Business machines

In offices, the presence of personal computers with peripheral devices and the common­place use of other electrically energised equipment, gives a significant contribution to the sensible heat gains. Although power dissipations as high as 80 W m~2 have been quoted for dealers’ rooms in applications such as merchant bankers and stockbrokers offices, such figures are exceptional and are not representative of small power in ordinary offices. The actual rate of energy dissipation is generally less than the nameplate power on the items of equipment. Furthermore, machines are used intermittently and the power consumed when idling is less than when operating at full duty. The CIBSE Applications Manual AM7 (1992) gives useful details of suitable allowances for design purposes and quotes half-hour average powers in relation to nameplate powers.

Examples of some values are given in Table 7.17, based on an office total floor area of 583.2 m2 (see Figure 7.21) and using data from CIBSE AM7 (1992).

Table 7.17 Examples of powers for business machines. (For an office floor area of 583.2 m2) Item Nameplate power W Half-hour average power W 27 colour monitors 27 x 185 = 4995 27 x 120= 3240 27 local memories 27 x 30 = 810 27 x 30= 810 1 electrostatic plotter 1 x 960 = 960 1 X 557 = 557 25 dot matrix printers 25 x 400= 10000 25 x 58 = 1450 2 laser printers 2 x 1680 = 3360 2 x 824= 1648 2 fascimile machines 2 x 820 = 1640 2 x 260 = 520 2 electric typewriters 2 x 105= 210 2 x 53 = 106 1 photocopier 1 x 2400 = 2400 1 x 1259 = 1259 2 coffee machines 2 x 3000 = 6000 2 x 600= 1200 Totals (W) 30375 10790

18 modules x 2.4 m = 43.2 m <— 2.4 ♦-» 2.4 6.0 Corridor 1.5 Total floor area = 43.2 x 13.5 = 583.2 m2 6.0 < 48 » 9 modules x 4.8 m = 43.2 m « 48 » « 48 » ■«——— Fig. 7.21 A notional office plan area, used to establish the typical power dissipation from office Machines (Table 7.17).

From the above table the specific totals, per unit of floor area, are 52.1 W m“2 for nameplate powers and 18.5 W m-2 for half-hour averages. Note that, for the above example, the coffee machines make a very large contribution to the total nameplate power but a good deal less to the half-hour average. For other cases the figures would be different.

Diversity factors that may be applied to the nameplate power to represent the load on the air conditioning system for the whole building are difficult to establish with any certainty. From Table 7.17 the ratio of total half-hour average power to total nameplate power gives a value of 10790/30375 = 0.36. From CIBSE AM7( 1992) such ratios can be deduced and some are given in Table 7.18.

The variation in the values quoted depends on the assumptions made for the time that the machines are running or idling.

Table 7.18 Ratios of half-hour average powers to nameplate powers according to CIBSEAM7 (1992) Item Half-hour average power Nameplate power Monochrome visual display terminal 0.60 to 0.65 Colour visual display terminal 0.60 to 0.79 Personal computers (inc. monochrome monitors) 0.56 to 0.61 Personal computers (inc. colour monitors) 0.59 to 0.65 Mini computer work-stations 0.25 Small graphics plotter, plotting 0.71 Small graphics plotter, idling 0.31 Continuous roll electrostatic, plotting 0.81 Continuous roll electrostatic, idling 0.35 Dot matrix printer 0.15 Laser printer (desk mounted) 0.27 Laser printer (floor mounted) 0.49 Facsimile machine (large) 0.32 Facsimile machine (small) 0.19 Photocopier (large) 0.52 Photocopier (small) 0.28

Reproduced by kind permission of the CIBSE, from AM7 (1992). See also CIBSE Guide A2 (1999): Internal heat gains, 6.4.

A cautious conclusion is that a typical allowance for small power for business machines is from 10 W m-2 to 20 W m-2, in the absence of firmer information to the contrary. As regards a diversity factor to be applied when calculating the total maximum sensible heat gain for the whole building (in order to determine the size of refrigeration plant) a value of 0.65 to 0.70 seems reasonable. For the purpose of calculating the maximum sensible heat gain for a particular room or module (to determine the amount of supply air necessary or the size of air conditioning unit to select), a diversity factor of unity must be applied to the heat gain from business machines, people and electric lights.

EXAMPLE 7.18

The dimensions of a west-facing module in a lightweight building (150 kg m-2) are: 2.4 m width x 2.6 m floor-to-ceiling height x 6.0 m depth. The floor-to-floor height is 3.3 m. A double glazed, 6 mm clear glass window of 2.184 m2 area is in the only exterior wall. Rooms on the other five sides of the module are air conditioned to the same temperature. The building is at latitude 51.7°N, approximately, and the window is protected by internal Venetian blinds, assumed to be drawn by the occupants when the window is in direct sunlight. The [/-value of the window is 3.0 W m-2 K_1. The time lag of the wall is 5 h and its decrement factor is 0.65.

Outside state: 28°C dry-bulb, 19.5°C wet-bulb (sling), 10.65 g kg-1.

Room state: 22°C dry-bulb, 50 per cent saturation, 8.366 g kg-1.

(a) Making use of Tables 7.8, 7.9 and 7.10 calculate the sensible and latent heat gains at 1500 h sun-time in July. When calculating the heat gain through the wall use the floor-to-floor height for determining the wall area.

(b) Repeat the calculation of the sensible heat gain using the data from Tables 7.11 and 7.12 for the solar load through glass. Take a haze factor of 0.95 and a blind factor of 0.54 (Table 7.6).

(c) Repeat the calculation for the sensible heat gain using the data from Tables 7.13 and 7.14 for the solar load through glass.

(d) Repeat the calculation using the solar heat gain data in Table A9.15 in the CIBSE Guide A9 (1986).

(e) Compare the results.

Answer

(a) First the relevant sol-air temperatures must be established from Table 7.8 for the month of July and any necessary corrections made:

Design outside air temperature at 15.00 h sun time: 28°C

Tabulated outside air temperature at 15.00 h sun time: 25.3°C

Correction to be applied to tabulated value: +2.7 K

Time of heat gain to room: 15.00 h

Time lag of wall: 5 h

Time of relevant sol-air temperature 10.00 h

Tabulated sol-air temperature at 10.00 h 25.0°C

Correction: +2.7 K

Corrected sol-air temperature at 10.00 h 27.7°C

Tabulated 24 h mean sol-air temperature: 23.0°C

Correction: +2.7 K

Corrected 24 h mean sol-air temperature 25.7°C

Use the simplified equation (7.24) for the calculation of heat gain through the wall.

From Tables 7.9 and 7.10 the following is determined for a lightweight building with blinds closed (because the window is in direct sunlight), 12 h plant operation and air temperature control.

Solar air conditioning load through a west window at 15.00 h sun time in July: 205 WnT2. Correction factor for a double glazed, clear, plate glass window: 1.00.

Sensible heat gain calculation:

TOC o "1-5" h z Glass transmission (equation (7.17)): W

2.184 x 3.0 x (28-22)= 39

Wall (equation (7.24)):

(3.3 x 2.4 — 2.184) x 0.45R25.7 — 22) + 0.65(27.7 — 25.7)] = 13

Infiltration (equation (7.41)):

0.33 x 0.5 x (2.4 x 2.6 x 6.0)(28 — 22) = 37

Solar gain through glass:

2.184x 1.00×205 = 448

People: 2 x 90 = 180

Lights: 17 x 2.4 x 6.0 = 245

Business machines: 20 x 2.4 x 6.0 = 288

Sensible heat gain = 1250

Latent heat gains:

34 W 100 W 134 W

Infiltration by equation (7.42):

0. 8 x 0.5 x (2.4 x 2.6 x 6.0) x (10.65 — 8.366) = People: 2 x 50 =

Latent heat gain =

(,b) From Table 7.11: maximum solar intensity: 695 W From Table 7.12: storage load factor: 0.67 From Table 7.6 the shading coefficient: 0.54 Solar load: 0.95 x 0.54 x 0.67 x 695 = 239 W nT2 Total sensible heat gain from (a): 1250 W

802 W 522 W 1324 W

Solar gain through glass from (a): 448 W

Remaining other sensible gain: Solar gain: 2.184 x 239 =

Sensible heat gain:

(c)

,-2

From Table 7.13:

Solar cooling load (271 + 325)/2 = 298 W m“

From Table 7.14, the correction factor for shading is 0.95 and the air-point control factor (because the tabulated data are for the control of dry resultant temperature) is 0.91 Remaining other sensible gain: 802 W

1365 W

Solar gain: 2.184 x 298 x 0.95 x 0.91 563 W

Sensible gain:

(d) From CIBSE Table A9.15 (1986) the cooling load due to solar gain through glass is 270 W m-2, the shading factor is 0.74 and the air-point control factor is 0.91.

Remaining other sensible gain: 802 W

397 W 1199 W

Solar gain: 2.184 x 270 x 0.74 x 0.91 Sensible gain:

(e) Comparing the results:

	Sensible		Glass
	Gain		Solar gain
(d) Table A9.15 (CIBSE 1986)	1199 W	100%	397 W	100%
(a) Tables 7.9 and 7.10 (Haden Young)	1250 W	104%	448 W	113%
(b) Tables 7.11 and 7.12 (Carrier Air
Conditioning Company 1965)	1324 W	110%	522 W	131%
(c) Tables 7.13 and 7.14 (CIBSE A2 1999)	1365 W	113%	565 W	142%

Note that the approximate percentages of the components of the sensible gain to a typical office module are: glass transmission 3 per cent, wall transmission 1 per cent, infiltration 3 per cent, solar gain through glass 36 per cent, people 14 per cent, lights 20 per cent and business machines 23 per cent. It is also worth noting that the approximate specific sensible gain is about 80 to 90 W m-2, referred to the treated modular floor area.

The effects of changing the summer outside design state and the state maintained in the room are worth consideration. Tables 5.3 and 5.4 give details of the percentages of the hours in the summer that outside dry-bulbs and wet-bulbs were exceeded at Heathrow for the period 1976-95. If lower outside design temperatures are chosen the heat gains will be reduced but the chances of the air conditioning system not giving full satisfaction are increased. Similarly, raising the dry-bulb temperature maintained in the room, with the risk of less comfort, may be a consideration. Further, if the outside wet-bulb or the room enthalpy are altered there will be an effect on the fresh air load (see sections 8.1 and 8.2). All these matters have implications for comfort, the satisfaction of the client, capital costs and running costs. The benefits of any measure considered must be balanced against its disadvantages, by considering Table 5.3 or 5.4.

EXAMPLE 7.19

{a) Ignoring heat gains through the wall, which are trivially small, investigate the effect on the sensible heat gain of changing the outside and inside summer design states for the module used in example 7.18. Use Tables 7.9 and 7.10 for calculating the solar heat gains through glass.

Answer

The sensible heat gains from solar gain through glass, lights and business machines are unchanged at: 448 + 245 + 288 = 981 W. The sensible gain from people reduces and the latent gain increases as the room temperature rises (see Table 7.16). The sensible gain from infiltration reduces for a given room condition, as the outside dry-bulb goes down. The sensible heat gains are considered as follows.

Sensible heat gain:
	O 00 CN	27°	26‘
Tr	22°	22°	22‘
Glass	39	33	26
Infiltration	37	31	25
People	180	180	180
S + L + M	981	981	981
Total	1237	1225	1212

If we assume that the fresh air allowance is 1.4 litres s’1 m-2 over the modular floor area of 14.4 m2 the supply is 20.16 litres s-1 of fresh air with a specific volume, v, expressed at the room state. Assuming the room is at 50 per cent saturation, the latent heat gain by infiltration can be calculated by equation (7.42) and we can also calculate the fresh air load (see example 8.1) by means of equation (7.43):

Qfa = (vt/vt(h0 — hr))

Where <2fa is the fresh air load in kW, vt is the volumetric flow rate of fresh air at temperature

T in m3 s“1, vt is the specific volume of the fresh air at temperature t, h0 is the enthalpy of the outside air in kJ kg-1 and hr is the enthalpy of the room air in kJ kg“1.

The following table is compiled.

To (°C)	28	27	27	26	26
To (°C)	20	19	18	19	18
Tr (°C)	22	22	22	22	22
8o (g kg“1)	10.65	9.719	8.354	10.18	8.859
Gr (g kg“1)	8.366	8.366	8.366	8.366	8.366
People latent gain,	100	100	100	100	100
See Table 7.16 (W)
Infiltration latent gain,	34	20	0	27	7
See equation (7.42) (W)
People + infiltration	134	120	100	127	107
Latent gain (W)
H0 (kJ kg“1)	55.36	51.96	48.47	52.10	48.74
Hr (kJ kg“1)	43.39	43.39	43.39	43.39	43.39
Vr (m3 kg-1)	0.847	0.847	0.847	0.846	0.847
Fresh air load (see	285	204	121	207	127
Equation (7.43) and section 6.7) (W)
Sensible gain	1636	1537	1446	1530	1442

+ latent gain + fresh air load (W)

Interpreting the data in Table 5.3 is difficult. One way might be to use mid-values of the bands and the averages of the limits of the bands of dry-bulb and wet-bulb temperatures quoted:

For 28°C dry-bulb and 20°C wet-bulb the average is (0.77 + 0.32 + 0.31 + 0.25)/4 = 0.41 per cent of the four summer months, namely 12.0 hours. For 27°C dry-bulb and 19°C wet — bulb it is 0.77 per cent or 22.5 hours. For 27°C dry-bulb, 18°C wet-bulb it is (0.42 + 0.77)/

2 = 0.60 per cent or 17.6 hours. For 26°C dry-bulb and 19°C wet-bulb it is (1.32 + 0.77)/

2 = 1.04 per cent or 30.4 hours and for 26°C dry-bulb and 18°C wet-bulb it is (1.37 + 1.32 + 0.42 + 0.77)/4 = 0.97 per cent which is 28.4 hours. The results are summarised in the following table.

1. Dry-bulb	28°	27°	27°	26°	26°
2. Wet-bulb	20°	19°	18°	19°	18°
3. Per cent exceeded	0.41%	0.77%	0.60%	1.04%	0.97%
4. Hours exceeded	12.0 h	22.5 h	17.6 h	30.4 h	28.4 h
5. Sensible gain	100%	99%	99%	98%	98%
6. Latent gain	100%	95%	83%	97%	90%
7. Fresh air load	100%	72%	43%	73%	45%
8. Totals	1636 W	1537 W	1446 W	1530 W	1442 W
	100%	94%	88%	94%	88%

208 Heat gains from solar and other sources Conclusions

1. The sensible gains do not change very much and the reduction is probably within the accuracy of their calculation. Any effect they have is most likely to be on the size of the air handling plant and duct system, although this depends very much on the type of system adopted.

2. For the case of an outside state of 27° dry-bulb, 18° wet-bulb, the large drop in the latent gain to 83 per cent must be disregarded since this is entirely due to the reduction of the infiltration gain to zero, because the outside moisture content is less than the room moisture content. The allowance of half an air change per hour for infiltration is very much open to question and the reduction must be ignored.

The reduction of the latent gains to 95 per cent and 90 per cent for the cases of 21° dry — bulb, 19° wet-bulb and 26 per cent dry-bulb, 18° wet-bulb look interesting but the latent gains are a fairly small proportion of sensible plus latent gain, namely, about 10 per cent. Any benefit in reducing the capital or running cost is likely to be in the size of the refrigeration duty. The impact of the reduction in latent gains on this is smaller still, at about 7 per cent.

3. If, as an approximation, the cooling load is taken as the sum of the sensible gain, the latent gain and the fresh air load, we can see that this is probably the most significant factor. There is an established correlation between the cooling load and capital cost. The running cost is also likely to correlate although other factors, such as system choice and the quality of maintenance, intervene. It must be remembered that this example is based on the heat gains and cooling load for a single, west-facing module and diversity factors for people, lights, and business machines have not been considered, whereas they would be for an entire building. Neither has the natural diversity in the solar load through glazing, as the sun moves round the building during the day, been taken into account. Nevertheless, designing the system for an outside state of 27°C dry-bulb with 19°C wet-bulb (screen) gives a 6 per cent reduction in the cooling load (implying a 6 per cent reduction in capital cost). This is at the expense of a failure in apparant comfort satisfaction for 22.5 h in the four summer months. The decision is commercial and the client must be fully aware of the risks involved for the benefit obtained.

The view of the author is that, with global warming likely to become increasingly important over the next 20 years, prudence is to be recommended. Air conditioning systems are likely to be required to do more than they were initially designed for in the immediate future.

EXAMPLE 7.20

Using the modular details from example 7.18 calculate the sensible and latent heat gains at 1500 h sun time on 21 January, assuming the location to be Perth, Western Australia. Take the same values for heat gains from lights and business machines, assume two people present and half an air change of infiltration. The window is single glazed (U = 5.6 W mf2 K-1) and fitted with internal Venetian blinds. The latitude of Perth is 32°S. Make the following design assumptions:

Outside state: 35°C dry-bulb, 19.2°C wet-bulb (screen), 5.876 g kg’1, 50.29 kJ kg-1,

0. 8809 m3 kg’1.

Room state: 25°C dry-bulb, 40 per cent saturation, 8.063 g kg-1, 45.69 kJ kg-1.

The load due to sensible heat gain through single glass by solar radiation for a fast response building with internal blinds, used intermittently when the sun shines on the west face of the building, is 241 W m-1, based on data from the CIBSE Guide A2 (1999). This should be increased by 7 per cent because the earth-sun distance is 3.5 per cent less in December than in June and the intensity of solar radiation follows an inverse square law with respect to distance. See Table 7.4 and section 7.16.

Answer

First the relevant sol-air temperatures should be calculated. Sol-air temperature is given by equation (7.21). Using the results of example 7.4, equation (7.9) and the data in Tables 7.3 and 7.4, the calculation of the sol-air temperature at a particular time is possible, but calculating the heat gain by equation (7.24) requires a knowledge of the 24 hour mean sol — air temperature. This is not possible here, without detailed weather data, on an hourly basis, for January at Perth. However, the heat gain through a wall usually amounts to about

1 per cent of the whole (see example 7.18) and is ignored in this case.

TOC o "1-5" h z Sensible heat gain calculation: W

Glass: 2.184 x 5.6 x (35 -25) 122

Infiltration: 0.33 x 0.5 x (2.4 x 2.6 x 6.0) x (35 — 25) 62

Solar through glass: 2.184 x 241 x 1.07 563

People*: 2 x 75 150

Lights: 17 x 2.4 x 6.0 245

Business machines: 20 x 2.4 x 6.0 288

Total sensible gain 1430

*Refer to Table 7.16

Specific sensible gain per unit of floor area:

1430/14.4 = 99.3 W m“2 Latent heat gain calculation:

TOC o "1-5" h z Infiltration (equation (7.42)): W

0. 8 x 0.5 x 2.4 x 2.6 x 6.0(5.876 — 8.063) -33

People:

2 x 65 130

Total latent gain 97

Since any rate of natural infiltration is uncertain, it might be prudent to take the latent gain as 130 W. However, local custom should be considered as well as meteorological data (see section 5.11). There is an on-shore breeze from the Indian Ocean that often occurs in the afternoons during summer months in Perth, which reduces the dry-bulb temperature and increases the moisture content. This could make the assumed outside design state temporarily irrelevant. The contribution of any infiltration in the latent heat gain calculation would then be positive with the total latent gain exceeding 130 W.

Exercises

1. (a) Why do the instantaneous heat gains occurring when solar thermal radiation passes

Through glass not constitute an immediate increase on the load of the airconditioning plant? Explain what sort of effect on the load such instantaneous gains are likely to have in the long run.

(b) A single glass window in a wall facing 30° west of south is 2.4 m wide and 1.5 m high. If it is fitted flush with the outside surface of the wall, calculate the instantaneous heat gain due to direct solar thermal radiation, using the following data:

Intensity of direct radiation on a plane normal to

The sun’s rays 790 W rrf2

Altitude of the sun 60°

Azimuth of the sun 70° west of south

Transmissivity of glass 0.8

Answers (,b) 870 W.

2. A window 2.4 m long x 1.5 m high is recessed 300 mm from the outer surface of a wall facing 10° west of south. Using the following data, determine the temperature of the glass in sun and shade and hence the instantaneous heat gain through the window.

TOC o "1-5" h z Altitude of sun 60°

Azimuth of sun 20° east of south

Intensity of sun’s rays 790 W m-2

Sky radiation normal to glass 110 W m-2

Transmissivity of glass 0.6

Reflectivity of glass 0.1

Outside surface coefficient 23 W nT2 K-1

Inside surface coefficient 10 W m-2 K-1

Outside air temperature 32°C

Inside air temperature 24°C

Answers

37.9°C, 29.6°C, 983 W.

3. An air conditioned room measures 3 m wide, 3 m high and 6 m deep. One of the two

3 m walls faces west and contains a single glazed window of size 1.5 m by 1.5 m. The window is shaded internally by Venetian blinds and is mounted flush with the external wall. There are no heat gains through the floor, ceiling, or walls other than that facing west and there is no infiltration. Calculate the sensible and latent heat gains which constitute a load on the air conditioning system at 16.00 h in June, given the following information.

Outside state Inside state Electric lighting

28°C dry-bulb, 19.5°C wet-bulb (sling) 22°C dry-bulb, 50% saturation 33 W per m2 of floor area

Number of occupants

Heat liberated by occupants

Solar heat gain through window with

258 W m~2 1.7 Wm-2K-‘ 5.7 W m“2 K"1 5 hours (= <)>) 0.62 (=/)

Venetian blinds fully closed [/-value of wall [/-value of glass Time lag for wall Decrement factor for wall

Diurnal variations of air temperature and sol-air temperature are as follows:

09.0

Sun-time Air temperature (°C) Sol-air temperature (°C)

10.00 11.00 12.00 13.00 14.00 15.00 16.00

20.6 22.0 23.3 24.7 25.8 26.8 27.5 28.0

23.7 25.3 26.8 28.3 39.4 47.3 53.6 57.0

The mean sol-air temperature over 24 hours is 29.9°C (= fem).

The heat gain through a wall, q^), at any time (0 + ((>), is given by the equation:

9(0+0) — UA(tem — t) + UA(te — tem)f

Where te is the sol-air temperature t is the inside air temperature 0 is the time in hours.

Answers 1662 W, 200 W.

4. (a) Derive an expression for sol-air temperature.

(.b) Using your derived expression determine the sol-air temperature for a flat roof if the direct radiation, normal to the sun’s rays, is 893 W nT2 and the intensity of scattered radiation normal to the roof is 112 W m-2 Take the absorption coefficient of the roof for direct and scattered radiation as 0.9, the heat transfer coefficient of the outside surface as

22.7 W m-2, the outside air temperature as 28°C and the solar altitude as 60°C.

(c) Given that the time lag of the roof structure is zero and its decrement factor is unity, calculate the heat gain to the room beneath the roof referred to in part (b) if the [/-value of the roof is 0.5 W nT2 K"1 and the room temperature is 22°C. The mean sol-air temperature over 24 hours is 37°C.

Answers

(b) 63.1°C, (c) 20.6 Wm“2.

5. Repeat the calculation of the sensible gain for the module used in example 7.18 but for an east-facing module, with a wall [/-value of 0.6 W m“2 KT1 and an infiltration rate of 2 air changes per hour.

Answer

1111 W.

Notation

Symbol A

Unit Wm“2 M2 M2 M M2 M2 Medians Degrees Degrees

Description

Apparent solar radiation in the absence of an atmosphere

Solar radiation constant area

Surface area of a structural element in a room internal duct dimension floor area

Area of glass or area of opening in a wall

Angular movement of the sun

A A’ B C C D D Fb F*

Altitude of the sun

Altitude of the sun at noon

Atmospheric correction factor

M KJ kg’1 K-1 m Degrees

Internal duct dimension

Dimensionless constant

Specific heat capacity

Internal duct diameter

Declination of the sun

Shading factor

Air-point control factor

Angle factor for the ground

Angle factor for the sky

Room conduction factor with respect to the air node

* ay / 80 gr h

Room admittance factor with respect to the air node

G kg 1 g kg-1 degrees W nT2 KT1 W nT2 KT1 W nT2 KT1

Decrement factor

Outside air moisture content

Room air moisture content

Hour angle

Coefficient of heat transfer

Hsi

Inside surface film coefficient of heat transfer

KJ kg kJ kg

Outside surface film coefficient of heat transfer

Enthalpy of the outside air

Hr I

Enthalpy of the room air

W m"2 or kW m~2 Wm’2 W m“2

Intensity of direct solar radiation on a surface

Normal to the rays of the sun

Component of direct solar radiation normal to a horizontal surface

Intensity of radiation reflected from surrounding surfaces

W nT Wm

-2

-2

Wm

Intensity of diffuse (sky) radiation normally incident on a surface intensity of total radiation on a surface component of direct solar radiation normal to a vertical surface

H

-2

Wm

Component of direct solar radiation normal to a tilted surface

Angle of incidence of a ray on a surface latitude of a place on the surface of the earth duct length

Degrees Degrees M M M or mm degrees H-1 M W nT2 W W rrf2 KW W W W W W W

I L I M N P Q & Qfa Qu Qm Qs Фsi (2e Фe+<t> ?max 4s R Rsi Rso Sc SHGC T

Thickness of the insulation on the duct

Dimension of a hypotenuse formed by R and x

Wall-solar azimuth

Number of air changes per hour

External duct perimeter

Rate of heat flow

Heat transfer through a duct wall

Rate of heat entry to an outer wall/roof surface

Fresh air load

Wm Wm M or mm Wm“2 m2 K W“1 m2 K W-1 H K °C H °C °C °c °c °c °c °c °c °c °c °c °c °c °c °c W m“2 KT1 3 M

Latent heat gain by natural infiltration mean rate of heat flow through a wall or roof cooling load due to solar gain through glass sensible heat gain by natural infiltration rate of heat flow into a room at time 0 rate of heat flow into a room at time 0 + <j) maximum instantaneous sensible solar heat gain through glass

Specific cooling load due to solar gain through glass depth of a window recess

Remainder term to cover long-wave radiation exchanges thermal resistance of an inside surface air film thermal resistance of an outside surface air film shading coefficient solar heat gain coefficient sun time

Absolute temperature dry-bulb temperature time

Wet-bulb temperature

Air temperature

Sol-air temperature

Inside environmental temperature

Mean sol-air temperature over 24 hours

Mean glass temperature

Outside air dry-bulb temperature

Room air temperature

Ambient air dry-bulb temperature

Mean radiant temperature

Inside surface temperature

Lso ‘ Slll H H U V

Outside surface temperature

Mean inside surface temperature

Initial air temperature in duct

Final air temperature in duct

Overall thermal transmittance coefficient

Volume of a room

V mean air velocity in a duct m s_1

Velocity of airflow through an opening m s-1

Vt volumetric flow rate of fresh air at temperature t m3 s-1

Vt specific volume of air at temperature t m3 kg-1

X horizontal co-ordinate m or mm

Y admittance of a surface W m-2 K~*

Y vertical co-ordinate m or mm

TOC o "1-5" h z dimensionless parameter related to duct heat gain —

Z azimuth of the sun degrees

A absorptivity of glass for direct solar radiation —

A’ absorptivity of glass for scattered solar radiation —

Ap pressure drop through an opening Pa

At temperature change per metre of duct length K trf1

8 angle between the ground and the horizontal degrees

Angle of a surface with the horizontal degrees

TOC o "1-5" h z 0 time h

X thermal conductivity of the insulation on a duct W m-1 K-1

P density of air kg itT3

Glass reflection coefficient for direct solar radiation —

Reflectivity of the ground —

X glass transmission coefficient for direct radiation —

X’ glass transmission coefficient for sky radiation —

<)) time lag h

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