AEEMM

The Macao Institution of Electrical and Mechanical Engineers

Webinar on
Psychrometry &
Design Cooling Load

Dr Francis W H Yik
Contents
• Part 1
• Psychrometry (測濕法)
• Basic concepts
• Psychrometric chart (焓濕表)
• Psychrometric processes (First Break)
• The conventional all air cycle
• Part 2
• Design cooling load
• Building heat transfer
• Outdoor and indoor design conditions (Second Break)
• Design cooling load calculation
• Q&A

2
Reference
• Fundamentals, Design and Control of Air-conditioning Systems
• Free-downloadable from: www.learnerthon.org/sharing/
Chapter No. & Title:

1 Introduction
2 Psychrometry
3 Building Heat Transfer and Cooling Load Calculation
4 Air-Side Air-Conditioning Systems
5 Space Air Diffusion, Fan Duct System and Mechanical
Ventilation
6 Water-Side Systems and Equipment
7 Water-Side Systems and Control
8 Water-Side System Pipe Sizing and Control Valve Selection
9 System Performance and Control Optimization
10 Heating Systems, Heat Recovery Chillers, Heat Pumps and
Absorption Chillers
3
Objectives of covering these topics
• Psychrometry
• A concise overview of the basis for
• Quantification of air state, heat transfer rate in an air-conditioning process
and air-side system performance
• Air-side air-conditioning system design
• Design cooling load
• Understanding of
• The factors affecting cooling load and hence the required data for cooling
load estimation and the means for reduction of cooling load
• The typical assumptions behind cooling load simulation methods
• The standard design cooling load estimation method

4
Part 1 - Psychrometry
Basic concepts
Psychrometric chart
Psychrometric processes
The conventional all air cycle

5
Basic Concepts
• Air-conditioning involves treatment of air, including heating or cooling, and
humidification or dehumidification of air.
• Being able to quantify the thermodynamic properties (特性) of (moist) air is a
prerequisite to estimation of the heating / cooling capacity required of air-
conditioning systems as well as to measurement of their performance.
• Psychrometry (or psychrometrics) (測濕法) is the study of the physical and
thermodynamic properties of gas-vapour mixtures, and our chief concern is on
the mixture of dry air and water vapour (moist air) (dry air and water vapour are each
assumed to be a pure substance).

mda, w1, h1 mda, w2, h2

Q M

6
Basic Concepts
• The thermodynamic state (狀態) of a substance is defined by a specific number of
different (intensive or specific) properties of the substance. Once the state of the
substance is defined, all the other properties of the substance are defined.
• For defining the state of a pure substance, two different properties need to be
defined, e.g., the temperature and pressure of liquid water or steam.
• For a mixture of pure substances, the number of properties to be defined for
defining its state equals 1 plus the number of constituent substances involved.
• It is often assumed without saying that the total pressure of a moist air sample
(pa; pa = pda + pw) is at one standard atmospheric pressure (pa = patm = 101,325Pa)
and thus only two more properties need to be defined.
• Note that saturation (飽和) may be regarded as a property. It follows that with
the temperature also specified, the state of a saturated moist air sample is
defined.
7
Psychrometric Properties of Moist Air
• Moisture content (UK) or humidity ratio (US), w (kg/kg)
• The moisture content of a moist air, w, is defined as the ratio of the mass of
water vapour, mw, to the mass of dry air, mda, contained in the moist air:
mw
w=
mda
• Using the perfect gas law (pV = mRT), and according to Dalton’s Law,
pda = patm − pw, the above may be re-written as:

pwV RdaT Rda pw 287 pw

w=  =  = 
RwT pdaV Rw patm − pw 461.5 patm − pw
pw
w = 0.621945 
patm − pw

8
Psychrometric Properties of Moist Air
• The saturation state
Moist air
• Consider an enclosed vessel containing both
air and liquid water, which may exchange
Liquid water
heat and water vapour with each other.
• When thermodynamic equilibrium (均衡) between the air and the water is
attained, no more liquid water can evaporate into vapour and go into the
moist air and no water more vapour in the moist air can condense into liquid
and go into the water.
• Further adding moisture into a saturated air will result in the moisture
condensing out as liquid.
• The moist air is described as saturated when the amount of water vapour it
contains is the maximum amount it can hold at the temperature or pressure
concerned.
9
Psychrometric Properties of Moist Air
• The saturation state (Cont’d)
• The equation above (slide #8) may as well be applied to a saturated moist air
sample:
pws
ws = 0.621945 
patm − pws

• Where
• ws is the saturation moisture content of the moist air
• pws is the saturation vapour pressure in the moist air
• Note that there is a one-one correspondent relationship between
temperature, t, and ws or pws under a given total moist air pressure.

10
Psychrometric Properties of Moist Air
• The saturation state (Cont’d)
• The saturated vapour pressure, pws (Pa), within the temperature range from 0
to 200oC can be evaluated by using the following equation:
C8
ln( pws ) = + C9 + C10T + C11T 2 + C12T 3 + C13 ln(T )
T
• Where
• T = absolute temperature, K
• C8 to C13 are coefficients with the following values:
C8 C9 C10 C11 C12 C13
-5.8002206E+03 1.3914993E+00 -4.8640239E-02 4.1764768E-05 -1.4452093E-08 6.5459673E+00

• The saturated moisture content (ws) can be evaluated once pws has been
evaluated.

11
Psychrometric Properties of Moist Air
• Degree of saturation, 
• The degree of saturation of a moist air, , is defined as the ratio of the
moisture content of the moist air, w, to the moisture content of saturated
moist air at the same temperature (and pressure), ws:
w
=
ws

• Degree of saturation is a measure of how close the moist air is to saturation,

and thus how humid is the air. Its value ranges from 0 to 1.
• Note:
• Degree of saturation is plotted as one of the major properties of moist air
in the psychrometric chart published by CIBSE (see later descriptions).

12
Psychrometric Properties of Moist Air
• Relative humidity, 
• Relative humidity, , is defined as the ratio of the water vapour pressure, pw,
of a given moist air sample to the water vapour pressure of a saturated moist
air sample at the same temperature and pressure, pws:
pw
=
pws

• Like degree of saturation, relative humidity may range from 0 to 1, and is a

measure of how close a moist air sample is to the saturation state at the same
temperature and pressure, and thus how humid is the air.

13
Psychrometric Properties of Moist Air
• Relation between degree of saturation and relative humidity
• It can be shown that:

=
1 − (1 −  )( pw / patm )

• Notes:
• Obviously, both  and  equal 0 for dry air and 1 for saturated air. The two
will differ ( > ) in intermediate states.
• However, given that pw << patm, their difference is within 2%, and in less
rigorous analysis, they are often used inter-changeably.
• Instead of degree of saturation, relative humidity is plotted in the
psychrometric chart published by ASHRAE (see later descriptions)

14
Psychrometric Properties of Moist Air
• Specific volume, v (m3/kg) (= 1/ where  is density of dry air in the moist air)
• The specific volume, v, of a moist air sample is defined as the volume of the
sample, V, per unit mass of dry air, mda, in the sample:
V
v=
mda

• Since the dry air, the water vapour and the moist air occupy the same volume,
the perfect gas law (pV = mRT) may be applied to yield:
RdaT RdaT
v= =
pda patm − pw
• From the above, it can be seen that 1 kg of dry air (with pw = 0) will occupy a
volume smaller than moist air with water vapour mixed with 1 kg of dry air
when the total pressure of both are equal to patm.
15
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg)
• Like temperature, measurement of the enthalpy of a substance needs to be
based on a datum (基準) level where enthalpy is defined as equal to zero.
• For dry air, the datum level is taken as at 0oC. The specific enthalpy of dry air
(kJ/kg) at a temperature t (oC) can then be evaluated from:
hda = C pd  t
• Where Cpd is the specific heat of dry air (kJ/kg-K).
• In practical calculations, the value of Cpd may be taken as a constant that
equals 1.006 kJ/kg-K

16
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg) (Cont’d)
• The datum for measurement of enthalpy of water is based on the triple point

triple point

• The triple point is the condition at which the solid (ice), liquid and vapour
phases of water can all exist at the same time. The corresponding
temperature and pressure are 0.01oC (taken as 0oC in practice) and 0.6112kPa,
respectively.

17
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg) (Cont’d)
• For simplicity, the specific enthalpy of liquid water at 0oC is taken as the
datum level and is defined as equal to zero.
• For water in the vapour phase at temperature t, its specific enthalpy is given
by:

hw = h fg , 0 + C ps  t
• Where
• hfg,0 = latent heat of vaporization at 0oC= 2501 kJ/kg
• Cps = specific heat of water vapour = 1.86 kJ/kg-K

18
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg) (Cont’d)
• By applying the Gibbs-Dalton law, the specific enthalpy of a mixture of dry air
and water vapour at temperature t (per unit mass of the mixture) is given by:
mm hm = mda C pd  t + mw (C ps  t + h fg , 0 )
• Dividing both sides of the above by the dry air mass mda and noting that w =
mw / mda, we get:
mm
hm = C pd  t + w  (C ps  t + h fg , 0 )
mda

• By using the dry air mass as the base, the specific enthalpy of moist air, h, is
defined as follows:
mda h = mm hm

19
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg) (Cont’d)
• Therefore, the specific enthalpy of moist air, h, can be expressed as:
h = C pd  t + w  (C ps  t + h fg , 0 )

• The above may be re-arranged to:

h = (C pd + w  C ps )  t + w  h fg , 0

• Defining the specific heat of moist air, Cpa, as

C pa = C pd + w  C ps

20
Psychrometric Properties of Moist Air
• Specific enthalpy, h (kJ/kg) (Cont’d)
• The specific enthalpy of moist air, h, can also be expressed as:

h = C pa  t + w  h fg , 0

• The first term at the RHS above may be regarded as the sensible heat
component and the second the latent heat component of the enthalpy of
moist air.
• In simplified calculations, Cpa may be regarded as a constant although it
actually is dependent on the moisture content. At w = 0.0075 kg/kg, the value
of Cpa is given by:
C pa = 1.006 + 0.0075 1.86 = 1.02kJ/kg - K

21
Psychrometric Properties of Moist Air
• Dew point temperature, tdp (oC)（露點）
• As discussed above, the moisture content (w) in a moist air sample cannot
exceed the saturation moisture content (ws) corresponding to the
temperature (t) and pressure (p) of the moist air.
• With p fixed at patm, ws is a function of t only, as depicted by the following
equation, because t and saturation are sufficient conditions for defining the
state of the moist air.

ws = ws (t ) ws (t )  w = ws (t dp ) t  t dp

• For a saturated air state at temperature tdp with moisture content ws(tdp), tdp is
the dew point temperature of any other moist air that is under patm and has a
moisture content, w, that equals ws(tdp).

22
Psychrometric Properties of Moist Air
• Dew point temperature, tdp (oC)

ws (t )  w = ws (t dp ) t  t dp
Saturation curve

• tdp → w
ws(t)

• Since w is a property, tdp is also w

a property

Note: Psychrometric chart is yet to be introduced.

tdp t

23
Psychrometric Properties of Moist Air
• Properties discussed above include:
• Temperature (dry-bulb temperature), t Can be measured by thermometers / sensors

• Vapour pressure, pw
• Moisture content, w
CANNOT be directly measured
• Specific volume (& density) , v
• Specific enthalpy, h
• Degree of saturation,  Inaccurate or instrument costly
• Relative humidity, 
• Dew point temperature, tdp Very accurate but instrument highly costly

• Assuming that the total pressure of moist air is one standard atmospheric
pressure, we need two measurable properties to define the state of a moist air
sample.

24
Psychrometric Properties of Moist Air
• The most used second property for defining the state of a moist air sample is its
wet bulb temperature (to be covered later).
• One further problem:
• Even if we can quantify two properties, other properties would still need to
be calculated by using the psychrometric relations among them, which can be
complex and time consuming.
• A convenient way to determine the psychrometric properties of moist air is to
make use of a psychrometric chart, such as those shown in the following slides.

25
Psychrometric Chart

26
Psychrometric Chart

Constant specific
enthalpy line for 40kJ/kg

27
Psychrometric Chart
• When the values of two properties of a
moist air sample are known, the state  or 
v
point of the air can be located on the
t’
chart.
h
• The values of other properties w
corresponding to the same state can
then be read from the chart, with
reference to the constant value lines of
the respective properties. t

28
Psychrometric Processes
When moist air undergoes a Psychrometric Processes include:

psychrometric process, its A - Sensible cooling

state on a psychrometric chart B – Cooling and dehumidification
will move in a direction C – Isothermal dehumidification
depending on the heat and D – Heating and dehumidification
moisture transfer taking place G E – Sensible heating
in the process. H F
Humidification F – Heating and humidification
A E G – Isothermal humidification
Dehumidification H – Cooling and humidification
B D
C
Cooling Heating

29
Psychrometric Processes
• Heat and moisture transfer process
• Consider the process below where moist air at w1 and h1 is flowing steadily
into a system at the dry air mass flow rate of mda and is leaving at w2 and h2,
as a result of heat and moisture injection into the system at the rates of Q and
M, respectively.1

mda, w1, h1 mda, w2, h2

Q M

• From heat balance on the system, we can write:

mda h2 = mda h1 + Q

1 The value of Q will become negative if heat is removed from the system; likewise for M if moisture
is removed from the system
30
Psychrometric Processes
• Heat and moisture transfer process
• From balance of mass of water vapour on the system:
mda w2 = mda w1 + M
• The above equations may be re-arranged into:
Q = mda (h2 − h1 )
M = mda ( w2 − w1 )
• Based on the equation for specific enthalpy:
Q = mda [(C pd + w2C ps )t 2 − (C pd + w1C ps )t1 + ( w2 − w1 )h fg , 0 ]
• As can be seen from the above equation, a change in moisture content in the
air will result in latent heat transfer, and a small change in the sensible heat
transfer as well.

31
Psychrometric Processes
• Heat and moisture transfer process
• By ignoring the effect of the difference in w1 & w2 on the sensible heat
transfer in the process, the equation can be simplified and broken down into
the sensible (QSen) and latent (QLat) components:

Q = mda [C pa (t 2 − t1 ) + ( w2 − w1 )h fg , 0 ]

QSen = mda C pa (t 2 − t1 )
QLat = mda ( w2 − w1 )h fg , 0

32
Psychrometric Processes
• Heat and moisture transfer process
• In the absence of moisture transfer (M = 0), there will be no change in the
moisture content of the air (w2 = w1) and the process becomes just a sensible
heat transfer process:
Q = mda (C pd + w1C ps )(t 2 − t1 )

Q = mda C pa (t 2 − t1 )

Since the moisture content of the air remains unchanged in a

sensible heat transfer process, the line joining the start and end
2 1 states of the process will be a horizontal line when shown on a
1 2 psychrometric chart, from left to right if heating and from right
to left if cooling.
33
Psychrometric Processes

• Sensible heating of moist air can be achieved by allowing the

moist air to exchange heat with hot water at a heating coil.
2 1 • Sensible cooling of moist air can be achieved if a cooling coil fed
1 2 with chilled water is used instead.
• There is a limit that moist air can be cooled down without
affecting its moisture content.
• The point of this limiting state lies on the saturation curve, at
the same moisture content as the moist air.
2 1
• This limiting temperature, by definition (as given above), is the
dew point temperature of the moist air.

t2 = tdp1

34
Psychrometric Processes
• If the chilled water is cold enough to maintain at least a portion
of the heat transfer surface in the cooling coil at a temperature
below the dew point temperature of the air, some water
1
vapour in the air will condense into liquid, resulting in cooling
2 and dehumidification of the moist air.
• In this case, the moist air is undergoing a cooling and
dehumidification process where coupled heat and mass
transfers occur.
• If condensation does not occur right at the on-coil plane
(where the air enters the coil), the air will first undergo a
1
sensible cooling process; its moisture content will start to drop
2 only when the air reaches the part of the coil where the surface
temperature is below the dew point temperature of the air.

35
Psychrometric Processes
• For a cooling and dehumidification process taking place in a cooling and
dehumidifying coil (note the change in order of the h, t and w terms):
QCC ,Tot = mda (h1 − h2 )
QCC , Sen = mda C pa (t1 − t 2 )
QCC , Lat = mda ( w1 − w2 )h fg , 0
M CC = mda ( w1 − w2 )
• Where
• QCC,Tot = Coil total load
• QCC,Sen = Coil sensible load
• QCC,Lat = Coil latent load
• MCC = Mass flow rate of condensate leaving coil

36
Psychrometric Processes
• Strictly speaking, the cooling coil load should take account of the heat carried
away by the condensate:
QCC ,Tot = mda (h1 − h2 ) − M CC CwtCC Cooling and
dehumidifying coil

mdah1 mdah2
M CC = mda (w1 − w2 )

• Where
• Cw = Specific heat of water, kJ/kg-K QCC,Tot MCCCwtCC
• tCC = Condensate temperature, oC

• However, the heat carried away by the condensate is normally very small
compared to the other heat transfer terms and can be ignored.

37
Psychrometric Processes
• Sensible heat ratio
• The cooling and dehumidification process (1-2)
may be regarded as comprising two processes:
QCC ,Tot = Q1−2 = Q1−0 + Q0−2
h1
• 1-0: An isothermal dehumidification
h0
process h2
w1
Q1−0 = mda (h1 − h0 ) = QCC , Lat 1

w2
• 0-2: A sensible cooling process 2 0

Q0−2 = mda (h0 − h2 ) = QCC ,Sen

38
Psychrometric Processes
• Sensible heat ratio Protractor available in chart for determining
slope of a process line when the SHR is known
• The ratio of the sensible cooling load to the
total cooling load is called the sensible heat
ratio (SHR)
QCC , Sen h1
SHR =
QCC ,Tot
h0
Q h2
SHR = 0− 2 1 w1
Q1− 2
w2
2 0
• The slope of the process line 1-2 on the
psychrometric chart will vary with the SHR

39
Psychrometric Processes
Protractor available in chart for
determining slope of a process
line when the SHR is known

40
Psychrometric Processes
SHR Protractor SHR = 0

A straight line the slope of which represents

a specific SHR can be constructed by: Cooling and
humidification
1. Locating a point on the circumference of Heating and
the protractor that corresponds to the dehumidification

SHR value with reference to the SHR SHR = 1.0

values represented by the graduations
along the circumference. Heating and
humidification

2. Using a straight edge to draw a line that Cooling and

dehumidification
passes through the centre point of the
protractor and the point determined in
Step 1 above
SHR = 0

41
Psychrometric Processes
• Heating and humidification process
• A stream of moist air will pick up heat and
moisture in a heating and humidification process
(which is the reverse of a cooling and
h2
dehumidification process)
• It may be: h1
h0
2 w2
• The process undergone by the cooled and
dehumidified supply air in an air-conditioned w1
1
space 0

• An air-handling process for raising the

temperature and moisture content of cold
and dry air to a desired state

42
Psychrometric Processes
• Heating and humidification process
• Space air conditioning process

hr
s
hs
qrs qrl r wr

r ws
s

Supply air at state s reaches state r after absorbing the sensible and latent
heat loads (qrs & qrl) of the space.
43
Psychrometric Processes
• Heating and humidification process
• Air-handling process
Heating coil
h2
1 1’ 2
h1
2 w2
Steam injection
w1
1 1’

• Process comprised of two stages: a

sensible heating stage by the heating coil
and a heating and humidification stage
by steam injection

44
Psychrometric Processes
• Heating and humidification process
• The rates of total, sensible and latent heat
gain, the rate of moisture gain, and the
sensible heat ratio of the process, are given
h2
respectively by:
h0
QTot = mda (h2 − h1 ) h1
2 w2
QSen = mda C pa (t2 − t1 )
w1
QLat = mda ( w2 − w1 )h fg ,0 1 0

M = mda (w2 − w1 )
QSen
SHR =
QTot

45
Psychrometric Processes
• Adiabatic mixing process
mda1, h1, w1 mda3, h3, w3
• When two steams of moist air merge and
mix with each other, the total dry air mass
mda2, h2, w2
flow rate of the mixture, mda3, is the sum of
the dry air mass flow rates of the two h1
mixing air streams (mda1, mda2):
h3
mda3 = mda1 + mda 2 1 w1
h2
3 w3

w2
2

46
Psychrometric Processes
• Adiabatic mixing process
mda1, h1, w1 mda3, h3, w3
• The total amount of heat energy in the
mixture is the sum of the heat energy in the
mda2, h2, w2
two mixing air steams:
h1
mda 3h3 = mda1h1 + mda 2 h2
h3
• Dividing all terms by mda3, we get: 1 w1
h2
3 w3
mda1 mda 2
h3 = h1 + h2
mda 3 mda 3 w2
2

47
Psychrometric Processes
• Adiabatic mixing process
mda1, h1, w1 mda3, h3, w3
• Likewise, the total amount of moisture in the
mixture is the sum of the moisture of the
mda2, h2, w2
two mixing air steams:
h1
mda 3 w3 = mda1w1 + mda 2 w2
h3
• Dividing all terms by mda3, we get: 1 w1
h2
3 w3
mda1 m
w3 = w1 + da 2 w2 w2
mda 3 mda 3 2

48
Psychrometric Processes
• Adiabatic mixing process
mda1, h1, w1 mda3, h3, w3
• It can be shown that the slopes of line 1-3
and line 1-2 are equal, and hence state point
mda2, h2, w2
3 lies on the straight line joining the state
points 1 and 2. h1
• It can also be shown that:
h3
l1−3 mda 2 w1
= h2
1
l1− 2 mda 3 3 w3

• Where l1-3 and l1-2 are respectively the linear w2

distances between points 1 & 3 and 1 & 2 on 2

a psychrometric chart

49
Psychrometric Processes
• Adiabatic saturation process
• Consider a very long, well insulated chamber, with a layer of liquid water on
the bottom surface. When moist air is flowing steadily through the chamber,
its moisture content will increase due to evaporation of the water until the air
is saturated.
mda mda

h, w, t h*, w*,
t*

mw & tw = t*

• Make up water at a temperature that equals the exit temperature of the

moist air (tw = t*) is fed into the chamber at a rate (mw) that can just
compensate for the rate of evaporation.

50
Psychrometric Processes
• Adiabatic saturation process
• The rate of evaporation of liquid water into vapour, mw, to sustain the
increase in moisture content of the air from w to w* (equals the rate of supply
of liquid water required to compensate for the loss) is given by:
mw = mda (w * −w)
• By heat balance on the chamber, we can write:
mda h* = mda h + mda (w * −w)Cwt *
• Where Cw is the specific heat of liquid water (= 4.18kJ/kg-K).
• Cancelling the common term mda in the above equation, we get:
h* = h + (w * −w)Cwt *

51
Psychrometric Processes
• Adiabatic saturation process
• Expanding h in the above equation in terms of temperature and moisture
content, and solving for w, we get:

h * −C pd t − w * Cwt *
w=
C ps t + h fg , 0 − Cwt *

• Since the chamber is very long, at the exit of the chamber, the air would have
been saturated.
• Hence, if the exit temperature of the air, t*, can be measured, the
corresponding values of w* and h* can be determined.

52
Psychrometric Processes
• Adiabatic saturation process
• The key implication of the above analysis is that:
• When an instrument that can serve the same function as the insulated
saturation chamber discussed above is available, the moisture content of
air, w, can be determined once the entry and exit temperatures of the air t
and t* can be measured.
• The temperature t* resulting from the adiabatic saturation process is called
the thermodynamic wet bulb temperature, which is a pychrometric property
of moist air.

53
Psychrometric Processes
• Adiabatic saturation process
• On a psychrometric chart, a line connecting
the entering state point and all the
intermediate state points of the air inside the
insulated chamber discussed above is a
constant thermodynamic wet bulb line.
• An adiabatic saturation process will lead to t*
saturation of the air along a constant wet bulb
line.
Process line of an adiabatic
• Since the heat of vaporization associated with saturation process
moisture gain of the air is sustained by lost of
sensible heat of the air in the process, the
process line points to left upward direction.

54
Psychrometric Processes
• Adiabatic saturation process
t*
• It can be seen (from last Eq. in slide#) that along a h1
constant thermodynamic wet bulb line: w
h
h 1
h = f ( w) t *=Const = Cwt * w + (h * − w * Cwt*) → = C wt *
w
h = f ( w) t *=Const
• Hence
• A constant thermodynamic web bulb temperature line is a straight line on
a psychrometric chart.
• The constant wet bulb line passing through a specific state point (e.g.,
Point 1 in the figure above) will rise above the constant specific enthalpy
line passing through the same state point (with h = h1).

55
Psychrometric Processes
• Adiabatic saturation process
• This is a practical adiabatic saturation 1 2

process taking place in an air washer or

spray humidifier.
• The air leaving a spray humidifier,
however, may only be close to saturation
and not actually saturated. t* ws
• The efficiency of a spray humidifier, , is s w2
2
given by: w1
1
w2 − w1
=
ws − w1

56
Let’s take a break

57
Basic Air-conditioning Cycle
• Air conditioning cycle
Air-conditioned Space
External sensible
loads, qext,s Supply air (SA)
r
Vfa
Internal sensible
Return air (RA) loads, qint,s Vs
Exhaust air (EA)

Vs - Vfa
r
l
Vfa s
o m

Fresh air (FA)

Air-handling Unit
58
Basic Air-conditioning Cycle
• In an air-conditioning system, the air being circulated in the system will undergo
several psychrometric processes in turn.
• The end state of a process will become the starting state of the next process and
hence two consecutive processes will be connected when shown on a
psychrometric chart.
• All the psychrometric processes involved in an air-conditioning system will form a
psychrometric cycle, represented by a series of lines on a psychrometric chart
that form a loop.
• The cycle formed by psychrometric processes under the design condition for an
all air system is called the Conventional All Air Cycle.

59
Basic Air-conditioning Cycle
• Air conditioning cycle
Air-conditioned Space
External sensible
loads, qext,s Supply air (SA)
r
Vfa
Internal sensible
Return air (RA) loads, qint,s Vs
Exhaust air (EA)

Vs - Vfa
r Adiabatic mixing process
l
Vfa s
o m

Fresh air (FA)

Air-handling Unit
60
Basic Air-conditioning Cycle
• Air conditioning cycle
Air-conditioned Space
External sensible
loads, qext,s Supply air (SA)
r
Vfa
Internal sensible
Return air (RA) loads, qint,s Vs
Exhaust air (EA)

Vs - Vfa
r Cooling and dehumidification process
l
Vfa s
o m

Fresh air (FA)

Air-handling Unit
61
Basic Air-conditioning Cycle
• Air conditioning cycle
Air-conditioned Space
External sensible
loads, qext,s Supply air (SA)
r
Vfa
Internal sensible
Return air (RA) loads, qint,s Vs
Exhaust air (EA)

Vs - Vfa Sensible heating process

r
l
Vfa s
o m

Fresh air (FA)

Air-handling Unit
62
Basic Air-conditioning Cycle
• Air conditioning cycle
Air-conditioned Space
External sensible
loads, qext,s Supply air (SA)
r
Vfa
Internal sensible
Return air (RA) loads, qint,s Vs
Exhaust air (EA)

Vs - Vfa
r Heating and humidification process
l
Vfa s
o m

Fresh air (FA)

Air-handling Unit
63
Basic Air-conditioning Cycle
The cycle formed by the
abovementioned psychrometric
processes under the design condition
is called the Conventional All Air
Cycle

State points:

r – Room Air
o – Outdoor/Fresh Air
m – Mixture; On Coil
l – Leaving Coil
s – Supply Air

64
Basic Air-conditioning Cycle
• Method for construction of the Protractor available in chart for determining
slope of a process line when the SHR is known
conventional all air cycle:
• Based on the design indoor air
condition, the state point
representing room air state, r, can be
located on the psychrometric chart.
r
• Let qrs and qrl be the design room
sensible and latent loads, the room
sensible heat ratio (RSHR) can be r
calculated as follows:
qrs
RSHR =
qrs + qrl
Tr

65
Basic Air-conditioning Cycle
• The slope of the process line s-r, can Protractor available in chart for determining
slope of a process line when the SHR is known
be determined based on the RSHR,
using the protractor provided in the
chart.
• A line parallel to the line drawn at RSHR
Parallel
the protractor according to the RSHR
can then be drawn to pass through r
the room air state r.
• The supply air state point, s, will line r
on this process line but, at this s

juncture, the exact location of state

point s remains unknown.
Tr

66
Basic Air-conditioning Cycle
• It may be assumed that the state of Protractor available in chart for determining
slope of a process line when the SHR is known
air leaving a cooling and
dehumidifying coil, l, will have a
relative humidity of 95%, and the 95% RH
temperature rise due to fan heat
gain, Tfan, is known (typically in the
Process line
range of 0.5-1.5oC). s-r r
• The state points l and s can then be
determined simultaneously by Horizontal
adjusting the location of a horizontal line r

line until it crosses the 95% RH line

and the process line s-r, with the
intersecting points separated from
each other by Tfan in the Tfan Tr
temperature scale.
67
Basic Air-conditioning Cycle
• The state point l lies at the Protractor available in chart for determining
slope of a process line when the SHR is known
intersecting point of the horizontal
line with the 95% RH line, and
95% RH
• The state point s lies at the
intersecting point of the horizontal
line with the process line s-r.
r
• Having determined the state points l
and s, their psychrometric properties l
can be read from the psychrometric r
chart. s

Tfan Tr

68
Basic Air-conditioning Cycle
• The required supply air flow rate, Vs, Protractor available in chart for determining
slope of a process line when the SHR is known
can now be determined as follows:
qrs
Vs =
 a C pa (Tr − Ts )

• Based on the design outdoor / fresh

r
air state, its state point, o, can be
located on the psychrometric chart.
• The mixture air state, m, can then be l s
r

determined with reference to the

supply air flow rate (Vs) and the
know fresh air flow rate (Vfa).
Tl Ts Tr

69
Basic Air-conditioning Cycle
• Assuming the mixing of the outdoor Protractor available in chart for determining
slope of a process line when the SHR is known
air and the return air from the room
is an adiabatic mixing process:
Vs − V fa V fa o
wm = wr + wo
Vs Vs

• The state point m lies on the straight m wm

line joining up state points o and r,
and having evaluated wm, it can be
r
located on the psychrometric chart. l s

Tl Ts Tr Tm

70
Basic Air-conditioning Cycle
• All state points of the conventional Protractor available in chart for determining
slope of a process line when the SHR is known
all air cycle have now been
determined.
• The sensible and total cooling output o
hm
required of the cooling and
dehumidifying coil can also be
determined as follows:
hl m
qcc , s =  aVs C pa (Tm − Tl )
r
l s
qcc ,t =  aVs (hm − hl )

Tl Ts Tr Tm

71
End of Part 1

72
Part 2 – Design Cooling Load
Building heat transfer
Outdoor and indoor design conditions
Design cooling load calculation

73
Heat Gains
• Heat gains of an air-conditioned space

Conduction

Solar Air duct

Infiltration
Lighting Occupant
Conduction

Outdoors
Equipment

Conduction

Heating/Air-
Building conditioning
envelope

Conduction Air-handling
unit

74
Heat Gains
• Once heat flow enters an air-conditioned space, it becomes a heat gain of the
space. The heat gains of a space include (R: Radiant; C: Convective):
• From external sources:
• Conduction heat gain through fenestrations (R+C)
• Conduction heat gain through external and internal walls and slabs (R+C)
• Solar heat gain through fenestrations (transmitted: R; absorbed R+C)
• Infiltration (C)
• Heat gains from internal sources:
• Lighting and appliances (R+C)
• Occupants (R+C)
• Materials at elevated temperatures brought into the space (R+C)

75
Heat Gain and Cooling Load
• The cooling load of a space is the rate that (sensible and latent) heat must be
taken out of the space in order to maintain the indoor air state of the space at
the design condition.
• Since air-conditioning is provided primarily through treating the air inside the
space, the cooling load comprises only the (sensible and latent) heat that is
imparted to the room air, which must be through convection.
• Accordingly, all convective heat gains will instantaneously become parts of the
cooling load of a space.
• Radiant heat gains will not become cooling load until their energy is absorbed by
objects inside the space, thus raising up the temperatures of the objects.
• Note that sensible heat gains may be radiant or convective while latent heat
gains are all convective.

76
Heat Gain and Cooling Load
• Heat extraction rate is the rate that heat is removed from the space by the air-
conditioning system.
• Room air temperature can be kept at set-point value only if sensible heat
extraction rate equals room sensible cooling load – imbalance between the two
will lead to drifting of the room air temperature from its set-point.

Instantaneous Instantaneous Heat Extraction

Heat Gain Convective Cooling Load Rate
Component

Radiant Convection from Fabric

Component and Furnishing Surfaces
(with time delay)
Absorbed by Fabric
Component and
Furnishing Surfaces

77
Heat Gain and Cooling Load
Conduction • Conduction heat gains from walls and roofs/
Solar
ceilings:
Air duct
Infiltration • This group of heat gains is subject to the
Lighting Occupant
influence of the thermal storage effect of
Conduction

Outdoors
the fabric components and exhibits a
Equipment time lag.
Conduction
• They are to be evaluated from the
Building
solution of the governing equation and
Heating/Air-
conditioning
envelope appropriate boundary conditions.

Conduction
• In theAir-handling
ASHRAE Method, the solution is
called theunitConduction Transfer Function
(CTF), which was obtained by using the
Transfer Function Method (TFM).

78
Heat Gain and Cooling Load
Conduction • The other heat gains, as listed below, may all
Solar
be regarded as instantaneous heat gains and
Air duct
may be calculated using the methods
Infiltration
Lighting Occupant outlined above.
Conduction

Outdoors
• Transmitted direct and diffuse solar heat
Equipment gain through fenestrations
Conduction
• Conductive heat gain from fenestrations
Heating/Air-
Building • Occupant heat gains
conditioning
envelope
• Lighting & appliances heat gains
Conduction Air-handling
• Heat gains
unitdue to infiltration

79
Conduction Heat Transfer
• The Fourier’s Law of Conduction as shown below describes the rate of one-
dimensional conduction heat transfer per unit area (q(x)) through a cross-
sectional plane within a wall or slab:

T ( x)
q ( x) = −k
x

• Where
• k is the thermal conductivity of the material, W/m-K
• T(x)/x is the temperature gradient at position x (+‘ve if T increases with x)
• The negative sign is to account for the thermodynamic principle that heat will
only flow from a high to a low temperature region

80
Conduction Heat Transfer
• Based on an elemental cross section within a wall or slab of a homogeneous
material, the following governing equation for one-dimensional conduction heat
transfer can be derived:
x x+x
T ( x)  T ( x)
2
x
=
t x 2 T(x) T(x+x)

• Where q(x) q(x+x)

•  = k/C is the thermal diffusivity of the material, m2/s

•  = density of the material, kg/m3 T

• C = specific heat of the material, J/kg-K

81
Conduction Heat Transfer
• The governing equation above can be solved when the initial (T(x,0)) and
boundary (e.g. q(0,t) and T(L,t), T(0, t) and T(L,t), etc.) conditions are known.
• The solution can allow us to predict the temperature in a wall or slab at any
position x and time t (T(x,t)), and from this the heat transfer rate (q(x,t)).
• Different methods may be used to solve the governing equation, including
analytical methods, such as Laplace Transformation, Response Factor Method,
Transfer Function Method, and numerical methods, such as Finite Difference
Method.
• Nowadays, computer programs are available for
building heat transfer simulation and cooling load
prediction (requires a range of input data), and
simulation of dynamic heat transfer through walls
and slabs is typically the most time consuming.
82
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Heat transfers at the outer surface of an external
wall include:
IT
• Solar (short-wave) radiation incident upon and qSol
absorbed by the surface (qSol) Tao qco qwo
ho Two
• Convection due to difference in temperature qro
between the outdoor air and the wall surface
(qco)
• Net (long-wave) radiation (qro) from the
surrounding surfaces (sky and ground)
• Conduction heat transfer into the wall (qwo)

83
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Solar (short-wave) radiation incident upon and
absorbed by each unit area of the surface (qSol):
IT
qsol =  o I T qSol
Tao qco qwo
• Where ho Two

• o is the solar absorption coefficient qro

• IT is the total (beam and diffuse) intensity of

solar radiation upon (normal to) the surface

84
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Convection due to difference in temperature
between the outdoor air and the wall surface (qco):
IT
qco = hco (Tao − Two ) qSol
Tao qco qwo
• Where ho Two

• hco is the external surface convection heat qro

transfer coefficient
• Tao and Two are the outdoor air and wall external
surface temperatures

85
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Net (long-wave) radiation (qro) from the surrounding
surfaces
IT
• For simplicity, all the surrounding surfaces (ground qSol
and sky included) are represented by a single Tao qco qwo
ho
fictitious black surface at the outdoor air Two
temperature (Tao) and with extensive area. qro

• Hence, qro is given by:

qro =  o (Tao4 − Two4 )

• Where o is the emissivity of the external wall

surface
86
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• The above equation is often simplified to

qro = hro (Tao − Two ) IT

qSol
• And combined with qco to Tao qco qwo
ho Two
qcro = ho (Tao − Two )
qro

• Where
• hro is the radiant heat transfer coefficient
• qcro is the total convection and long wave radiation heat transfer rate
• ho (= hco + hro) is the combined convection and radiation heat transfer coefficient

87
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• For vertical walls, the simplification above can give
reasonably accurate estimation of the convection and
long-wave radiation heat transfer at the external surface. IT
qSol
• However, for a horizontal surface facing the sky, e.g. a Tao qco qwo
ho
roof, the equation needs to be corrected for the radiant Two
heat loss to the sky vault as follows: qro
qcro = ho (Tao − Two ) −  o R

• The equations for vertical and horizontal walls may be

combined by setting:
• R = 63W/m2 for horizontal surface
• R = 0 for vertical surface

88
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• The heat transfers taking place at the external surface of a
wall or slab can now be combined as:
IT
qo = I t + ho (Tao − Two ) −  o R qSol
Tao qco qwo
• Which can be re-arranged to: ho Two
I  R 
qo = ho  t + Tao − Two − o  qro
 ho ho 
• By defining sol-air temperature (Teo) as:
I t  o R
Teo = Tao + −
ho ho
• We get
qo = ho (Teo − Two )

89
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Conduction heat transfer into the wall is given by:
Tw
qwo = −k IT
x x =0
qSol
• Where k is the thermal conductivity of the wall material Tao qco qwo
ho Two
• From heat balance on the external surface:
qo = qwo qro

Tw
ho (Teo − Two ) = −k
x x =0

• The above is one of the needed boundary conditions for

solving the governing heat transfer equation for an
external wall or roof.

90
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Assumptions on radiant heat gains at internal surfaces of
walls, slabs and fenestrations:
• The total amount of solar radiation transmitted into qri
the space through fenestrations will be evenly qwi qci Tai
distributed onto the floor. hi
Twi
qTS
• All other radiant heat gains are assumed to be evenly
distributed to the surfaces of the building fabric
elements (usually with the window/skylight surfaces
excluded) according to their surface areas.
• These radiant heat gains will be absorbed by the
surfaces without reflection and no further stages of
absorption and reflection will take place.

91
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Heat transfers at the inner surface of an external wall
include:
• Radiation from various sources, including transmitted qri
qwi
solar radiation (for floor slab only) and radiation from qci Tai
other indoor sources, that is absorbed by the surface, hi
Twi
qTS qTS

• Convection from the surface to the indoor air due to

the temperature difference between the wall surface
and the indoor air, qci
• Net (long wave) radiation loss from the surface to
other surfaces enclosing the indoor space, qri
• Conduction from within the wall toward the wall
surface, qwi
92
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Convection from the surface to the indoor air due to the
temperature difference between the wall surface and
the indoor air, qci, is given by: qri
qwi qci Tai
qci = hci (Twi − Tai ) hi
Twi
• Where qTS
• hci = convection heat transfer coefficient
• Twi = internal surface temperature of wall
• Tai = indoor air temperature

93
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• Net (long wave) radiation loss from the surface to other
surfaces enclosing the indoor space, qri
• Similar to the external surface, a fictitious surface at qri
qwi
the room air temperature is used to represent all the qci Tai
surfaces enclosing the space, except the one under hi
Twi
concern; and qTS

• The net radiant heat transfer rate from the surface to

the other surfaces is estimated using a linearized
model as follows:
qri = hri (Twi − Tai )
• Where
• hri is the radiant heat transfer coefficient
94
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• The combined convection and radiation heat transfer
can be estimated by:
qcri = hi (Twi − Tai ) qri
qwi qci Tai
• Where hi
Twi
• hi (= hci + hri) is the combined convection and qTS
radiation heat transfer coefficient
• The net rate of heat transfer from the surface into the
space, qi, is given by:
qi = hi (Twi − Tai ) − qTS

95
Heat Transfer at a Building Fabric Element
• Opaque wall or slab
• By defining an environmental temperature, Tei, as:
qTS
Tei = Tai +
hi
qri
• Then, qi, may be written as: qwi qci Tai
qi = hi (Twi − Tei ) Twi
hi
qTS
• Conduction from within the wall toward the wall surface,
qwi, is given by:
Tw
qwi = − k = qi
x x=L

• The two equations above provide the next needed

boundary condition for solving the governing equation
for heat transfer through a wall or slab.
96
Heat Transfer at a Building Fabric Element
• Fenestration
• The heat transfers taking place at an external wall or
slab discussed above apply to a window or skylight.
• Additionally, a window or skylight will transmit a
portion of the incident solar radiation, and will IT
absorb part of the solar energy as the radiation qSol qri
qG
passes through the glass. Tao q
co
qci Tai
ho hi
TG
• The transmitted solar radiation entering an air- qro
conditioned space is a major source of heat gain of GIT
the space. It, however, will not become cooling load
until it is absorbed by fabric or furniture surfaces
inside the space.
• Simplified methods are adopted to predict the heat
transfers at a fenestration.
97
Heat Transfer at a Building Fabric Element
• Fenestration
• Because the glass pane in a window or skylight is
relatively thin (in the order of several mm to slightly
over 10 mm):
• Its thermal mass is low and its resistance to IT
conduction heat transfer is small. qSol qri
qG qci Tai
Tao q
• These allow the following simplifications to be made: ho
co
hi
qro TG
• A steady-state model may be used to describe GIT
the state of, and the heat transfer through, the
glass pane.
• The entire glass pane can be represented simply
by a single temperature, TG.

98
Heat Transfer at a Building Fabric Element
• Fenestration
• Note also that although a glass pane can transmit
solar (short-wave) radiation, it can be regarded as
opaque to long-wave radiation (which is the reason behind
the greenhouse effect).
IT
• For simplicity, the heat transfer due to incident solar qSol qri
qG
radiation (called solar heat gain) and that due to Tao q
co
qci Tai
indoor/outdoor temperature difference (called ho hi
qro TG
conduction heat gain) are decomposed and dealt with GIT
separately.
• However, like external walls and roofs, the long-wave
radiation heat transfers at the external and internal
surfaces of a glass pane are combined with the
convection heat transfers at the respective surfaces.
99
Heat Transfer at a Building Fabric Element
• Fenestration
• When subject to an incident solar radiation of
intensity IT:
• The reflected portion (GIT) does not enter the
building and thus has no effect on the cooling IT
load of the indoor space; qSol qri
qG qci Tai
• The transmitted portion (GIT) becomes part of Tao q
ho
co
hi
TG
the space heat gain but has no effect on the qro
state of the glass pane; and GIT

• The absorbed portion (GIT) will affect the

glazing temperature and thus the conduction,
convection and radiation heat transfer rates.

100
Heat Transfer at a Building Fabric Element
• Fenestration

GIT IT
Tao GIT qSol qri
qG qci Tai
Tao q
TG co
ho hi
qro TG
Tai
GIT

Conduction heat gain Solar heat gain

101
Heat Transfer at a Building Fabric Element
• Fenestration
• The heat transfer rate due to indoor/outdoor
temperature difference (conduction heat gain), qGT,
can be determined by using:
qGT = U (Tao − Tai ) IT
qri
• Where, with thermal resistance of the glass pane qSol
qG qci Tai
Tao q
ignored, U can be evaluated from: ho
co
hi
qro TG
1 hh GIT
U= = i o
1 / ho + 1 / hi hi + ho

• With the use of combined convection and radiation

heat transfer coefficients hi and ho, the long-wave
radiation heat exchanges with the surrounding
surfaces are included.
102
Heat Transfer at a Building Fabric Element
• Fenestration
• With the conduction heat gain dealt with separately, the effect
of the absorbed solar radiation can be treated by
assuming that both sides of the glass pane are exposed
to the same ambient air temperature, Ta (and thus there
IT
will be no heat transfer due to an in/out temperature difference). qri
qSol
qG
• The absorbed solar radiation will raise the glass pane Tao q
co
qci Tai
temperature, from Ta to TG, and this temperature ho hi
qro TG
difference (value of Ta is arbitrary) will cause the GIT
absorbed heat to flow toward both the indoor and the
outdoor sides.
• The rate of heat flow toward the outdoor side, and
thus it will not affect the space, is:
qout = ho (TG − Ta )
103
Heat Transfer at a Building Fabric Element
• Fenestration
• The rate of heat flow toward the indoor space is:
qin = hi (TG − Ta )

• Heat balance on the glass pane allows us to write:

IT
 G IT = hi (TG − Ta ) + ho (TG − Ta ) qSol qri
qG qci Tai
 G IT = (hi + ho )(TG − Ta ) Tao q
co
ho hi
qro TG
• Using also U defined above, qin, the heat transfer GIT
rate that will contribute to the cooling load of the
space can be expressed as:
hi U G
qin =  G IT = IT
hi + ho ho

104
Heat Transfer at a Building Fabric Element
• Fenestration
• Therefore, the total rate of heat transfer through the fenestration into the
indoor space is:
 U G 
qG =  G +  I T + U (Tao − Tai )
 ho  IT
qSol qri
• The term within the bracket of the first term at the Tao q
qG qci Tai
co
RHS of the above equation is called the Solar Heat ho hi
qro TG
Gain Coefficient (SHGC) (= f (glass properties, wind speed)). GIT
• The SHGC of a Double Strength, heat Absorbing (DSA)
glass is 0.87.
• The Shading Coefficient (SC) of a fenestration is defined as:
SC = SHGC SHGC DSA = SHGC 0.87

105
Heat Transfer at a Building Fabric Element
• Fenestration
• With reference to the standard DSA glass, a series of Solar Heat Gain Factors
(SHGFs; SHGF = SHGCDSA  IT ) may be pre-evaluated for:
• A specific location on earth
• A range of standard exposure directions IT
qri
qSol
• Daytime hours in a day Tao q
qG qci Tai
co
ho hi
• Solar heat gain calculations are much simplified qro TG
when pre-calculated SHGFs are available. GIT

• The solar heat gain from a particular glazing at a

particular time can be determined from the SHGF for the hour and the SC of
the glazing:
qGSol = SC  SHGF
106
Heat Transfer at a Building Fabric Element
• More Detailed Treatment of Solar Heat Gain through Fenestration
• The method discussed above ignored the
variation in the reflectance, transmittance, and
absorptance of glazing with the incident
angle ( ) of direct solar radiation.
• For more accurate calculation of solar heat gain
through fenestration, solar heat gain coefficient
that varies with the solar incident angle, SHGC( ), would need to be used to
calculate heat gain from direct radiation at a given incident angle.
• The heat gain due to diffuse radiation would need to be evaluated using a
solar heat gain coefficient for all angles, <SHGC>d.
• We shall come back to this issue later when we discuss the standard cooling load
calculation method.
107
Heat Transfer at a Building Fabric Element
• More Detailed Treatment of Solar Heat Gain through Fenestration
• When the effects of external shading devices,
such as overhang, side-fin, awning, etc.
need to be accounted for, the areas of the parts
of the glazing surface that are shaded and not
shaded would need to be determined separately
based on the incident angle of direct radiation
and the geometry of the shading device.
• For internal shading devices, such as venetian blinds, drapers, etc.,
appropriate indoor solar attenuation coefficient (IAC) for direct and diffuse
radiation for the specific device would need to be used to account for their
effects.

108
Let’s take a break

109
Outdoor Design Conditions
• Design cooling load calculations are typically based on the following outdoor
weather condition:
• Solar radiation intensities that would be available under a clear sky
• Outdoor dry-bulb and wet-bulb temperatures that would represent a
condition where the cooling load estimated based on that condition would
only be surpassed by a small enough percentage of time in the year.

Top of atmosphere

m = l / h  1 / sin
l
except when  is < 15o
h Direct radiation

Diffuse radiation

Earth’s surface

110
Outdoor Design Conditions
Clear Sky Direct Normal Solar Radiation Intensity (IDN) in Hong Kong

LST Jun Jul Aug Sep Oct Nov Dec

6 14.56 0.89 0.01 0.00 0.00 0.00 0.00
7 253.27 236.99 140.61 74.18 36.40 8.67 0.04
8 439.74 449.31 370.88 300.30 261.50 254.51 196.99
9 554.29 574.31 511.87 450.34 422.55 445.47 416.85
10 624.43 649.11 596.05 540.16 517.91 553.91 542.77
11 664.86 692.07 643.96 590.09 569.35 611.17 610.55
12 682.77 711.77 665.40 610.29 587.86 632.05 638.68
13 681.04 711.68 664.27 604.47 577.09 621.35 633.92
14 659.41 691.79 640.37 571.60 534.94 576.66 595.17
15 614.34 648.58 589.31 505.37 452.64 486.92 512.82
16 537.62 573.41 500.50 391.57 311.39 326.63 363.45
17 412.61 447.81 351.86 205.29 92.48 70.15 112.89
18 209.87 234.45 112.62 3.19 2.60 0.00 33.20
19 1.24 0.70 24.70 0.00 0.00 0.00 0.00

111
Outdoor Design Conditions
Clear Sky Diffuse Horizontal Solar Radiation Intensity (IdH) in Hong Kong

LST Jun Jul Aug Sep Oct Nov Dec

6 17.90 5.64 1.18 0.00 0.00 0.00 0.00
7 100.45 84.47 69.45 52.01 34.10 16.35 2.76
8 162.77 145.54 149.21 147.00 129.75 103.21 86.84
9 206.47 187.57 203.92 213.12 197.25 163.69 154.00
10 236.20 216.05 240.44 256.42 240.74 202.03 196.71
11 254.62 233.84 262.88 282.07 265.71 224.01 221.90
12 263.11 242.40 273.38 292.82 275.00 232.37 232.91
13 262.29 242.36 272.81 289.70 269.58 228.06 231.02
14 252.08 233.72 261.15 272.42 248.88 210.60 216.02
15 231.76 215.84 237.39 239.24 210.62 177.90 186.12
16 199.76 187.24 199.24 186.44 150.08 125.33 137.10
17 153.14 145.07 142.31 107.57 60.78 45.15 60.95
18 86.83 83.78 59.70 9.07 8.76 0.00 31.62
19 6.12 5.19 24.29 0.00 0.00 0.00 0.00

Maximum value of IdH occurs in April

112
Outdoor Design Conditions
• Because outdoor dry and wet bulb temperatures both vary from time to time and
from year to year, selection of the design outdoor weather condition needs to be
based on statistical analysis of weather records of a particular region over a long
enough period (typically 25 years) to yield:
• Design outdoor dry bulb temperatures that could be exceeded by different
percentages of time in the cooling period, and
• For each outdoor air temperature with known probability of exceedance, a
mean coincident wet bulb temperature (MCWB).
• Alternatively, design outdoor wet bulb temperatures at known probabilities of
exceedance and mean coincident dry bulb (MCDB) temperatures may be
compiled for use in designs with particular concern on dehumidification
capacity.

113
Outdoor Design Conditions

114
Outdoor Design Conditions
• With the statistical information about the outdoor weather condition of a region,
selection of the dry and wet bulb temperatures as the reference for design
cooling load calculation can then be made based on:
• The acceptable risk level that a plant sized based on the design weather
condition may not have sufficient capacity to cope with the load.
• The 0.4, 1.0, 2.0 and 5.0% values are exceeded on average by 35, 88, 175 and
438 hours out of the 8,760 hours in a year.
• A commonly used design weather condition for Hong Kong is 33.3oC dry bulb,
28oC wet bulb (see statistical figures based on weather data records at the Hong
Kong Observatory given below).

115
Outdoor Design Conditions
• Design dry bulb (DB) and mean coincident wet bulb (MCWB) temperatures and
design wet bulb (WB) and mean coincident dry bulb (MCDB) temperatures, at
0.4% exceedance level, based on the weather records at the Observatory of HK:
0.4% Month Jan Feb Mar Apr May Jun
DB 22.1 23.1 26.0 28.6 31.2 32.2
MCWB 18.5 19.8 22.7 24.3 26.2 26.5

Month Jul Aug Sep Oct Nov Dec

DB 33.0 32.9 32.5 30.6 26.9 24.0
MCWB 26.8 26.6 25.6 25.2 21.9 19.3
0.4% Month Jan Feb Mar Apr May Jun
WB 19.5 21.1 23.6 25.3 26.9 27.7
MCDB 21.0 22.4 25.2 27.1 29.8 30.6

Month Jul Aug Sep Oct Nov Dec

WB 27.7 27.7 27.3 26.2 23.9 20.1
MCDB 30.9 31.1 30.3 28.9 25.6 22.6
116
Outdoor Design Conditions
• Hourly design outdoor dry and wet bulb temperatures (tao & t’ao) are to be
evaluated based on the design dry bulb (DB) and wet bulb (MCWB)
temperatures for individual months as given above, adjusted to hourly values by
using the daily range (DR) of the design temperatures for the month and the
percentage of the daily range (X) for individual hours.
tao = DB − DR  X

t 'ao = MCWB − DR  X

• Note that
• The same DR and X values are applicable to both the design dry bulb and wet
bulb temperatures.
• There is only one daily profile of outdoor weather condition for each month.

117
Outdoor Design Conditions
• Values of DR and X for evaluation of the hourly outdoor design conditions for
Hong Kong are as given below:
Month Jan Feb Mar Apr May Jun
DB/WB DR 3.5 3.1 3.4 3.3 3.3 3

Month Jul Aug Sep Oct Nov Dec

DB/WB DR 3.5 3.5 3.4 3.2 3.5 3.8

Time, hr X Time, hr X Time, hr X Time, hr X

1 0.88 7 0.91 13 0.05 19 0.39
2 0.92 8 0.74 14 0 20 0.5
3 0.95 9 0.55 15 0 21 0.59
4 0.98 10 0.38 16 0.06 22 0.68
5 1 11 0.23 17 0.14 23 0.75
6 0.98 12 0.13 18 0.24 24 0.82

118
Outdoor Design Conditions
Hourly Design Dry and Wet Bulb Temperatures for Hong Kong (oC)
Time Jun Jul Aug Sep Oct Nov Dec
Hour DB WB DB WB DB WB DB WB DB WB DB WB DB WB
1 29.6 23.9 29.9 23.7 29.8 23.5 29.5 22.6 27.8 22.4 23.8 18.8 20.7 16.0
2 29.4 23.7 29.8 23.6 29.7 23.4 29.4 22.5 27.7 22.3 23.7 18.7 20.5 15.8
3 29.4 23.7 29.7 23.5 29.6 23.3 29.3 22.4 27.6 22.2 23.6 18.6 20.4 15.7
4 29.3 23.6 29.6 23.4 29.5 23.2 29.2 22.3 27.5 22.1 23.5 18.5 20.3 15.6
5 29.2 23.5 29.5 23.3 29.4 23.1 29.1 22.2 27.4 22.0 23.4 18.4 20.2 15.5
6 29.3 23.6 29.6 23.4 29.5 23.2 29.2 22.3 27.5 22.1 23.5 18.5 20.3 15.6
7 29.5 23.8 29.8 23.6 29.7 23.4 29.4 22.5 27.7 22.3 23.7 18.7 20.5 15.8
8 30.0 24.3 30.4 24.2 30.3 24.0 30.0 23.1 28.2 22.8 24.3 19.3 21.2 16.5
9 30.6 24.9 31.1 24.9 31.0 24.7 30.6 23.7 28.8 23.4 25.0 20.0 21.9 17.2
10 31.1 25.4 31.7 25.5 31.6 25.3 31.2 24.3 29.4 24.0 25.6 20.6 22.6 17.9
11 31.5 25.8 32.2 26.0 32.1 25.8 31.7 24.8 29.9 24.5 26.1 21.1 23.1 18.4
12 31.8 26.1 32.5 26.3 32.4 26.1 32.1 25.2 30.2 24.8 26.4 21.4 23.5 18.8
13 32.1 26.4 32.8 26.6 32.7 26.4 32.3 25.4 30.4 25.0 26.7 21.7 23.8 19.1
14 32.2 26.5 33.0 26.8 32.9 26.6 32.5 25.6 30.6 25.2 26.9 21.9 24.0 19.3
15 32.2 26.5 33.0 26.8 32.9 26.6 32.5 25.6 30.6 25.2 26.9 21.9 24.0 19.3
16 32.0 26.3 32.8 26.6 32.7 26.4 32.3 25.4 30.4 25.0 26.7 21.7 23.8 19.1
17 31.8 26.1 32.5 26.3 32.4 26.1 32.0 25.1 30.2 24.8 26.4 21.4 23.5 18.8
18 31.5 25.8 32.2 26.0 32.1 25.8 31.7 24.8 29.8 24.4 26.1 21.1 23.1 18.4
19 31.0 25.3 31.6 25.4 31.5 25.2 31.2 24.3 29.4 24.0 25.5 20.5 22.5 17.8
20 30.7 25.0 31.3 25.1 31.2 24.9 30.8 23.9 29.0 23.6 25.2 20.2 22.1 17.4
21 30.4 24.7 30.9 24.7 30.8 24.5 30.5 23.6 28.7 23.3 24.8 19.8 21.8 17.1
22 30.2 24.5 30.6 24.4 30.5 24.2 30.2 23.3 28.4 23.0 24.5 19.5 21.4 16.7
23 30.0 24.3 30.4 24.2 30.3 24.0 30.0 23.1 28.2 22.8 24.3 19.3 21.2 16.5
24 29.7 24.0 30.1 23.9 30.0 23.7 29.7 22.8 28.0 22.6 24.0 19.0 20.9 16.2
119
Indoor Design Conditions
• The following indoor design conditions are influential to the cooling load of air-
conditioned spaces and thus need to be defined before design cooling load
calculation can proceed:
• Indoor air state, including dry bulb temperature and relative humidity that
are considered to be comfortable to the occupants or suitable for the activity
or process carried out in individual spaces;
• Occupancy rate, in terms of number of occupants per unit floor area or
square meters of floor area occupied by each person;
• Activity level of the occupants, in terms of the sensible and latent heat
emitted by each person;
• Ventilation rate, in l/s per occupant, m3/s, air-change per hour, etc.
• Casual heat gains, including heat gains from all indoor heat sources, such as
lighting and appliances.
120
Indoor Design Conditions
• Selection of indoor design conditions is largely determined by the end-users’
choices and situations that would arise from use of the spaces, but building and
AC system designers may also make appropriate recommendations.
• Some associated data, e.g. sensible and latent heat gains from occupants, may be
obtained from standard references, such as ASHRAE Handbook, but some others
would need to be ascertained from knowledge about the operating conditions,
such as electricity consumption of equipment / machines for specific processes.
• There may also be regulatory requirements that govern certain indoor design
conditions, such as lighting power density and ventilation rate.
• Though may sometimes be inevitable, use of conservative data for design cooling
load calculations can lead to oversized plants and equipment and degraded
energy efficiency.

121
Indoor Design Conditions
• Typical indoor design conditions for office buildings in Hong Kong

Parameter Value
Indoor design temperature 24 – 25.5oC
Indoor design relative humidity 50 – 60%
Occupancy density 7 – 10m2/p
Sensible heat gain from occupant 65 – 75 W/p
Latent heat gain from occupant 45 – 55 W/p
Ventilation rate 7 – 10 l/s-p
Lighting heat gain 10 – 15 W/m2
Appliances heat gain 10 – 30 W/m2

122
Indoor Design Conditions
• Building Energy Code requirements on indoor/outdoor design temperature and
relative humidity

123
Indoor Design Conditions
• Building Energy Code requirements on lighting power density

124
Design Cooling Load Calculation Method
• The Heat Balance Method is the rigorous method for determining the rate of
heat flow to the air zone and thus the cooling load.
• Based on a detailed heat balance model, a Transfer Function Model can be
developed to allow the cooling load of a space due to heat gains of the space to
be calculated.
• All simplified cooling load calculation methods introduced by ASHRAE were
developed based on the transfer function method.
• Among the simplified manual cooling load calculation methods, the Cooling Load
Temperature Difference / Cooling Load Factor (CLTD/CLF) method was most
widely used. In this method:
• Conduction cooling load = A U CLTD
• Other cooling load = Heat Gain x CLF for the type of load concerned

125
Design Cooling Load Calculation Method
• In the 2001 edition of the
ASHRAE Handbook –
Fundamentals, a new manual
cooling load calculation method,
called the Radiant Time Series
(RTS) method, was introduced
as the standard hand
calculation method, which is
meant to replace all previous
hand calculation methods.

126
 Design Cooling Load Calculation Method

(See Note 1)

[1] absorbed solar heat gain according to Spitler.

Steps of Design Cooling Load

Calculation using the Radiant
Time Series Method
127
Design Cooling Load Calculation Method
• In the RTS method:
• The assumptions are made that the 24 hourly design outdoor weather
conditions for a given month would repeat day after day and the indoor air
state is kept steadily at the design value.
• Conduction Time Series (CTS) is used to estimate conduction heat gain from
an external wall or roof at a particular time step (n):

qn = c0 qi ,n + c1qi ,n−1 + c2 qi ,n−2 +    + c23qi ,n−23

• Where
• qn is the conduction heat gain for the surface at the current time

128
Design Cooling Load Calculation Method
• RTS method (Cont’d)

qn = c0 qi ,n + c1qi ,n−1 + c2 qi ,n−2 +    + c23qi ,n−23

• qi,n-j, for j = 0, 1, … 23, are respectively the input conduction heat gains j
hours ago if the outdoor state were to stay at the same level steadily,
which is given by:
qi ,n− j = AU (Teo,n− j − Tai )

• cj is the conduction time factor (CTF) for j hours ago.

• Values of CTFs for representative walls and roofs can be found in the ASHRAE
Handbook, Fundamentals.

129
Design Cooling Load Calculation Method

130
Design Cooling Load Calculation Method
• RTS method (Cont’d)
• When the conduction heat gains and other heat gains have been calculated,
each would need to be split into its radiant and convective components.
• The convective components will immediately become parts of the total
cooling load of the space under concern.
• The radiant components, however, would need to be converted into cooling
load by using the appropriate radiant time series (RTS), as depicted by the
following equation:

Qr ,n = r0 qr ,n + r1qr ,n−1 + r2 qr ,n−2 +    + r23qr ,n−23

131
Design Cooling Load Calculation Method
• RTS method (Cont’d)
Qr ,n = r0 qr ,n + r1qr ,n−1 + r2 qr ,n−2 +    + r23qr ,n−23
• Where
• Qr,n is the radiant cooling load for the current hour
• qr,n-j is the radiant heat gain at j hours ago, for j = 0, 1, 2, …, 23.
• rn-j is the radiant time factor (RTF) for heat gain at j hour ago , for j = 0, 1,
2, …, 23.
• Typical splits between radiant and convective components of major types of
heat gains of a space are given in the next slide.

132
Design Cooling Load Calculation Method
• RTS method (Cont’d)
• Recommended split between radiant and convective components of major
types of heat gains
Heat Gain Radiant portion Convective portion
Wall, window conduction 0.63 0.37
Roof conduction 0.84 0.16
People 0.70 0.30
Lighting 0.67 0.33
Equipment 0.20 0.80
Transmitted solar 1.00 0.00
Absorbed solar 0.63 0.37
Infiltration 0.00 1.00

133
Design Cooling Load Calculation Method
• RTS method (Cont’d)
• Two types of RTFs are used in design cooling load calculations, for solar heat gains
and for non-solar radiant heat gains in an air-conditioned space:
• RTFs for solar heat gains are applied to transmitted solar heat gains through
fenestrations (Spitler: transmitted total; AHSRAE: transmitted beam only).
• RTFs for non-solar radiant heat gains are applied to every other type of heat gain.
• The difference was due to the practice that transmitted solar heat gains were
assumed to be distributed to the floor only whilst the non-solar radiant heat gains
were assumed to be distributed to all surfaces.
• Representative RTFs for spaces with different thermal mass, denoted by light,
medium and heavy weight constructions are provided in ASHRAE Handbook,
Fundamentals (see Table 19 of Chapter 18 in ASHRAE Handbook, Fundamentals,
2009).

134
Design Cooling Load Calculation Method

135
Design Cooling Load Calculation Method

136
Design Cooling Load Calculation Method
• Method for calculating solar heat gain from fenestration
• A simplified method for calculating solar heat gain through windows and
skylights, which employs solar heat gain factors (SHGFs) based on the
standard DSA glass and a shading coefficient (SC) for the glass concerned, has
been introduced earlier.
• However, in using the radiant time series method for design cooling load
calculation, the transmitted solar heat gain and absorbed solar heat gain
need to be dealt with separately, as different sets of radiant time factors
(RTFs) are to be used for converting the heat gains into cooling loads.
• Therefore, the method for calculating solar heat gains through fenestrations
needs to be modified. The modified method utilizes separate transmitted and
absorbed solar heat gain factors, also derived from the DSA glass.

137
Design Cooling Load Calculation Method
• Method for calculating solar heat gain from fenestration
• Transmitted solar heat gain (TSHG) = A·SC·TSHGF
• Absorbed solar heat gain (ASHG) = A·SC·ASHGF·Ni
• Where
• A & SC are respectively the area and shading coefficient of the
window glazing under concerned
• TSHGF & ASHGF are, respectively, the transmitted solar heat gain
factor and absorbed solar heat gain factor, both based on the standard
DSA glass
• Ni is the fraction of absorbed solar heat that flows toward the indoor
space

138
Design Cooling Load Calculation Method
• Simplified method for calculating solar heat gain from fenestration
• Ni is given by:
hi
Ni =
ho + hi

• Where ho and hi are the combined convection and radiant heat transfer coefficients for
the external and internal surfaces of the glass, respectively
• The transmitted and absorbed solar heat gain factors are given by:
TSHGF =  D I D +  d I d

ASHGF =  D I D +  d I d
• Where ID and Id are respectively the direct and diffuse solar intensities incident upon the
glass (diffuse intensity includes diffuse radiation from the sky as well as ground
reflectance)

139
Design Cooling Load Calculation Method
• Simplified method for calculating solar heat gain from fenestration
• Transmittance and absorptance of DSA glass:
5 5 tj
 D =  t j (cos  ) j
d = 2
j =0 j =0 j+2
5 5 aj
 D =  a j (cos  ) j
d = 2  
j =0 j =0 j+2

• D = Transmittance for direct radiation

• d = Transmittance for diffuse radiation
• D = Absorptance for direct radiation
• d = Absorptance for diffuse radiation
•  = incident angle of direct radiation
140
Design Cooling Load Calculation Method
• Simplified method for calculating solar heat gain from fenestration
• Based on DSA glass performance:
• Values of aj and tj are as given below
j aj tj
0 0.01154 -0.00885
1 0.77674 2.71235
2 -3.94657 -0.62062
3 8.57811 -7.07329
4 -8.38135 9.75995
5 3.01188 -3.89922

• Values of TSHGF and ASHGF · Ni for fenestrations of buildings in a given

location (e.g., Hong Kong) for various principal directions may be calculated
once and used for other buildings.

141
Design Cooling Load Calculation Method
• Calculation of cooling load due to internal heat gains
• Sensible and latent heat gains from occupants, Qocc,s & Qocc,l:
Qocc , s = qocc , s  N occ

Qocc ,l = qocc ,l  N occ

• Where
• qocc,s & qocc,s are, respectively, the sensible and latent heat gains per occupant
(dependent on activity level of the occupant)
• Nocc is the number of occupants in the space (often determined from an occupancy
density and floor area of space)
• The sensible part comprises a radiant and a convective portion, and the
radiant portion needs to be converted into cooling load using the non-
solar RTFs.

142
Design Cooling Load Calculation Method
• Calculation of cooling load due to internal heat gains
• Heat gains from lighting and appliances, Qlgt & Qapp:
Qlg t = A  qlg t

Qapp = A  qapp

• Where
• qlgt & qapp are, respectively, the lighting and appliances heat gains per unit floor area
(both are sensible heat gains)
• A is the floor area of the space
• Each comprises a radiant and a convective portion, and the radiant
portion needs to be converted into cooling load using the non-solar RTFs.

143
Design Cooling Load Calculation Method
• Calculation of cooling load due to ventilation
• Sensible and latent cooling load due to fresh air supply, Qfa,s & Qfa,l:
Q fa, s = V faCpa (To − Tr )

Q fa,l = V fa ( wo − wr )h fg ,0
• Where
• Vfa is the fresh air supply rate for the space(s), often determined from the occupancy
density, floor area and ventilation rate per person to be allowed
• To and wo are the dry bulb temperature and moisture content of outdoor air at the
design condition for the month and hour under concern
• Tr and wr are the dry bulb temperature and moisture content of indoor air at the
design condition

144
Design Cooling Load Calculation Method
• Calculation of cooling load due to ventilation (Cont’d)
• Remarks:
• The abovementioned equations can be applied directly for the purposes
of determining:
• The block cooling load on the central chiller plant; and
• The capacity required of an air-handling equipment serving a
collection of spaces where outdoor air for ventilation is drawn in
locally by the air-handling equipment (i.e. with local fresh air intake).

145
Design Cooling Load Calculation Method
• Calculation of cooling load due to ventilation (Cont’d)
• Remarks:
• Where a central fresh air system is installed to provide pre-treated fresh
air supply to air-conditioned spaces:
• The cooling load due to ventilation may be ignored in determining the
cooling load on the air-handling equipment serving the spaces (this
ignores also the cooling effect that the treated fresh air is able to
provide).
• For determining the capacity required of the fresh air-handling units,
the indoor temperature and moisture content of the indoor air should
be replaced by those of the leaving coil air state of the fresh air-
handling units.

146
Design Cooling Load Calculation Method
• Calculation of cooling load due to infiltration
• Sensible and latent cooling load due to infiltration, Qinf,s & Qinf,l:
Qinf, s = Vinf Cpa (To − Tr )

Qinf, l = Vinf ( wo − wr )h fg ,0

• Where
• Vinf is the infiltration rate for the space, often determined from the air change rate of
infiltration (e.g. 0.5 air change per hour) and the internal volume of the space
• To and wo are the dry bulb temperature and moisture content of outdoor air at the
design condition for the month and hour under concern
• Tr and wr are the dry bulb temperature and moisture content of indoor air at the
design condition

147
Design Cooling Load Calculation Method
• Remarks on cooling load calculation
• Hourly design cooling load calculation for each air-conditioned space needs to
be carried out for one design day per month from June to Dec.
• This is needed to allow the peak cooling load of individual spaces, which may
arise at different times among different spaces, to be identified from the
results.
• The peak value of the total cooling load of a group of spaces, such as rooms
on the same floor served by a common air-handling system, may differ from
the sum of peak cooling loads of the spaces.
• The air-handling system serving a group of spaces should be sized with
reference to the simultaneous peak cooling load of the spaces while terminal
devices serving individual spaces should be sized according to the peak
cooling load of the space concerned.
148
Design Cooling Load Calculation Method
• Remarks on cooling load calculation
• In sizing the cooling capacity of the central chilled water plant, the following
allowances should be made to cater for the fan and pump heat gains:
• An allowance of about 5% of the block total sensible cooling load, to cater
for the fan heat gain;
• An allowance of about 3% of the block total cooling load (including the
above allowance for fan heat gain) to cater for the heat gains from the
chilled water pumps.

Plant Capacity = 1.03 x (Block Total Latent Load + 1.05 x Block Total Sensible Load)

149
End of Part 2

150
Any Questions?

151
The End – Thank You!

152