Department of Mechanical Engineering

ME 322 – Mechanical Engineering

Thermodynamics

Lecture 35

Analysis of Air Conditioning Processes

The Five HVAC Processes

• Heating

– With and without humidification

• Adiabatic humidification

• Cooling

– With and without dehumidification

• Adiabatic mixing of moist air streams

• Evaporative cooling

2

Heating Without Humidification

3

HQ

1 2

1T 2T

1

2#

1h

#

2h

12

1 2

# #

2 1H aQ m h h

• Constant humidity ratio

• Relative humidity

decreases

• Outlet relative humidity

may be too dry to be

comfortable

Heating with Humidification

4

HQ

1 2

water

1T 1'T

1

1'

#

1h

#

1'h

11'

1

1'

2

#

2h

22

# #

2 1 2 1

H

water

a

Qh h h

m

# #

1 2H a water water aQ m h m h m h

1 2

2 1

2 1

w water w

water w w

a a a

m m m

m m m

m m m

2T

Adiabatic Humidification

5

1 2

water

1T

1

1 1

2b

# #

2 1 2 1 0waterh h h

# #

1 2a water water am h m h m h

1 2

2 1

2 1

w water w

water w w

a a a

m m m

m m m

m m m

2c2a

The location of state 2 (2a,

2b, or 2c) depends on the

state of the water being

injected for humidification

Cooling Without Dehumidification

6

CQ

1 2

1T2T

1

2

#

1h

#

2h

12 1 2

# #

1 2C aQ m h h

This process is not very

common in HVAC systems.

Often, the surface of the

heat exchanger is below

the dew point which causes

water to condense

1'T

Cooling With Dehumidification

7

CQ

1 2

1T2T

1

2

#

1h

#

2h

121

If Twater is not given, it is

common to assume

that it is equal to T2

water

dpT

2

# #

2 1c a water water aQ m h m h m h

2 1

1 2

1 2

w water w

water w w

a a a

m m m

m m m

m m m

# #

1 2 1 2

C

water

a

Qh h h

m

Adiabatic Mixing

8

1 (cold)

2 (hot)

#

1h

#

2h

1

2

1

2

# # #

1 1 2 2 3 3a a am h m h m h

3 (warm)

3

#

3h

3

1 2 3a a am m m

# # #

1 1 2 2 1 2 3

# #

1 2 3

# #

2 3 1

a a a a

a

a

m h m h m m h

m h h

m h h

1 1 2 2 1 2 3

1 2 3

2 3 1

a a a a

a

a

m m m m

m

m

1 1 2 2 3 3a a am m m

# #

2 3 2 3

# #

3 1 3 1

h h

h h

1-2-3 are on a straight line!

Evaporative Cooling

9

1 2

water

1T

1

11

# #

2 1 2 1 0waterh h h

# #

1 2a water water am h m h m h

1 2

2 1

2 1

w water w

water w w

a a a

m m m

m m m

m m m

2

2

2

2T

This is the adiabatic

humidification

process when the

water used for

humidification is

colder than T1

This system works very well in hot,

dry climates. Notice that there can

be a significant increase in the

humidity levels (both relative

humidity and humidity ratio).

Department of Mechanical Engineering

ME 322 – Mechanical Engineering

Thermodynamics

Example

Combined Cooling and Heating

Processes

Example

11

Given: In a combined cooling/heating system, moist air enters the

cooling section at 90°F, = 50% at a volumetric flow rate of 5000 cfm.

Saturated, moist air and liquid condensate leave the cooling section at a

temperature that is 15 degrees below the dew point of the entering moist

air. After leaving the cooling section, the saturated, moist air enters the

heating section. After passing through the heater, the moist air leaves

the heating section at 68°F. The pressure throughout the system can be

assumed to be constant at normal sea-level pressure (29.921 inHg –

consistent with the psychrometric chart).

Find:

(a) The volumetric flow rate of the condensate (gpm)

(b) The required refrigeration capacity of the cooling section (tons)

(c) The relative humidity of the air leaving the heating section

(d) The heat transfer rate required in the heating section (Btu/hr)

Example

12

A sketch of the system and a psychrometric chart showing

the processes is shown below.

CQ

1 3

1T2T

1

2

#

1h

#

2h

121

water

dpT

2 3

HQ

2

3

#

3h

3

3T

1

1

1

90 F50%

5000 cfm

T

V

3 68 FT

2 1 15 RdpT T T

Properties from the Chart and Tables

13

1 90 FT

2 15°F 69 15 F 54°FdpT T

1 50%

2

#

1 38.4 Btu/lbmah

#

2 22.5 Btu/lbmah

121 0.0152

69 FdpT

2 3 0.0089 3

#

3 26.0 Btu/lbmah

3 61%

3 68 FT

3

1 14.19 ft /lbmav

3

2Table C.1aTable C.1a

54 F 22.1 Btu/lbm 0.01605ft / lbmwater water w wT T h v

Example

14

CQ

1 3

water

HQ

2

1

1

1

90 F50%

5000 cfm

T

V

3 68 FT

2 1 15 RdpT T T Cooling section analysis …

# #

1 2 1 2

C

water

a

Qh h h

m

3

1

3

1

ft5000

lbm60 minmin 21141.6ft hr hr

14.19lbm

aa

a

Vm

v

# #

1 2 1 2

lbm lbmBtu Btu21141.6 38.4 22.5 0.0152 0.0089 22.1

hr lbm lbm lbm

Btu333,208 27.8 tons

hr

C a water

a wC

a a w

C

Q m h h h

Q

Q

1 90 FT

2 15°F 69 15 F 54°FdpT T

1 50%

2

#

1 38.4 Btu/lbmah

#

2 22.5 Btu/lbmah

121 0.0152

69 FdpT

2 3 0.0089 3

#

3 26.0 Btu/lbmah

3 61%

3 68 FT

3

1 14.19 ft /lbmav

2Table C.1a

54 F 22.1 Btu/lbmwater water wT T h

Example

15

CQ

1 3

water

HQ

2

1

1

1

90 F50%

5000 cfm

T

V

3 68 FT

2 1 15 RdpT T T

1 90 FT

2 15°F 69 15 F 54°FdpT T

1 50%

2

#

1 38.4 Btu/lbmah

#

2 22.5 Btu/lbmah

121 0.0152

69 FdpT

2 3 0.0089 3

#

3 26.0 Btu/lbmah

3 61%

3 68 FT

3

1 14.19 ft /lbmav

2Table C.1a

54 F 22.1 Btu/lbmwater water wT T h

The condensate flow is determined

by conservation of mass around

the cooling section,

2 1

1 2

1 2

w water w

water w w

a a a

m m m

m m m

m m m

1 2

lbm lbm lbm21141.6 0.0152 0.0089 133.2

hr lbm hr

water a

a w wwater

a

m m

m

3

3

Table C.1a

lbm ft hr gal133.2 0.01605 0.267 gpm

hr lbm 60 min 0.13368 ft

wwater w wV m v

Example

16

CQ

1 3

water

HQ

2

1

1

1

90 F50%

5000 cfm

T

V

3 68 FT

2 1 15 RdpT T T

1 90 FT

2 15°F 69 15 F 54°FdpT T

1 50%

2

#

1 38.4 Btu/lbmah

#

2 22.5 Btu/lbmah

121 0.0152

69 FdpT

2 3 0.0089 3

#

3 26.0 Btu/lbmah

3 61%

3 68 FT

3

1 14.19 ft /lbmav

2Table C.1a

54 F 22.1 Btu/lbmwater water wT T h

The relative humidity leaving the

heating section can be read from

the psychrometric chart,

3 61%

Heating section analysis …

# #

3 2H aQ m h h

lbm Btu Btu

21141.6 26.0 22.5 73,996hr lbm hr

aH

a

Q

Example

17

CQ

1 3

water

HQ

2

1

1

1

90 F50%

5000 cfm

T

V

3 68 FT

2 1 15 RdpT T T

1 90 FT

2 15°F 69 15 F 54°FdpT T

1 50%

2

#

1 38.4 Btu/lbmah

#

2 22.5 Btu/lbmah

121 0.0152

69 FdpT

2 3 0.0089 3

#

3 26.0 Btu/lbmah

3 61%

3 68 FT

3

1 14.19 ft /lbmav

2Table C.1a

54 F 22.1 Btu/lbmwater water wT T h

EES Solution (Key Variables)

These are a bit different due to reading the psychrometric chart