INTRODUCTION
The energy demand in the world is increasing very fast due to the increasing
number of developing countries and further growth of energy consumption in developed
countries has led to a global effort to develop and use alternative energies
such as wind, solar, hydro, biomass, etc. Among these, sun is a primary source
of energy and all form of energy on the earth are derived from it. Solar energy
with its endless origin and being free from pollution and its safety use may
be the answer to the energy problems of the coming centuries. It is also one
of the intermittent forms of energy and therefore requires the methods of utilization,
which are different from those of the conventional form of energy. If we make
the solar energy as a target of daytoday consumption of energy in various
forms, then at least 60% of our energy requirements shall come from solar energy
sources (Ghosh, 1997).
The solar chimney consists of a chimney coupled with a translucent collector,
which heats the air near the absorbing media and guides it to the base of a
tall chimney. The buoyant air ascends in the chimney and electricity is generated
by the warm air moving through one or more wind turbines at the base of the
chimney.
In 1981, a solar chimney power plant was built in Manzanares, Spain. Which
was funded by the German Ministry of Research and Technology (BMFT), has been
a significant milestone in the development of solar chimney technology, as it
has motivated many researches to further study on the potential of generating
power using solar chimneys.
Throughout the day, solar energy is being partially absorbed by earth surface,
which is covered in part by buildings and houses. Solar chimney is an effort
to develop a new technique to utilize the outside surface of houses roof to
accumulate solar radiation. Suitable absorbing medium is required to be investigated
for use as absorbing and storage media of solar radiation. The thermal energy
will convert to kinetic energy in the adjacent air particles resulting in stream
flow. By installing a transparent cover, the flow is guided to operate a Savonius
wind rotor mounted horizontally on top of the structure.
In Spain 50 kW experimental plant was built which produced electricity for
eight years, thus proving the feasibility and reliability of this novel technology.
The chimney tower was 194.6 m high and the collector had a radius of 122 m.
It produced an upwind velocity of 15 m sec^{1} under no load conditions.
Operating costs of this chimney were minimal. Fundamental investigations for
the Spanish system were reported by Haaf (1983). In
which a brief discussion of the energy balance, design criteria and cost analysis
was presented. Pasumarthi and Sherif (1997) developed
a mathematical model to estimate the temperature and power output of solar chimneys
as well as to examine the effect of various ambient conditions and structural
dimensions on the power output.
Von Backstrom and Gannon, (2000) presented a onedimensional
compressible flow approach for the calculation of all the thermodynamic variables
as dependence on chimney height, wall friction, additional losses, internal
drag and area exchange. They developed an analysis of the solar chimney including
chimney friction, system turbine, exit kinetic losses and a simple model of
the solar collector. The use of solar chimneys in areas as crop drying and ventilation
is considered beyond the scope of the present work. Ong
(2003) proposed a mathematical model of heat transfer in a steady state
for a solar chimney, and contrast the model with a real solar chimney. Bernardes
(2003) developed solar chimneys, aimed particularly at a comprehensive analytical
and numerical model to estimate power output of solar chimneys as well as to
examine the effect of various ambient conditions and structural dimensions on
the power output. Gannon and Backstrom (2004) presented
analytical equations in terms of turbine flow and load coefficient and degree
of reaction, to express the influence of each coefficient on turbine efficiency.
Berdahl and Martin (1984) designed a solar chimney system
for power production at high latitudes, and its performance has been evaluated.
A mathematical model and a code on MATLAB platform have been developed based
on monthly average meteorological data and thermodynamic cycle. Pretorius
and Kroger (2005) studied the influence of convective heat transfer equation,
more accurate turbine inlet loss coefficient, quality of collector roof glass
and various type of soil on the performance of a large scale solar chimney power
plant. Results indicate that the new heat transfer equation reduces plant power
output considerably.
Fluri and Backstrom (2008) investigated analytically
the validity and applicability of the assumption that, for maximum fluid power,
the optimum ratio of turbine pressure drop to pressure potential (available
system pressure difference) is 2/3. A more comprehensive optimization scheme,
incorporating the basic collector model of Schlaich in the analysis, showed
that the power law approach is sound and conservative. Castillo
(1984) have proposed dimensionless variables to guide the experimental study
of flow in a smallscale solar chimney. Computational Fluid Dynamics (CFD) methodology
was employed to obtain results that are used to prove the similarity of the
proposed dimensionless variables. Bhatti and Shah (1987)
studied analytical and numerical theory of roof top solar chimney for ventilation
purpose. In 2008 they studied the inclination angle on space flow pattern and
applied to roof solar chimney and to enhance the natural ventilation. Chungloo
and Limmeechokchai,( 2008) applied CFD technology for simulation to the
roof solar chimney for ventilation purpose.
The main objective of the this study is to present the development of the utilization
of the solar as energy source by using the solar chimney technique. Also, a
modification is suggested to use the roof top solar chimney as a system for
solar energy conversion to generate small scale of power. For that, a mathematical
model is established and presented based on thermal and mass balances. Preliminary
results have been predicted and presented to show the applicability of the technique.
WORKING PRINCIPLES OF ROOF TOP SOLAR CHIMNEY
For the system to be in ideal conditions, different geometries could be tested
in order to find the most suitable in attaining the optimum power. Using CFD
simulation of the solar chimney under various conditions is made to determine
the most optimum performance of the smallscale chimney. The results from the
analytical and CFD simulation are compared with experimental model measurements.
A solar chimney consists of three main components; a: the solar collector or
the greenhouse, b: the chimney and c: the turbine.
The cover and collector are inclined at an angle, θ and at a perpendicular
distance, d apart. Due to the distance between the cover and the collector,
a pathway is created for air flow. During sunny days, solar radiation will penetrate
the transparent cover and heat up the collector. The thermal energy transfers
to the air in the pathway causing an increase in the air temperature. The hot
air rises and exits at the top while cooler air is drawn in from the bottom,
providing a continuous air flow. Ambient air at temperature, T_{a} enters
the pathway from the bottom of the chimney and flows upward to the top and exits
at temperature, T_{ext} and velocity of V_{ext}. A Savonius
rotor linked to generator is to be installed in the chimney to convert the kinetic
energy of the airflow to electric power. A schematic diagram of the Rooftop
solar chimney has been shown in Fig. 1.
Solar radiation (I) passes through the transparent cover, with some energy
reflected from the cover, q_{ref,cover} and some energy absorbed by
the cover, q_{abs,cover}. The remaining energy, I_{τ} reaches
the collector which is painted black to enhance heat absorbance.

Fig. 1: 
Schematic of rooftop solar chimney (Ghosh,
1997) 
Upon striking the collector, the energy further dissipates into two main components;
the energy irradiated from the collector, q_{rad, collector} and the
energy absorbed by the collector, q_{abs,,collector}. The heat absorbed
by the collector is transferred to the adjacent air by convention. Due to the
heat transfer, q_{conv,air }from the collector surface, the air
gains kinetic energy. The power output from the rotor is influenced by the energy
of the air. Hence, the ultimate goal is to maximise the energy transferred to
air, q_{conv,air}.
MATHEMATICAL MODELING
Solar radiation on tilted surfaces: In order to find the beam energy
falling on a surface having any orientation, it is necessary to convert the
value of beam flux from the sun to an equivalent corresponding to the normal
surface. The total solar radiation is the sum of beam , I_{b} and diffuse
radiation, I_{d} on a surface:
The declination, δ: The declination δ is the angle made by
the line joining of the centers of the sun and the earth with its projection
on the equatorial plane. Cooper has given the relation for calculating the declination
(Padki and Sherif, 1992):
where, n is the day of the year.
Local apparent time is the time used for calculating the hour angle (ω).
This can be obtained from the standard time observed on a clock by applying
two corrections. The first correction arises because of the difference between
the longitude of a location and the meridian on which the standard time is based.
The correction has a magnitude of 4 min for every degree difference in longitude.
The second correction called the equation of time correction is due to the fact
that the earth’s orbit and rate of rotation are subject to small fluctuations:
Local apparent time = Standard time + 4(L_{st}L_{loc})+E 
Where:
E = 229.2 (0.000075+0.001868 cos B0.032077
sin B 0.014615 cos 2B0.04089 sin 2B 
where, B = (n1)360/365.
Hour angle (ω) Is defined as:
The angle of incidence of beam radiation on a surface is:
The zenith angle (θ_{z}): It is the angle made by the sun’s
rays with the normal to a horizontal surface. In this case the surface is assumed
to be horizontal surface, β is 0°:
It is often necessary for calculation of daily solar radiation to an integrated
daily extraterrestrial radiation on a horizontal surface:
where, ω_{2} and ω_{1 }limits as time rather than
hours.
The effect of atmosphere in scattering and absorbing radiation is visible with
time as atmospheric conditions and air mass change. Duffie
and Beckman (1991) has presented a method of estimating the beam radiation
transmitted through clear atmosphere which takes in to account of zenith angle
and altitude for a standard atmosphere and for four climate types. The atmospheric
transmittance for beam radiation (τ_{b}) is given by:
The constant:
a_{0 }= 0.4237  0.00821(6ht)^{2
}a_{1} = 0.5055 +0.00595(6.5ht)^{2
}k = 0.2711 + 0.01858(2.5 ht)^{2} 
Therefore, the beam radiation is:
Liu and Jordan (1960) have developed an empirical relationship
between the transmission coefficients for beam and diffuse radiation:
Beam radiation: The ratio of the beam radiation flux falling on a tilted
surface to that falling on a horizontal surface is called the tilt factor (r_{b})
for beam radiation:
Diffuse radiation: The tilt factor r_{d} for diffuse radiation
is the ratio of the diffuse radiation flux falling on the tilted surface to
that falling on a horizontal surface:
Reflected radiation: The tilt factor on reflected radiation is given
by:
Flux on tilted surface (I_{t}): The ratio of flux falling on
a tilted surface at any instant to horizontal surface is:
Thermal analysis: The main objective of the mathematical model was to
predict the airflow rate through the solar chimney with inclined absorber. For
predicting the performance of solar chimney, study of the heat transfer through
natural convection was conducted. Major parameters in this study are temperature
of absorber and glass surface, temperature of air inlet and outlet, ambient
temperature, flow velocity, area of inlet and outlet opening. Writing energy
balance equations for absorber surface, glass surface and air column and solving
them for (T_{g}), (T_{c}) and (T_{f})to calculate airflow
rate have sought a mathematical solution. Air enters the chimney at the bottom
opening with an inlet temperature, (T_{f,i}) which is assumed equal
to the uniform room air temperature (T_{r}). Hot air exits from the
top of the chimney at outlet temperature (T_{f,o}). Temperatures at
the surfaces of the glass (T_{g}) and wall (T_{w}) are assumed
to be uniform. The inlet opening at the bottom of the chimney is assumed to
be equal to or smaller than the top outlet opening. Resistance to flow due to
friction along the surfaces is assumed negligible compared to the pressure drops
at the inlets and outlet openings.
The thermal network for the physical model considered is shown in Fig.
2 . The following equations may be written by considering the heat balance
at the points:
At the glass (T_{g}):
At the collector (T_{c}):
Mean air temperature in the air channel T_{f}:
The mean air temperature also calculated from:
The heat transferred to the air stream flowing upwards under natural convection
in the air gap between the glass and wall.

Fig. 2: 
Solar energy pathways 
The useful heat transferred to the air flowing in the gap is given by:
substitute the value of T_{f,o} from Eq.17, we get:
Introducing:
Then, the useful heat transferred may be expressed as:
Heat transfer coefficients and fluid properties may be evaluated at the respective
mean temperatures. By substitution, we obtain:
The mean temperatures are determined by arranging (22) (23) and (24) in matrix
form as:
Which may be determined by matrix inversion, as:
Air flow analysis: The volumetric air flow rate at the outlet opening
for uniform air temperature is given by:
The air mass flow rate is thus:
where, A_{r} = A_{o}/2A_{i}.
The air velocity is then:
Radiation heat transfer coefficient from glass cover to sky: The radiation
heat transfer coefficient from the top glass surface to the sky referred to
the ambient temperature is obtained:
The sky temperature was calculated as:
T_{s} = 0.0552T_{a}^{1.5} 
Heat transfer convection from glass cover due to wind: The convection
heat transfer due to wind is:
U_{t} is the overall top heat loss coefficient from glass cover to
ambient, due to the combined effect of convection by wind, radiative heat transfer
from glass cover to sky:
Heat transfer between collector and glass: The radiation heat transfer
coefficient between collector and glass cover may be obtained from:
In the present study, the flow has been examined whether it is free or forced
convection and the criteria to estimate the heat transfer coefficient in the
present work; the flow has been examined whether it is free or forced convection
and the criteria to estimate the heat transfer coefficient in the gab is selected
accordingly. In determining the mean convection heat transfer coefficient, ,
the combined (forced and natural) convection model is considered. Based on the
combined convection model, the resultant Nusselt number Nu_{c} is related
to the Nusselt numbers of forced convection Nu_{F} and natural convection
Nu_{N} as:
Where:
and for forced turbulent flow, and 0.6 < Pr < 60:
For the natural convection:
For 1708 < Ra cos β < 5900:
for 5900 < Ra cosβ < 9.23x10^{4}:
For 9.23x10^{4} < Ra cos β < 10^{6}
Solar radiation: According to Ghosh and Tiwari (2008),
the solar radiation heat flux absorbed by the glass cover is given by:
and the solar radiation heat flux absorbed by the blackened wall is given by:
_{}
Instantaneous efficiency: The instantaneous efficiency of heat collection
by the solar chimney is calculated:
The produced electrical power, p_{e} in watts is evaluated by:
RESULTS AND DISCUSSION
Theoretical performance of solar chimney was calculated. From the graph we
can see that if the intensity of solar radiation increases correspondingly increases
the temperature of air, mass flow rate and velocity of air.
Figure 3 shows the intensity of the solar radiation from
morning 8 am to 6 pm From the graph it is noticed that intensity of solar radiation
is maximum at 12pm to 1pm and after that it starts to decrease.
From Fig. 4, it can be seen that mass flow rate inside the
solar chimney increases corresponding increase the intensity of solar radiation.
It reaches maximum at 1pm after that start to decrease.
Same thing happens in the case of velocity also, as in Fig. 5.
It reaches its maximum point in between 12 to 2 pm.
Figure 6 shows that the overall performance of solar chimney.
Performance of chimney starts to increase from 8 am up to 1 pm.

Fig. 4: 
Transient behavior of the mass flow rate in the system 

Fig. 5: 
Velocity values of air at chimney base during the day time 

Fig. 6: 
Hourly performance index of system 
At 1 pm it reaches its maximum performance after that start to decreases. At
6 pm the performance of RTSC is very low, in this case we must use any back
up source of heat.
CONCLUSION
Roof Top Solar Chimney is the subject of investigation in the present project.
Roof top solar chimney is slightly modified version of the traditional solar
chimney power plant that has been built around the world. To make the system
more efficient, enhancing heat resource is proposed to be utilized. This system
will be modeled and studied under various operational conditions and different
geometries. The chimney operation is modeled under the assumption of solar operational
mode by specifying the heat transfer and the fluid flow mechanism. The modeling
tools are analytical and computational. The chimney operation is modeled under
the assumption of solar operational mode by specifying the heat transfer and
the fluid flow mechanism. From the analytical result after the 6 p.m. the performance
of chimney is very low. To develop the technique for smallscale power generation,
there are two requirements. First is to enhance the solar energy conversion
by better absorbing media. Secondly is the use of thermal backup to allow continuous
operation of the system during night and cloudy days.
ACKNOWLEDGMENT
The authors acknowledge Universiti Teknologi PETRONAS for sponsoring the project
under STIRF internal fund.
NOMENCLATURE
A_{o}, A_{i} 
: 
Cross sectional areas of outlet and inlet to air flow channel 
A_{r} 
: 
Ratio of A_{o }/A_{i} 
C_{f} 
: 
Specific heat of air 
Cd 
: 
Coefficient of discharge of air channel inlet 
d 
: 
Distance between collector and glass 
h_{g} 
: 
Convective heat transfer coefficient between glass cover and air channel 
h_{c} 
: 
Convective heat transfer coefficient between collector and air. 
h_{rs} 
: 
Radiative heat transfer coefficient between glass cover and sky. 
h_{rcg} 
: 
Radiative heat transfer coefficient between collector and glass 
h_{wind} 
: 
Convective wind heat loss coefficient 
m· 
: 
Mass flow rate 
q" 
: 
Heat transfer to air stream 
S_{1} 
: 
Solar radiation heat flux absorbed by glass cover 
S_{2} 
: 
Solar radiation heat flux absorbed by collector 
T_{a} 
: 
Ambient temperature 
T_{f} 
: 
Mean temperature of air in channel 
T_{f,i} 
: 
Inlet temperature of air in channel 
T_{f,o} 
: 
Outlet temperature of air in channel 
T_{g} 
: 
Mean glass cover temperature 
T_{s} 
: 
Sky temperature 
T_{c} 
: 
Mean collector temperature 
U_{b} 
: 
Overall convective heat transfer coefficient between collector and air
channel 
U_{t} 
: 
Overall convective heat transfer coefficient from top of glass cover 
α_{1} 
: 
Absorptivity of glass 
α_{2} 
: 
Absorptivity of collector 
γ 
: 
Constant for mean temperature approximation 
ε_{g} 
: 
Emissivity of top of glass cover 
A1 
: 
Area of the transparent cover 
A2 
: 
Area of the collector 