Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
OPTIMUM DESIGN OF AN EXPANDED CUMULATIVE EXERGY CONSUMPTION
IN A STRAWBALE-WALLED BUILDING
A A Adedeji
Department of Civil Engineering,
University of Ilorin, Ilorin, Nigeria
ABSTRACT
An optimization approach is presented in this paper to minimize the effects of environmental impacts,
in terms of expanded cumulative energy consumption during a building service life, resulting to
negative effects on the occupants due to waste emission. The optimal solution was obtained using the
strong-searched and structured genetic algorithms. A numerical example of a multistorey building,
which was assumed to be built with cement plastered strawbale panels and was compared with the
conventional sandcrete block wall for its life-cycle, is presented as a case study. From this study, the
cumulative exergy consumption obtained for strawbale walled building is 25% of sandcrete walled
building. The results have further shown that strawbale building has high service cost (LCC) at the
initial state of its life cycle, but low energy resource consumption (LCEI). Strawbale building at 30o
orientation has the same values for LCC and LCEI, while LCC is higher than LCEI in case of sandcrete
walled building for 0o and 30o orientation.
Keywords: strawbale, wall, environmental impact, genetic algorithms
INTRODUCTION
It has been established by the international panel of Climate Change (IPCC, 2001) that beside natural
climatic impact, man-made gas emissions are the major root of the climate problem. The enhanced gas
and other artificial emissions affect weather patterns, especially in an enclosure and the entire
hydrological cycle. Beside the climate changes, there are also some other environmental challenges
such as acidification (acid rain), stratospheric ozone depletion, urban air pollution, loss of biological
diversity and so on. Both climates change and other environmental problems result to a large extent
from emissions arising from human activities, in particular, the burning of fossil fuel (IPCC, 2001).
Buildings are energy gluttons and have a large impact on the global climate change and other
energy–related environmental issues. It is reported by the U.S. Department of Energy that buildings
account for 36% of total primary energy consumption and 67% of electricity consumption (DOE 2002),
even in developing countries like Nigeria. More than 35% of energy consumption in our buildings
(residential and manufacturing (Oviemuwo 2001, Jekayinfa, 2006)}, especially in Nigeria, is as a result
of environmental control (use of mechanical ventilators, such as fan, air conditioners etc) for ventilation
because of excessive heat in dry season. As a direct result, buildings account for nearly 35% of CO 2
emissions, 48% of SO2 and 20% of NO2 (DOE, 2002). In response to the buildings’ major impact on
the environment, it is importance to explore ways for a better building design that considers
environmental performance. Appropriate choice and design of materials that would respond to
environmental ecological system is the first and the best approach to this problem.
Many studies have been done in order to optimize building design for energy efficiency. These
studies used the operating energy consumption or life-cycle cost as the performance criterion to
establish optimization model (Adedeji 2002, Miller 1992, Weller 2001, Coley and Schukat 2002).
Because the optimal solutions due to energy consumption is usually different, the cost is treated as a
constraint on energy–efficient measures. Despite the above efforts, Weimim et al (2003) explained that
two major limitations undermine this application in practical building design. These are:
(a) Inappropriate environmental performance criterion: This may be due to (i) the unavailability or
inconsistency of data for environmental impact of building material and component, (ii) few lifecycle environmental impacts simulation programs are available, (iii) both designers and clients
have little interests in reducing embodied environmental impacts because they are not directly
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
related to building costs. These make it necessary to incorporate the holistic impact categories
covering the choice of the material that will transfer the climatic condition into the internal
microclimate for the use of the tenants.
(b) Improper Variable Determination: The inappropriateness of variables can be seen as a variable may
not be properly defined. It is not difficult to observe that many parameters such as window types
can only take discrete values. For example, the window type is represented by its thermal resistance
value (Miller, 1992). Secondly, some variables in the model are not directly design-oriented, but are
sort of auxiliary used data as design options. Sometime this gap cannot be easily handled because
they are not initially incorporated in to the design.
In recognition of the above limitations of former studies, a new optimization model is proposed in
this paper as proposed and used by Weimim et al (2003). Since this model relies on exergy and its
related concepts which according to Moran and Sciubba (1994) is the maximum theoretical work that
can be extracted from a combined system, consisting of a system under consideration. An environment
as a system may pass from a given state to an equilibrium state of the environment. In other words the
system passes to the dead state at which the combined system (a given state and an equilibrium state)
possesses energy but no exergy. These are introduced in the second section. Then the optimization
model and the algorithm employed to solve the formulated problem are described. Finally, a case study
is presented.
EXERGETIC LIFE-CYCLE ASSESSMENT
Life-cycle Assessment (LCA) is an analytical tool that can help in understanding and evaluating the
resource consumption and waste emissions associated with products, packaging, processes and
activities across all stages of their life cycle from materials acquisition to final disposition). The life
cycle of buildings is shown in Figure 1 ((ISO, 1997) where the dashed line denotes the scope
considered in this optimization study. In Figure1, building material properties are incorporated with its
production, since production affects the properties which in turn affect the construction of the structural
elements in its life service. Transportation serves for the movement of materials during construction.
Natural
resource
extraction
Building
material property
and production
Transportation
Element
construction
in-situ
Operation
and service
Maintenance
Demolition
Transportation
Figure 1 Life circle process of a building ((ISO,1997)
As indicated by Barnthouse et al. (1998) global, long-lived impact categories usually have
characteristics that can be dealt with by LCA with acceptable theoretical accuracy, but aggregated LCA
indication for local and transient impact categories have little practical meanings. Therefore, impact
categories considered in this optimization study are the waste emissions that have long-lasting impacts
on the internal microclimate namely, sun radiation, moisture and acid rain and its associated chemicals
that are penetrating the building envelop material (wall and roof).
It is difficult, however, to characterize natural resource depletion and to integrate various impact
categories with different units and magnitudes in the context of LCA as reviewed by Finnveden (1994).
Though, normalization may not completely address this difficulty because different normalization
coefficients may lead to conflicting conclusions when weighting integration alone is used as a
technique compare alternatives in conjunction with the exergy process.
Unlike energy, exergy is always destroyed because of the irreversible nature of the process. Exergy
is an extensive property whose value is fixed by the state of the system once the environmental impact
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
has been specified. Therefore, the evaluation of exergy depends on both the state of a system under
consideration and the conditions of the reference environment. Most applications of exergy analysis in
the published literatures concentrate on thermal system design (Moran 1982, Adedeji 2002) chemical
and metallurgical process analysis (Szargut et al.1988). The exergy can also be incorporated into LCA to
address the issues of the natural resource depletion characterization and valuation
Cumulative exergy consumption (CExC) was proposed by Szargut et al (1988) of all natural
resources consumed in all the exergy of a production process. Unlike cumulative energy consumption,
exergy takes into account the non-energetic raw materials obtained from the environment in which the
building is built. Therefore, cumulative exergy consumption can be used to measure natural resource
depletion.
Exergy is not only a measure of resource consumption; it is also a measure of waste emissions.
Because, exergy can be used to evaluate the degree of equilibrium between a substance and meaningful
relationship can be established between the environment impact potentials and the energy of waste
emissions (Ayres et al. 1998). Abatement or lessen energy is employed in this study to evaluate the
required energy to remove or isolate the emissions from the building environment. Although the value
of abatement energy for a given waste emissions is technology-dependent, it is possible to determine an
average abatement for each emission. One of the randomly generated solutions used by Caldas and
Norford (2003) in the first generation has performed almost as well as the best Pareto solution in
terms of energy, but its construction costs were about 33% higher. Pareto optimization, in genetic
algorithm, as the process of the optimizer, is towards the pareto front rather than towards an absolute
minimum or maximum. This demonstrates the usefulness of applying the Pareto–front the first to the
hundredth generation of only 6% on average (from 24.7 MWh to 23 MWh), but the reduction
construction costs was about 41% (from $8434 to $4965) including materials.
Costs in the Pareto-front studies may be an effective measure for achieving similar energy
performance at lower first costs. Costs for the different materials were obtained by averaging prices
provided by several retailers in Nigeria.
Thus, by extending the cumulative exergy consumption to include abatement exergy (the beating
down of exergy), all the resource inputs and waste outputs can be unified together. This expanded
cumulative exergy consumption can consider both resource inputs and waste emissions to the
environment. It is particularly suitable for the life cycle optimization with respect to environmental
performance. The main advantages of the cumulative exergy consumption are that:
 Resource depletion and waste emissions can combine together, and therefore, the life cycle
environmental impacts can be condensed into one single objective function.
 Exegetics resources and non-energetic materials can combine together to characterize the resource
depletion.
 Only one criterion is employed to avoid weights or other qualitative judgment in the evaluation of
environmental impacts.
A demanding task in applying energetic life-cycle assessment is to collect consistent and reliable
data for analysis. Because there is available database that can directly provide cumulative energy
consumption and environmental impacts covering typical building materials and constructions, a life
cycle assessment tool specially developed for buildings, is employed here to extract the natural resource
consumption and waste emissions. These data can be used to derive cumulative exergy consumption
and abatement exergy. Strawbale masonry (straw bale plastered with cement or other types of suitable
mortars) has been selected because of its prominent advantages over conventional wall materials
(sandcrete, earth, concrete) in the following aspects.
 It can offer values of environmental impacts (high insulation material against heat and cold
respectively) for each life-cycle stage of a building (Adedeji, 2002). These values are essential to
drive cumulative exergy consumption and other building envelopes.
 The availability of straw (stalks from maize, sorghum, rice, elephant grass etc) they have been
considered a wasteful material and may be used rarely for animal feeds. This particular advantage
makes it convenient to locate corresponding cost found in data and can be compared with other
common materials (sandcrete, earth etc).
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
OPTIMIZATION MODEL AND ALGORITHM
Optimization Model
Variables in this work represent those parameters that define a building design and were passed to a
building simulation program. For example, window-type is a variable in the system. Several window
types can be set as alternatives to other window types to the designer’s requirement. Some variables
such as window type can only be of discrete type while some variables (e.g., orientation) can be either
continuous or discrete.
a
Side 3
Side 4
Side 2
b
North
(building)
Orientation 30
True North
Figure 2 Definition of orientation and aspect ratio.
In this research, the types of buildings considered are limited to a rectangular shape with known
total floor area. Figure 2 illustrates the definition of some variables, as proposed by Weimin et al
(2003) are:
 Building Orientation (Orientation)
 Aspect Ratio (aspect Ratio) defined as a/b, where a and b are shown in Figure 2.
 Window Type (WinType).
 Window area ratio for each building façade (WinRatio)
 Wall Type (WallType) in terms of materials
 Each layer of wall (WallLayer). The total number and the arrangement of layers are dependent on
wall type.
 Roof Type (RoofType).
Because it is essential to explore the relationship between economical performance and
environmental performance, Life cycle Cost and Life-Cycle Environmental impact (LCEI) are coupled
together using weighted secularization method. Assuming (x) is the variable vector, the integrated
objective function F(x) can be expressed as:
F(x) = w1 LCEI (x) + w2 LCC (x)
(1)
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where w1 and w2 are predefined weights for life-cycle environmental impact and life-cycle cost
respectively. LCEI is the life-cycle environmental impact using energy as an indicator criterion, LCC.=
life-cycle cost for service. If the weights were reversed and set to (w1 = 1 and w2 = 0) then all the
emphasis is placed on minimizing the variance of the objective function without regard to the mean.
There are an infinite number of possible weights that are each Pareto optimal, in which its solution is
not possible to improve one of the objectives without worsening the others. The weighted sum
approach does not generate all the Pareto solutions for some problem, but since this work is focusing on
the extreme points of the Pareto front, adoption of this method is adequate (Parkinson et al, 1998). The
general expression (for construction and operational or services) to calculate LCEI is:
LCEI (x) = EE (x) + OE (x)
(2)
where EE = Embodied energy, that is the expanded cumulative energy consumption due to building
construction and is assumed 0 initially, because most of the sources data before the commencement of
the construction are not certain and that the building is assumed not yet in service, and only OE which is
the operating energy is considered as the expended cumulative energy consumption due to building
operation and service. EE (x) and OE (x) were employed in the analysis when the building is
assumed in service. The general expression to calculate LCC is:
LCC (x) = IC(x) + OC (x)
(3)
where, IC = Construction cost due to waste emission, was not as well considered initially in the analysis
because the analytical building was assumed not to be in service, but are used during the service life,
OC = Operating and service cost, including both demand and energy consumption costs.
In this work however, the building load calculations is coupled with the optimization model to
estimate the annual peak energy consumption and demand (CExC) due to ventilation in the room as the
results of heat produced (QH) by human, lighting (QL), electric motor engine (QE), radiation by heater or
wall materials(QR) and ventilators (fan or air conditioner) (QV).
Structured Genetics Algorithm
The selection of an optimization algorithm depends on the peculiarities of a problem domain. The
previous formulated problem in section 3.1, equations (1) to (3) has the following characteristics:



If the following variables and corresponding number of alternatives (the number in parenthesis) are
considered: orientation (2), aspect Ratio (1), WinType (3), WallType (3), RoofType (1), WinRatio
(1), each WallLayer (1), then there are about 2xE6 or 2.5xE10 possible solutions to explore.
Both continuous and discrete variables may exist in the same optimization problem.
The shape of criteria space is unknown.
The genetic algorithm works in the following manners: The first step is to represent a legal solution to
the problem to be solved by using a string of genes (a gene is a unit in chromosome controlling
heredity), that can take on some value from a specified finite range. This string of genes that represents
a solution is the chromosome. Then an initial population of legal chromosomes is constructed at
random. And at each generation, the fitness of each chromosome in the population is measured. The
fitter chromosomes are then selected to produce offspring for the next generation, which inherit the best
characteristics of both the parents – the survivor of the fittest by Darwin’s theory of evolution. After
many generations of selection, for the fitter chromosomes, the result is expected to be a population that
is substantially fitter than the original. Genetic algorithms consist of: Chromosomal Representation,
initial population, fitness evolution, selection, crossover and mutation.
Genetic Algorithms (GAs) are good at exploring large search space because of its implicit parallel
computation mechanism. The binary string representation can deal with both continuous and discrete
variable. Compared with conventional numerical methods, genetic algorithms are able to locate global
optimum without trapping into local extreme point. All these advantages determine that GA is an
appropriate candidate to solve the above formulated problem. Structured GA lies in its redundant
genetic materials and a genetic activation mechanism.
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
CASE STUDY
Problem Formulation
The 14th (last) floor of a multi-story (Shell House) office building located in Lagos Island, Nigeria,
is a building in which the environmental and physical data has been measured and used in this work.
The results of measurement and data (size of the rooms, area of opening sizes and types, wall materials
and finishes, electrical lighting, fans and air-conditioning power outputs) used were parts of the work
carried out by Ojediran (2004). The floor plan has a total area of 238.336m2 with 50-year life
expectancy.
The following assumptions (materials, and other physical properties) were made and used in the
analysis:





Only the energy, consumed in the hot season of March, April and May, has been used in
the analysis.
Rooftop units of aluminum are assumed to be used.
Two wall types are considered; cement plastered straw bale and sandcrete block (used for
the construction of the specimen building) walls. Other properties are shown in Table 1.
Because the sizes of the relatively expensive windows were small, even in the best energyperformance cases, the size values are not used in the analysis.
Only one roof type has been considered with asbestos cement hanging ceiling, shielding the
heat away from the room. So, the energy factor, through the roof at this stage, is negligible
and it was not used in the analysis.
Table 1 Average properties of materials
Properties
Size, L x B x H (mm)
Density (kg/m3
U-value (W/m2K)
R-value (m K/W)
Reliability of wall
Strawbale wall
1066 x 406.4 x 584
9300
0.13 (of 420mm thick)
13.21(of 420mm thick)
0.89
Sandcrete wall
445 x 215 x 215
1500
1.73 (of 250mm thick)
0.58 (of 250mm thick)
0.77
Note: U –value = thermal conductivity, R-value = thermal resistivity
Energy factors produced and consumed during the three months as the annual peak energy
consumption and demand (CExC) in section 3.1 are shown in Table 2 and were obtained using equations
(a1) to (a5) in Appendix A.).
Energy
factor
Table 2. Energy consumed per hour
Energy consumed (MJ)
Strawbale wall
Sandcrete wall
South East
East
South East
East
QH
QL
QE
QR
QV
Total
0.076
0.076
0.362
0.362
0.476
0.476
0.133
0.133
0.162
0.162
0.567
0.567
0.059
0.067
0.222
0.222
1.417
1.417
6.909
6.909
2.190
2.190
8.193
8.193
Note: (QH) by human, lighting (QL), electric motor engine (QE), radiation
by heater or conduction from sun’s heat through wall materials(QR) and
ventilators (fan or air conditioner) (QV).
For definitions of the energy factors, see Appendix A.
Cumulative energy consumption per hour is 2.190 MJ for the building walls built with strawbale
and 8.193 MJ for the building with sandcrete. The general inflation rate, discount rate, and energy
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
escalation rate of 30% is not included in the computation as that varies and the addition could be made
as required. In October 2005, the electricity rate was N5.187/h (kW) of billing demand of the electricity
consumption.
Single glazing is the window panel-type used for this building. There are two wall types: masonry
sandcrete block wall built as infill into the reinforced concrete frame. In this analysis, the first wall type
is composed of cement plastered strawbale as shown in Figure 3a. The second wall type is composed of
sandcrete blocks, and finished with cement plasters as shown in Fig.3b. The south-wall absorptivity
was always at high values, either 0.6 or 0.8 while the north-wall absorptivity had more random values,
because solar gains were not significant in that direction. Hence, its absorptivity values were not used in
the analysis.
Plaster – Strawbale – Plaster
Plaster – Sandcrete - Render
Direction of
Environmental
conditions
Microclimatic
Region
tplaster
tstraw
t
tplaster
tplaster
tsandcrete
tplaster
t
Figure 3 Sections of the walls
Another set of simulation was done with the building rotated by 30o so that it would face South-East.
Energy-consumption levels were always higher for this orientation than for South-North, as expected.
However, costs remained lower,
Considered Genetic algorithms operations are:
-
Global search algorithms: GA
Local search algorithm: gradient method
Population size: 20
Crossover rate 0.1
Mutation; 0.1
Reproduction rate: 2 offsprings
Generations: 3 of 0.15
Tournament selection and elitist strategy are used in this GA implementation.
RESULTS AND DISCUSSION
Four weighting sets are used in this study. The two extreme cases (case 1 and case 3) are actually single
performance criterion optimization with the life cycle environmental impact and life-cycle cost as the
objective function respectively. The minimum function value was obtained from the two extreme
weighting cases 2 and 4. The programme for each weighting set are used to normalize the life-cycle
environmental impact and life-cycle cost in weighting sets are used to normalize the life-circle
environmental impact and life –cycle cost in weighting case 2 and 4. The optimal values of variables
obtained from the best run of each weighting set are presented in Table 3 and in Figures 4 and 5. It can
be seen from this table and the figures that:
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
(1) The optimal aspect ratio is about 0.33 when the optimization criterion is the life-cycle
environmental impact, for the strawbale-walled building and 0.80 for the life-cycle cost for
sandcrete-walled building.
(2) When environmental performance is the only criterion, the plastered strawbale walled building is
economically viable than the building of sandcrete walls. However, sandcrete block wall is
recommended when the life-cycle cost is considered in the overall criterion.
(3) The minimum allowed window area is preferred for both environmental and economical
performance.
(4) Threshold is 0.48 in the sandcrete walled building and 076 in strawbale house when considering the
cost of material and service as a design criterion.
(5) At the weight value of 1, the energy consumption of the two wall materials is the same. It
was observed that the energy consumption of strawbale house increases with time, but
decreases in the building of sandcrete walls.
Table 3 Optimal values of variables from the weighting sets
Variables &
performance
Orientation
Aspect ration
WinRatio
WallType 1
(Strawbale)
WallType 2
(Sandcrete)
LCEI (MJ)
LCC (N)
w1=0.7, w2=0.3
1
w1=0.3, w2=0.7
2
w1=1, w2=0
3
W1=0, w2=1
4
30
0.1
0.54
1
0
0.9
0.54
1
0
0.8
0.54
1
0
0.33
0.54
1
1
1
1
1
SB
77066.97
7398234
SC
108537.18
32447643.75
SB
4778.74
36240238.1
SC
130927.95
13984805.
SB
27532.36
10568806.71
SC
150617.35
15070.
SB
100612.68
46315075.72
SC
85005.53
90302.50
60
2
Sandcrete wall R = 0.4617
6
50
40
30
Strawbale wall, R2 = 0.7824
20
10
0
-10 0
0.3
0.7
1
WEIGHTS (w 1 and w 2)
Figure 4 Priority cases (w1, w2) due to life cycle for
cost criteria on microclimate condition
ENERGY CONSUMPTION
ON LIFE-CYCLE (L
CEi) MJ
80
70
x10 (N)
COST DUE TO MATERIAL
AND SERVICES (LCC)
Note: LCEI = Life-cycle by environmental impact due to energy resource consumption, LCC =cost
due to service. SB = strawbale wall, SC = sandcrete block wall. Note: 1N = $0.0074 (Nov., 2004).
40
35
30
25
20
15
10
5
0
Sandcrete w all, y = -11.237Ln(x) + 37.18
Straw bale w all, y = 12.926Ln(x) + 4.8086
0
0.3
0.7
WEIGHTS (w 1, w 2)
Figure 5. Priority cases(w1, w2) due to life-cycle
for energy consumption on microclimate
The building performance corresponding to each optimal solution is also shown at the bottom of
Table 3. The evolution of the best solution ever found for life-cycle environmental impact and lifecycle cost in Figures 4. The process evolves rapidly during the first 30 generations and then slowly at
later generations. This demonstrates that genetic algorithms can perform better in locating the optimal
region than in local search. It can be observed that the optimization is effective to improve building
performance. In Figure 4 and 5, it is shown that cost of materials and the service is low in a sandcrete
walled building during its life cycle. The strawbale building consumes less energy during its early
service at the weighted value of 1. it is shown in Figure 6 that strawbale walled building resists
environmental impact than the sandcrete-walled house at the generation of 0.6 and 0.1 respectively.
1
Paper published by: Nigerian Journal of Construction Technology and Management, Vol. 7, No.1, 2006, pp. 146-156
1.2
Sandcrete wall
FITTNESS
1
Strawbale wall
0.8
0.6
0.4
0.2
0
10
20
30
40
50
60
GENERATION
Figure 6 Life-cycle environmental impact convergence.
CONCLUSION
Exergy is a useful concept to be employed in life-cycle environmental optimization problems. It can
overcome the difficultly brought by integrating impacts with varied magnitudes and units. With
expanded cumulative energy consumption, the optimization problem can be simplified by incorporating
all impact categories into one objective function.
The results have shown that threshold is 0.48 in the sandcrete walled building and 076 in strawbale
house when considering the cost of material and service as a design criterion.
At the weight value of 1, the energy consumption of the two wall materials is the same. It
was observed that the energy consumption of strawbale house increases with time, but
decreases in the building of sandcrete walls.
Because the economical performance and environmental performance cannot take optimal values at
the same time, a multi-criteria optimization model is highly useful for decision-making in an
environmental – friendly building design. A disadvantage of the weighted scarlarization technique is
that only one optimal value is obtained for each weighting set. Different weighting sets need to be
tested to explore different optimal solution. Nevertheless, the application of the weighted values gives
the quick view of the conditions to take into consideration in design.
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APPENDIX A
QH = Ψ(He, Hc,, Hr,, Hs)
(a1)
where He is Heat loss due to evaporation, Hc is the heat loss/gained by convention, Hr is the heat gained
by radiation and Hs is the restored in the body.
QL = Ψ(P, c1, c2),
(a2)
where P is the total energy loss due to radiation, c1 = coefficient of light which depends on the
production of heat and c2 = coefficient of electric light (average of 13.0)
QE = Ψ(c3, c4, n, m)
(a3)
where c3, c4 are coefficients for moving electric motor (average of 0.7), residual coefficient (1.0), n =
power of motor(maximum of 3000 Watts and m is the motor efficiency ranging from 0.5 kW to 40 kW
for efficiency of 70% to 92% respectively.
QR = Ψ(Ao, Aos, Lo, Co, S),
(a4)
where Ao is the effective window area of incoming air, Aos is the area of window exposed to sun’s
radiation Lo is total intensity of the sun heating the window, Co is the corrective coefficient ( 1 for a city
like Lagos, and1.5 for a rural area) and S is shadow coefficient (ranging from 0.13 to 0.56 of a 45o
opened but dark window to translucent semi-dark open 450 illumination) for window glass panel.
QV = Ψ (V, Pv, nfa)
(a5)
where V is the air flow rate given off by ventilator, Pv is the total pressure of ventilation nfa is the
ventilation offect on the ventilator (= 0.5)