible Heat

The sensible heat in a heating or cooling process of air (heating or cooling capacity) can be calculated in SI-units as

hs = cp ρ q dt                                              (1)

where

hs = sensible heat (kW)

cp = specific heat of air (1.006 kJ/kg oC)

ρ = density of air (1.202 kg/m3)

q = air volume flow (m3/s)

dt = temperature difference (oC)

Or in Imperial units as

hs = 1.08 q dt                                            (1b)

where

hs = sensible heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dt = temperature difference (oF)

Example - Heating Air, Sensible Heat

Metric Units

An air flow of 1 m3/s is heated from 0 to 20oC. Using (1) the sensible heat added to the air can be calculated as

hs = (1.006 kJ/kg oC) (1.202 kg/m3) (1 m3/s) ((20 oC) - (0 oC))      

    = 24.2 (kW)

Imperial Units

An air flow of 1 cfm is heated from 32 to 52oF. Using (1b) the sensible heat added to the air can be calculated as

hs = 1.08 (1 cfm) ((52 oF) - (32 oF))      

    = 21.6 (Btu/hr)

Sensible Heat Load and Required Air Volume Chart

Sensible heat load and required air volume to keep the temperature constant at various temperature differences between make up air and room air:

Latent Heat

Latent heat due to the moisture in air can be calculated in SI-units as:

hl = ρ hwe q dwkg                                      (2)

where

hl = latent heat (kW)

ρ = density of air (1.202 kg/m3)

q = air volume flow (m3/s)

hwe = latent heat evaporization water (2454 kJ/kg - in air at atmospheric pressure and 20oC)

dwkg = humidity ratio difference (kg water/kg dry air)

Latent evaporation heat for water can be calculated as

hwe = 2494 - 2.2 t                  (2a)

where

t = evaporation temperature (oC)

Or for Imperial units:

hl = 0.68 q dwgr                                      (2b)

or

hl = 4840 q dwlb                                     (2c)

where

hl= latent heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dwgr = humidity ratio difference (grains water/lb dry air)

dwlb = humidity ratio difference (lb water/lb dry air)

Example - Cooling Air, Latent Heat

Metric Units

An air flow of 1 m3/s is cooled from 30 to 10oC. The relative humidity of the air is 70% at the start and 100% at the end of the cooling process.

From the Mollier diagram we estimate the water content in the hot air to be 0.0187 kg water/kg dry air, and the water content in the cold air to be 0.0075 kg water/kg dry air.

Using (2) the latent heat removed from the air can be calculated as

hl = (1.202 kg/m3(2454 kJ/kg) (1 m3/s) ((0.0187 kg water/kg dry air) - (0.0075 kg water/kg dry air))      

    = 34.3 (kW)

Imperial Units

An air flow of 1 cfm is cooled from 52 to 32oF. The relative humidity of the air is 70% at the start and 100% at the end of the cooling process.

From the psychrometric chart we estimate the water content in the hot air to be 40 grains water/lb dry air, and the water content in the cold air to be 26 grains water/lb dry air.

Using (2b) the latent heat removed from the air can be calculated as

hl = 0.68 (1 cfm) ((40 grains water/lb dry air) - (26 grains water/lb dry air))      

    = 9.5 (Btu/hr)

Latent Heat Load and Required Air Volume Chart

Latent heat load - humidifying and dehumidifying - and required air volume to keep temperature constant at various temperature differences between entering air and room air are indicated in the chart below:

Total Heat - Latent and Sensible Heat

Total heat due to both temperature and moisture can be expressed in SI units as:

ht = ρ q dh                                            (3)

where

ht = total heat (kW)

q = air volume flow (m3/s)

ρ = density of air (1.202 kg/m3)

dh = enthalpy difference (kJ/kg)

Or - in imperial units:

ht = 4.7 q dh                                        (3b)

where

ht= total heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dh = enthalpy difference (btu/lb dry air)

Total heat can also be expressed as:

ht = hs + hl

    = 1.08 q dt + 0.68 q dwgr                                      (4)

Example - Cooling or Heating Air, Total Heat

Metric Units

An air flow of 1 m3/s is cooled from 30 to 10oC. The relative humidity of the air is 70% at the start and 100% at the end of the cooling process.

From the Mollier diagram we estimate the water enthalpy in the hot air to be 77 kJ/kg dry air, and the enthalpy in the cold air to be 28 kJ/kg dry air.

Using (3) the total sensible and latent heat removed from the air can be calculated as

ht = (1.202 kg/m3) (1 m3/s) ((77 kJ/kg dry air) - (28 kJ/kg dry air))      

    = 58.9 (kW)

Imperial Units

An air flow of 1 cfm is cooled from 52 to 32oF. The relative humidity of the air is 70% at the start and 100% at the end of the cooling process.

From the psychrometric chart we estimate the water enthalpy in the hot air to be 18.7 Btu/lb dry air, and the enthalpy in the cold air to be 11.8 Btu/lb dry air.

Using (3b) the total sensible and latent heat removed from the air can be calculated as

ht = 4.7 (1 cfm) ((18.7 Btu/lb dry air) - (11.8 Btu/lb dry air))      

    = 32.4 (Btu/hr)

SHR - Sensible Heat Ratio

The Sensible Heat Ratio can be expressed as

SHR = hs / ht                              (6)

where 

SHR = Sensible Heat Ratio

hs = sensible heat

ht = total heat (sensible and latent)

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Share

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Topics

Unit Converters

Temperature

oC
oF


Load Calculator!

Length

m
km
in
ft
yards
miles
naut miles


Load Calculator!

Area

m2
km2
in2
ft2
miles2
acres


Load Calculator!

Volume

m3
liters
in3
ft3
us gal


Load Calculator!

Weight

kgf
N
lbf


Load Calculator!

Velocity

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


Load Calculator!

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O


Load Calculator!

Flow

m3/s
m3/h
US gpm
cfm


Load Calculator!

3 30

This website use cookies. By continuing to browse you are agreeing to our use of cookies! Learn more