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4 Cooling Load Calculation

4.1 Space Heat Gain and Space Cooling Load

Space heat gain is the rate at which heat enters a space, or heat generated within a spaceduring a time interval.

Space cooling load is the rate at which heat is removed from the conditioned space to maintaina constant space air temperature.

Figure 3 shows the difference between the space heat gain and the space cooling load. The

difference between the space heat gain and the space cooling load is due to the storage of aportion of radiant heat in the structure. The convective component is converted to spacecooling load instantaneously.

???

Figure 3 Differences between Space Heat Gain and Space Cooling Load


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1 Thermal Control

The thermal system of a building is described in Figure 1. The main heat flow quantities arelisted as follows:

Qi = Internal heat gain from electric lights, people, power equipment and appliances.

Qs = Solar heat gain through fenestration areas and, conduction heat gain through roofs andexternal walls by using the sol-air temperature.

Qc = Conduction heat gain or heat loss through the enclosing elements, caused by atemperature difference between outside and inside.

Qv = Ventilation heat gain or heat loss due to natural or mechanical ventilation and infiltration.

Qm = Mechanical heating or cooling produced by some energy-based installation.

Qe = Latent heat gain or loss from moisture transfer through permeable building materials.

(1)


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If Eqn. (1) = 0, a thermal balance exists. If Eqn. (1) > 0, the indoor temperature increases. IfEqn. (1) < 0, the indoor temperature decreases. Except Qm which is quite small, net value ofall heat flow quantities in Eqn. (1) determines the requirement ofSPACE HEATING ANDCOOLING.

Figure 1 Thermal System of Building Figure 2 Outdoor Dry-bulb and Wet-bulb


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Temperature Curves for A Typically Hot

2 Design Conditions


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In principle, the heating and cooling loads are calculated to maintain the indoor designconditions when the outdoor weather data do not exceed the design values.

2.1 Outdoor Design Conditions

It is not economical to choose either the annual maximum or annual minimum values of theoutdoor weather data in determining the outdoor conditions. The outdoor design data isusually determined according to the statistical analysis of the weather data so that 1 to 5% ofthe total possible operating hours is equalled or exceeded the outdoor design values.

2.1.1 Summer Design Condition

The recommended summer design and coincident wet bulb temperature, when chosen asbeing equalled to or exceeded by 2.5% of the total number of hours (i.e. 2928 hours) in June,

July, August and September, are

(i) 23 oC dry bulb temperature, and

(ii) 28 oC wet bulb temperature

Figure 2 shows the outdoor dry bulb temperature and wet bulb temperature curves for atypically hot summer day in Hong Kong. Usually the maximum temperature of 33 oC occurs at2 p.m. and the minimum temperature of 28 oC occurs just before sunrise. The daily range ofdry bulb temperature is about 5 to 6 oC, and the daily mean dry bulb temperature is 30.5 oC.


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2.1.2 Winter Design Condition

The recommended winter design and coincident relative humidity, when chosen as beingequalled to or exceeded by 1% or 2.5% of the total number of hours (i.e. 2160 hours) inDecember, January and February, are

(i) 9 oC dry bulb temperature, and

(ii) 50% relative humidity

Minimum temperature occurs at 6 a.m. or 7 a.m. before sunrise and the daily range is about 6to 8 oC during very cold winter days.

2.2 Indoor Design Conditions


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For most of the comfort air-conditioning systems used in the commercial and public buildings,the recommended indoor temperature and relative humidity are as follows:

(i) Summer: 23.5 - 25.5 oC dry bulb temperature, 40 - 60 % relative humidity

(ii) Winter: 21 - 23.5 oC dry bulb temperature, 20 - 30 % relative humidity


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3 Heating Load CalculationThe heat loss is divided into two groups:

(i) the heat transmission losses through the confining walls, floor, ceiling, glass, or othersurfaces, and

(ii) the infiltration losses through cracks and openings, or heat required to warm outdoor air

used for ventilation.

As a basis for design, the most unfavourable but economical combination of temperature andwind speed is chosen. The wind speed has great effect on high infiltration loss and on outsidesurface resistance in conduction heat transfer.

Normally, the heating load is estimated for winter design temperature usually occurring atnight, therefore, internal heat gain is neglected except for theaters, assembly halls, industrialplant and commercial buildings. Internal heat gain is the sensible and latent heat emittedwithin an internal space by the occupants, lighting, electric motors, electronic equipment, etc.

3.1 Heat Transmission Loss

Heat loss by conduction and convection heat transfer through any surface is given by:


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(2)

where Q = heat transfer through walls, roof, glass, etc.

A = surface areas

U = air-to-air heat transfer coefficient

Ti = indoor air temperature

To = outdoor air temperature

Heat transfer through basement walls and floors to the ground depends on:

(i) difference between room air temperature and ground temperature/outdoor air temperature,

(ii) materials of walls and floor of the basement, and

(iii) conductivity of the surrounding earth.

These portion of heat transmission is neglected in Hong Kong because of the fact that the

weather in winter is not so severe and the values are very small in comparison with otherforms of heat transmission.

3.2 Infiltration and Ventilation Loss


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The heat loss due to infiltration and controlled natural ventilation is divided into sensible andlatent losses.

3.2.1 Sensible Heat Loss, Qsb

The energy associated with having to raise the temperature of infiltrating or ventilating air upto indoor air temperature is the sensible heat loss which is estimated by:

(3)

where r = air density

V = volumetric air flow rate

Cpa = specific heat capacity of air at constant pressure


To = outdoor air temperature

3.2.2 Latent Heat Loss, Qla


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The energy quantity associated with net loss of moisture from the space is latent heat losswhich is given by:

(4)

where r = air density

V = volumetric air flow rate

wi = humidity ratio of indoor air

wo = humidity ratio of outdoor air

hfg = latent heat of evaporation at indoor air temperature


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Cooling Load Calculation

4.1 Space Heat Gain and Space Cooling Load

Space heat gain is the rate at which heat enters a space, or heat generated within a spaceduring a time interval.

Space cooling load is the rate at which heat is removed from the conditioned space to maintaina constant space air temperature.

Figure 3 shows the difference between the space heat gain and the space cooling load. Thedifference between the space heat gain and the space cooling load is due to the storage of aportion of radiant heat in the structure. The convective component is converted to space

cooling load instantaneously.

???


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Figure 3 Differences between Space Heat Gain and Space Cooling Load

4.2 Cooling Load Temperature Difference (CLTD) and Cooling Load Factor (CLF)

Cooling load temperature difference and cooling load factor are used to convert the space sensible heatgain to space sensible cooling load.

4.2.1 Cooling Load Temperature Difference

The space sensible cooling load Qrs is calculated as:

(5)

where A = area of external wall or roof

U = overall heat transfer coefficient of the external wall or roof.

CLTD values are found from tables, as shown in Tables 1 and 2, which are designed for fixed conditions ofoutdoor/indoor temperatures, latitudes, etc. Corrections and adjustments are made if the conditions aredifferent.


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4.2.2 Cooling Load Factor

The cooling load factor is defined as:

(6)

CLF is used to determine solar loads or internal loads. Some CLF values are shown in Table 3.

Table 1 Cooling Load Temperature Difference for Conduction through Window Glass

Solar time, hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

CLTD,oC 1 0 -1 -1 -1 -1 -1 0 1 2 4 5 7 7 8 8 7 7 6 4 3 2 2 1

The values are calculated for an inside temperature (Ti) of 25.5oC and outdoor daily mean temperature (Tom) of 29.4oC.

Correct CLTD = CLTD + (25.5 - Ti) + (Tom - 29.4)

Table 2 Cooling Load Temperature Difference (40 degree North Latitude in July) for Roof

and External Walls (Dark)


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Solar time, hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Roof 14 12 10 8 7 5 4 4 6 8 11 15 18 22 25 28 29 30 29 27 24 21 19 16

External wall

North

North-east

East

South-east

South

South-west

West

North-west

8

9

11

11

11

15

17

14

7

8

10

10

10

14

15

12

7

7

8

9

8

12

13

11

6

6

7

7

7

10

12

9

5

5

6

6

6

9

10

8

4

5

5

5

5

8

9

7

3

4

5

5

4

6

7

6

3

4

5

5

4

5

6

5

3

6

7

5

3

5

5

4

3

8

10

7

3

4

5

4

4

10

13

10

4

4

5

4

4

11

15

12

5

5

5

4

5

12

17

14

7

5

6

5

6

13

18

16

9

7

6

6

6

13

18

17

11

9

8

7

7

13

18

18

13

12

10

8

8

14

18

18

15

15

12

10

9

14

18

18

16

18

17

12

10

14

17

17

16

20

10

15

11

13

17

17

16

21

11

17

11

13

16

16

15

21

12

18

10

12

15

15

14

20

11

17

10

11

13

14

13

19

11

16

9

10

12

12

12

17

19

15

The values are calculated for an inside temperature of 25.5oC and outdoor daily mean temperature of 29.4oC.

Correction values for 22 degree north latitude in July are as follows:

Roof: +0.4oC

Wall: N NE E SE S SW W NW

+1.8oC +1.5oC -0.4oC -2.3oC -3.6oC -2.3oC -0.4oC +1.5oC

Table 3 Cooling Load Factor for Window Glass with Indoor Shading Devices

(North Latitude and All Room Construction)


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Solar time,

hour

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Orientation:

North

North-east

East

South-east

South

South-west

West

North-west

Horizontal

0.08

0.03

0.03

0.03

0.04

0.05

0.05

0.05

0.06

0.07

0.02

0.02

0.03

0.04

0.05

0.05

0.04

0.05

0.06

0.02

0.02

0.02

0.03

0.04

0.04

0.04

0.04

0.06

0.02

0.02

0.02

0.03

0.04

0.04

0.03

0.04

0.07

0.02

0.02

0.02

0.03

0.03

0.03

0.03

0.03

0.73

0.56

0.47

0.30

0.09

0.07

0.06

0.07

0.12

0.66

0.76

0.72

0.57

0.16

0.11

0.09

0.11

0.27

0.65

0.74

0.80

0.74

0.23

0.14

0.11

0.14

0.44

0.73

0.58

0.76

0.81

0.38

0.16

0.13

0.17

0.59

0.80

0.37

0.62

0.79

0.58

0.19

0.15

0.19

0.72

0.86

0.29

0.41

0.68

0.75

0.22

0.16

0.20

0.81

0.89

0.27

0.27

0.49

0.83

0.38

0.17

0.21

0.85

0.89

0.26

0.24

0.33

0.80

0.59

0.31

0.22

0.85

0.86

0.24

0.22

0.28

0.68

0.75

0.53

0.30

0.81

0.82

0.22

0.20

0.25

0.50

0.81

0.72

0.52

0.71

0.75

0.20

0.17

0.22

0.35

0.81

0.82

0.73

0.58

0.78

0.16

0.14

0.18

0.27

0.69

0.81

0.82

0.42

0.91

0.12

0.11

0.13

0.19

0.45

0.61

0.69

0.25

0.24

0.06

0.06

0.08

0.11

0.16

0.16

0.16

0.14

0.18

0.05

0.05

0.07

0.09

0.12

0.12

0.12

0.12

0.15

0.04

0.05

0.06

0.08

0.10

0.10

0.10

0.10

0.13

0.04

0.04

0.05

0.07

0.09

0.08

0.08

0.08

0.11

0.03

0.03

0.04

0.06

0.07

0.07

0.07

0.07

0.10

0.03

0.03

0.04

0.05

0.06

0.06

0.06

0.06

4.3 Space Cooling Loads

Space cooling load is classified into three categories:

4.3.1 External Cooling Loads

External cooling loads have the following components:


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4.3.1.1 Solar Heat Gain through Fenestration Areas, Qfes

(7)

where As = unshaded area of window glass

Ash = shaded area of window glass

max. SHGFsh = maximum solar heat gain factor for the shaded area on window glass (Table 4)

max. SHGF = maximum solar heat gain factor for window glass (Table 5)

SC = shading coefficient (Table 6)

The corresponding space cooling load Qfs is:

(8)

Table 4 Maximum Solar Heat Gain Factor of Shaded Area

Month Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

SHGFsh, W/m2 98 107 114 126 137 142 142 133 117 107 101 95


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Table 5 Maximum Solar Heat Gain Factor for Sunit Glass on Average Cloudness Days

Month Maximum solar heat gain factor for 22 degree north latitude, W/m2

North North-east /

north-west

East / west South-east /

south-west-

South Horizontal

January.

February.

March.

April

May

June

July

August

September

October

November

December

88

97

107

119

142

180

147

123

112

100

88

84

140

265

404

513

572

589

565

502

388

262

142

101

617

704

743

719

687

666

671

694

705

676

606

579

789

759

663

516

404

355

391

496

639

735

786

790

696

578

398

210

139

134

140

223

392

563

686

730

704

808

882

899

892

880

877

879

854

792

699

657


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Table 6 Shading Coefficient for Window Glasses with Indoor Shading Devices

Windowglass

Nominal

thickness,

mm

Solartransmission

Shading coefficient

Venetian Roller shade, opaque Draperies, light colour

Medium Light Dark White Openb Closedb

Clear 3 - 12 0.78 - 0.79 0.64 0.55 0.59 0.25 0.65 0.45

Heat-absorbing

5 - 6 0.46 0.57 0.53 0.45 0.30 0.49 0.38

Heat-absorbing

10 0.34 0.54 0.52 0.40 0.28

Reflectivecoated

SCa=0.30

SCa=0.40

SCa=0.50

SCa=0.60

0.25

0.33

0.42

0.50

0.23

0.29

0.38

0.44

0.23

0.33

0.41

0.49

0.21

0.28

0.34

0.38

Insulatingglass:

Clear out- 6 0.80 0.57 0.51 0.60 0.25 0.56 0.42


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clear in

SCa=0.84

Heat

absorbingout-clearin

SCa=0.55

6 0.56 0.39 0.36 0.40 0.22 0.43 0.35

Reflective

SCa=0.20

SCa=0.30

SCa=0.40

6

0.80

0.19

0.27

0.34

0.18

0.26

0.33

0.18

0.27

0.36

0.16

0.25

0.29

a Shading coefficient with no shading device.

b Open weave means 40% openness, and closed weave indicate 3% openness.

Table 7 Overall Heat Transfer Coefficient for Window Glasses

Window Glass Overall heat transfer coefficient, W/m2K

Summer (outdoor wind velocity = 3.33m/s) Winter (outdoor wind velocity = 6.67m/s)

3 mm

thickness

5 mm

thickness

6 mm

thickness

12 mm

thickness

3 mm

thickness

5 mm

thickness

6 mm

thickness

12 mm

thickness


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Single-glazed

Reflective

Double-glazed 6mm airspace

Double glazed 12mm airspace

5.4

3.2

2.8

5.2

3.0

2.7

5.0

4.7

2.9

2.6

4.3 6.1

3.1

2.7

5.7

2.9

2.6

5.4

5.0

2.8

2.4

4.6

4.3.1.2 Conduction Heat Gain through Fenestration Areas, Qfe

The space cooling load due to the conduction heat gain through fenestration area is calculated as:

(9)

where A = fenestration area

U = overall heat transfer coefficient for window glass (Table 7)

CLTD = cooling load temperature difference (Table 1)

4.3.1.3 Conduction Heat Gain through Roofs (Qrs) and External Walls (Qws)

The space cooling load due to the conduction heat gain through roofs or external walls is calculated as:

(10)


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where A = area for external walls or roofs

U = overall heat transfer coefficient for external walls or roof

CLTD = cooling load temperature difference (Table 2)

4.3.1.4 Conduction Heat Gain through Interior Partitions, Ceilings and Floors, Qic

The space cooling load due to the conduction heat gain through interior partitions, ceilings and floors iscalculated as:

(11)

where A = area for interior partitions, ceilings or floors

U = overall heat transfer coefficient for interior partitions, ceilings or floors

Tb = average air temperature of the adjacent area


4.3.2 Internal Cooling Loads

4.3.2.1 Electric Lighting

Space cooling load due to the heat gain from electric lights is often the major component for commercialbuildings having a larger ratio of interior zone. Electric lights contribute to sensible load only. Sensible heatreleased from electric lights is in two forms:


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(i) convective heat from the lamp, tube and fixtures.

(ii) radiation absorbed by walls, floors, and furniture and convected by the ambient air after a time lag.

The sensible heat released (Qles) from electric lights is calculated as:

(12)

where Input = total light wattage obtained from the ratings of all fixtures installed

Fuse = use factor defined as the ratio of wattage in use possibly at design condition to the installationcondition

Fal = special allowance factor for fluorescent fixtures accounting for ballast loss, varying from 1.18 to 1.30

The corresponding sensible space cooling load (Qls) due to heat released from electrical light is:

(13)

CLF is a function of

(i) number of hours that electric lights are switched on (for 24 hours continuous lighting, CLF = 1), and

(ii) types of building construction and furnishings.

Therefore, CLF depends on the magnitude of surface and the space air flow rates.


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4.3.2.2 People

Human beings release both sensible heat and latent heat to the conditioned space when they stay in it.The space sensible (Qps) and latent (Qpl) cooling loads for people staying in a conditioned space arecalculated as:

(14)

(15)

where n = number of people in the conditioned space

SHG = sensible heat gain per person (Table 8)

LHG = latent heat gain per person (Table 8)

Adjusted values for total heat shown in Table 8 is for normal percentage of men, women and children ofwhich heat released from adult female is 85% of adult male, and that from child is 75%.

CLF for people is a function of

(i) the time people spending in the conditioned space, and

(ii) the time elapsed since first entering.

CLF is equal to 1 if the space temperature is not maintained constant during the 24-hour period.

Table 8 Heat Gain from Occupants at Various Activities (At Indoor Air Temperature of 25.5 oC)


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Activity Total heat, W Sensible heat, W Latent heat, W

Adult, male Adjusted

Seated at rest

Seated, very light work, writing

Seated, eating

Seated, light work, typing,

Standing, light work or walking slowly,

Light bench work

Light machine work

Heavy work

Moderate dancing

Athletics

115

140

150

185

235

255

305

470

400

585

100

120

170b

150

185

230

305

470

375

525

60

65

75

75

90

100

100

165

120

185

40

55

95

75

95

130

205

305

255

340

b Adjusted for latent heat of 17.6W person released from food.

4.3.2.3 Power Equipment and Appliances


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In estimating a cooling load, heat gain from all heat-producing equipment and appliances must be takeninto account because they may contribute to either sensible or latent loads, and sometimes both. Theestimation is not discussed in this lecture note. For more information, Chapter 26 of ASHARE Handbook -1993 Fundamentals can be referred.

4.3.3 Loads from Infiltration and Ventilation

Infiltration load is a space cooling load due to the infiltrated air flowing through cracks and openings andentering into a conditioned room under a pressure difference across the building envelope. Theintroduction of outdoor ventilation air must be considered in combination with the infiltrated air. Table 9shows the summer outdoor design dry bulb and wet bulb temperatures at 22 degree north latitude.

Infiltration and ventilation loads consist of both sensible and latent cooling loads. Eqns (3) and (4) are validto estimate the sensible and latent cooling loads respectively.

Table 9 Summer Outdoor Design Dry Bulb And Wet Bulb Temperatures At 22 Degree North Latitude

Solar time,hour

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Dry bulbtemp. oC

28.4 28.3 28.2 28.1 28.0 28.0 28.2 29.0 29.9 30.8 31.8 32.2 32.8 33.0 32.7 32.5 31.8 31.1 30.4 29.7 29.1 28.8 28.6 28.4

Wet bulbtemp. oC

25.8 25.7 25.7 25.6 25.6 25.5 25.7 26.4 26.7 27.0 27.5 27.6 27.8 28.0 27.9 27.6 27.4 27.1 26.8 26.7 26.5 26.3 26.1 25.9


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