Heat Gains - Calculations - Page 1 2 3 4 5


Calculating Heat Gains

 

 

The load on an air-conditioning system can be divided into the following sections:

 

            1.        Sensible Transmission through glass.

            2.        Solar Gain through glass.

3.           Internal Heat gains

            4.        Heat gain through walls. 

            5.        Heat gain through roof.  

            6.        Ventilation and/ or infiltration gains.

 

The heat gain through the glass windows is divided into two parts since there is a heat gain due to temperature difference between outside and inside and another gain due to solar radiation shining through windows.

 

The method adopted uses the CIBSE guide A (2006) and CIBSE Guide J (2002) .

The Tables that are referred to are CIBSE guide A (2006) Solar cooling loads in Tables 5.19 to 5.24.

CIBSE Guide J (2002) Air and Sol-air temperatures in Table 5.36 (London), Table 5.37 (Manchester) and Table 5.38 (Edinburgh)

This set of Tables is in Appendix A6 at the end of the guide. Table 5.36 (London) starts at page A6-121.

If internal gains are to estimated then CIBSE Guide A (2006) Table 6.4 to 6.17 are also required.

It would be helpful to have these Tables close by, to complete the calculations.

An example of a heat gain claculation is given in CIBSE Guide A (2006) section 5.8.2 example 5.3.

 

Heat gains through solid ground floors are minimal and can be neglected.

 

1.0 Sensible Transmission Through Glass

 

This is the Solar Gain due to differences between inside and outside temperatures. In very warm countries this can be quite significant.

This gain only applies to materials of negligible thermal capacity  i.e. glass.

 

 

                   Qg     =        Ag . Ug (to- tr)                                            ........ eqn. 1

 

Where;

                        Qg       =          Sensible heat gain through glass (W)

                        Ag        =          Surface area of glass (m2)

                        Ug        =          'U' value for glass  (W/m2 oC)  (see CIBSE guide A (2006)  Table 3.23 to 3.32).

                        to         =          outside air temperature (oC). Can be obtained from CIBSE Guide J (2002) - Tables 5.36 to 5.38 for various months and times in the day.

                        tr          =          room air temperature (oC)

 

2.0 Solar Gain Through Windows

 

This gain is when the sun shines though windows.

The cooling loads per metre squared window area have been tabulated in CIBSE guide A (2006) Tables 5.19 to 5.24 for various; locations, times, dates and orientations.

These figures are then multiplied by correction factors for; shading and air node correction factor.

Heat load is found from;

 

                        Qsg    =        Fc . Fs . qsg . Ag                                                     ........ eqn. 2

 

where              Qsg      =          Actual cooling load (W)

qsg      =          Tabulated cooling load from CIBSE Guide A (2006) Table 5.19 to 5.24  (W/m2)

Fc         =          Air node correction factor from Table below.

Fs         =          Shading factor from Table below.

Ag         =          Area of glass   (m2)

 

The Air point control factors (Fc) and Shading factors (Fs) are given in the Table below for various types of glass, building weights and for open and closed blinds.

 

Air node correction factors (Fc)

 

Building Weight

Single Glazing

Double glazing

Horizontal blind

Horizontal blind

Light

0.91

0.91

Heavy

0.83

0.90

Shading factors (Fs)

Type of glass

Building Weight

Single Glazing

Double glazing

 

Open horizontal blind

Closed horizontal blind

Open horizontal blind

Closed horizontal blind

Clear 6mm

Light

1.00

0.77

0.95

0.74

Heavy

0.97

0.77

0.94

0.76

Bronze tinted 6mm

Light

0.86

0.77

0.66

0.55

Heavy

0.85

0.77

0.66

0.57

Bronze tinted 10mm

Light

0.78

0.73

0.54

0.47

Heavy

0.77

0.73

0.53

0.48

Reflecting

Light

0.64

0.57

0.48

0.41

Heavy

0.62

0.57

0.47

0.41

 

The CIBSE guide method of calculating solar gains through glazing  in Guide A (2006), section 5.8.1.1 uses a slightly different formula as follows;

Qsg    =        S . qsg . Ag                                                  

 

where              Qsg      =          Actual cooling load (W)

qsg      =          Tabulated cooling load from CIBSE Guide A (2006) Table 5.19 to 5.24  (W/m2)

S          =          Mean solar gain factor at the environmental node or air node from CIBSE Guide A (2006) Table 5.7.

Ag         =          Area of glass   (m2)

3.0 Internal Heat Gains - CIBSE Guide A (2006)

 

Internal gains can account for most heat gain in buildings in the U.K.

These gains are from occupants, lights, equipment and machinery, as detailed below.

OCCUPANTS - Sensible and latent heat gains can be obtained from CIBSE Guide A (2006) - Table 6.3.

Typical gains are shown below.

 

 

 

Conditions

Typical building

Sensible Heat Gain (Watts)

Latent Heat Gain (Watts)

Seated very light work

Offices, hotels, apartments

70

45

Moderate office work

Offices, hotels, apartments

75

55

Standing, light work; walking

Department store, retail store

75

55

Walking standing

Bank

75

70

Sedentary work

Restaurant

80

80

Light bench work

Factory

80

140

Athletics

Gymnasium

210

315

 

 

 

LIGHTING – Average power density from CIBSE Guide A (2006) - Tables 6.4.

 

ELECTRICAL  EQUIPMENT - PC’s and Monitors - CIBSE Guide A (2006) - Tables 6.7 and 6.8.

Laser Printers and Photocopiers - CIBSE Guide A (2006) - Tables 6.9 and 6.10

Electric Motors – CIBSE Guide A (2006) - Table 6.13 and 6.14.

Lift Motors – CIBSE Guide A (2006) - Table 6.15.

Cooking equipment – CIBSE Guide A (2006) - Table 6.17.

 

Heat load is found from;

 

Q int.   =          Heat from Occupants   +    Heat from Lighting   +   Heat from Electrical Equipment  +  Heat from Cooking

 

 

4.0  Heat Gain Through Walls

 

This is the unsteady-state heat flow through a wall due to the varying intensity of solar radiation on the outer surface.

 

4.1  Sol-Air Temperature

 

In the calculation of this heat flow use is made of the concept of sol-air temperature, which is  defined as;

 

the value of the outside air temperature which would, in the absence of all radiation exchanges, give the same rate of heat flow into the outer surface of the wall as the actual combination of temperature difference and radiation exchanges.

 

SOL-AIR TEMP,                                                                    

 


          teo     =        ta  +  (                                               )                  ........ eqn. 4.1

 

 

where 

                        teo      =          sol-air temperature (oC)

                        ta         =          outside air temperature (oC)

                        a         =          absorption coefficient of surface

                        I          =          intensity of direct solar radiation on a surface at right angles to the rays of the sun. (W/m2)

                        a          =          solar altitude (degrees)

                        n          =          wall-solar azimuth angle (degrees)

                        Is        =          intensity of scattered radiation normal to a surface (W/m2)

                        hso      =          external surface heat transfer coefficient (W/m2oC)

 

 

The U.K. values of sol-air temperature are found from CIBSE Guide J (2002) Table 5.36 (London), Table 5.37 (Manchester) and Table 5.38 (Edinburgh).

Table 5.36 (London) starts at page A6-121.

 

 

4.2  Thermal Capacity

 

The heat flow through a wall is complicated by the presence of thermal capacity, so that some of the heat passing through it is stored, being released at a later time.

 

Thick heavy walls with a high thermal capacity will damp temperature swings considerably, whereas thin light walls with a small thermal capacity will have little damping effect, and fluctuations in outside surface temperature will be apparent almost immediately.

 

The thermal capacity will not affect the daily mean solar gain but will affect the solar gain at a particular time.

The particular time q of a solar gain is normally the time of the maximum gain.

The heat gain arrives at the inside of a thick wall some time after the sun hits the outside surface of the wall.

This time lag is f.

 

The calculation is, therefore, again split into two components.

1. Mean gain through wall,

 

                   Qq     =        A . U ( tem  -  tr)                                          ........ eqn. 4.2

 

where,             Qq        =          heat gain through wall at time q

                        A          =          area of wall (m2)

                        U          =          overall thermal transmittance  (W/m2 oC) (See Thermal Transmission in Science section of the notes) or (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

                        tem      =          24 hour mean sol-air temperature (oC) CIBSE Guide J (2002) - Table 5.36 to 5.38.

                        tr          =          constant dry resultant temperature (oC). In practice room dry bulb is used.

 

2. The variation from the mean solar gain is subject to both a decrement factor and time lag.

 

                        Qf     =        f ( teo  -  tem)                                                         ........ eqn. 4.3

 

where              Qf       =          Heat gain through wall at time (q - f)

                        f          =          time lag in hours (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

                        teo       =          sol-air temperature at time (q - f) (oC) CIBSE Guide J (2002) - Table 5.36 to 5.38.

                        tem      =          24 hour mean sol-air temperature (oC) CIBSE Guide J (2002) - Table 5.36 to 5.38.

                        f           =          decrement factor (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

 

Therefore the Solar Gain through a wall at time ( q - f) is;

 

 

                   Qq+f  =        A . U [( tem  -  tr)   + f ( teo  -  tem)]                 ........ eqn. 4.4

 

where,             Qq+f     =          heat gain through wall at time q+f (Watts)

                        f          =          time lag in hours (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

                        A          =          area of wall (m2)

                        U          =          overall thermal transmittance  (W/m2 oC) (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

                        tem      =          24 hour mean sol-air temperature (oC) CIBSE Guide J (2002) - Table 5.36 to 5.38.

                        tr          =          constant dry resultant temperature (oC) In practice room dry bulb is used.

                        f           =          decrement factor (see CIBSE guide A (2006)  Table 3.49 to 3.55) for typical wall constructions.

teo       =          Sol-air temperature at time (q - f) (oC) CIBSE Guide J (2002) - Table 5.36 to 5.38

 

 

5.0  Heat Gain Through Roof

 

 

The heat gain through a roof uses the same equation as for a wall as shown below.

 

 

          Q q+f Roof  =       A U [( tem  -  tr)  +  f ( teo  -  tem)]            ........ eqn. 5

6.0 Ventilation and/or Infiltration Gains

 

Heat load is found from;

 

                   Qsi    =        n  . V  (to- tr)  /  3                                       ........ eqn. 6

 

where              Qsi       =          Sensible heat gain (W)

                        n          =          number of air changes per hour (h-1) (see note below)

                        V          =          volume of room   (m3)

                        to         =          outside air temperature (oC) Can be obtained from CIBSE Guide J (2002) - Tables 5.36 to 5.38 for various months and times in the day.

                        tr          =          room air temperature (oC)

 

Infiltration gains should be added to the room heat gains.

Recommended infiltration rates are 1/2 air change per hour for most air-conditioning cases or 1/4 air change per hour for double glazing or if special measures have been taken to prevent infiltration.

 

Ventilation or fresh air supply loads can be added to either the room or central plant loads but should only be accounted for once.

 

Total Room Load From Heat Gains

 

Q total     =         Qg    +    Qsg      +    Qint.   +    Qq+fWall    +    Q q+f Roof    +    Qsi    

 

 

Q total           =          Ag . Ug (to  -  tr)                                          1. Sensible Glass

 

+          Fc . Fs . qsg . Ag                                          2. Solar Glass.

 

+          Qint.                                                               3. Internal

 

                        +          A.U [( tem  -  tr)  +  f ( teo  -  tem)]         4. Walls

           

+          A.U [( tem  -  tr)  +  f ( teo  -  tem)]         5. Roof         

                       

                        +          n  . V  (to  -  tr)   /  3                                    6. Ventilation

 

                                                                                                            ........ eqn. 7

 

 

In the majority of cases, by far the greatest external fluctuating component is the solar heat gain through the windows.

Therefore, it will be this gain which determines when the total heat gain to the room is a maximum.

 

Heat gains may be calculated and displayed in table form as shown below.

 

Heat Gain from

Watts

%

1. Sensible transmission through glass

 

 

2. Solar gain through glass

 

 

3. Internal

 

 

4. External walls

 

 

5. Roof

 

 

6. Ventilation

 

 

                                              Total

 

100%

Heat gain per m2 floor area  =

 

Heat gain per m3 space   =

 

Latent Gains

Latent heat gains are calculated so that the Total heat gain can be determined to complete a psychrometric chart.

Total heat gain   =    Sensible heat gain  +  Latent heat gains

Also Latent heat gains are required to size Chillers.

 

Latent heat gains are comprised of latent gain from occupants and from natural infiltration fresh air.

Latent heat gains from occupants can be obtained from CIBSE Guide A (2006) - Table 6.3 shown above.

 

The following formula gives the infiltration latent heat gain.

 

Qli      =        0.8 .  n .  V  ( mso –msr )

 

Where;

Qli        =          Infiltration latent heat gain (W)

n          =          Number of air changes per hour (h-1)

V          =          Room volume (m3)

mso       =          Moisture content of outside air (g/kg d.a.) from psychrometric chart.

msr       =          Moisture content of room air (g/kg d.a.) from psychrometric chart.

 

 

 


Heat Gains - Calculations -Page 1 2 3 4 5