INTRODUCTION
Solar energy currently represents the most abundant, inexhaustible, nonpolluting,
effective and free energy resource available in almost all parts of the world
(Safari and Gasore, 2009; Sreejaya
et al., 2011; Andoh et al., 2007).
If the available solar energy on the earth is properly harnessed the world may
not have need for fossil fuel any more (Efurumibe et
al., 2012; Chattopadhyay et al., 2011).
In recent years, considerable attention has been paid to solar thermal concentrating
systems which are regarded as environmentally friendly alternatives to conventional
thermal power systems. In solar thermal concentrating systems, incident solar
radiation is converted into thermal energy at the focus (Khatib
et al., 2009). These systems are classified as either point focus
concentrators (parabolic dishes and central receiver systems) or line focus
concentrators (parabolic trough collectors and linear Fresnel collectors).
The PTC focuses Direct Normal Irradiance (DNI) or beam radiation onto a focal line on the collector axis. An absorber tube with water or temperature stable synthetic oil flowing inside, absorbs the concentrated solar energy and raises its temperature at the focal line.
There are several promising developments going on in the field of PTC and their
applications. A comprehensive review of the usage of the PTC for various applications
of thermal energy up to 400°C was presented by FernandezGarcia
et al. (2010). Lupfert et al. (2007)
summarized the various techniques available for the analysis of the PTC’s
optical performance. Brooks et al. (2006) conducted
the baseline performance study of the PTC, using ASHRAE standard 93. Kalogirou
studied the viability of PTCs for industrial process heat by Kalogirou
(2002). In an effort to obtain the maximum possible collector efficiency,
special attention was given to the intercept factor and mode of tracking (Kalogirou,
1996). An extensive survey on various types of solar thermal collectors
and applications was conducted by Kalogirou (2004).
The PTC optical test and thermal test up to 200°C with pressurized water
was performed by Kruger et al. (2008). These
studies showed a significant improvement in the reduction of radiative and convective
losses. Opitmisation of the collector’s aperture, the rim angle and the
selection of the receiver’s diameter was performed by Kalogirou
et al. (1994). The idea of using thermal storage for parabolic trough
power plants was widely accepted to ensure continuous power delivery even during
off sunshine hours. The performance test of the PTC power plant integrated with
solid media thermal storage at Plataforma Solar de Almeria in Spain was performed
by Laing et al. (2006). The design and manufacture
of a 90° rim angle fibre glass reinforced PTC for hot water generation was
described by Arasu and Sornakumar (2007). The thermal
performance of the newly developed fibre glass reinforced parabolic collector
was determined according to ASHRAE Standard 93. A stand alone single axis tracking
parabolic trough system was designed by Odeh et al.
(2004). The system can operate independently at remote area to produce hot
water or steam pressure close to ambient for small factories. Odeh
and Morrison (2006) developed a transient simulation model for analyzing
the performance of industrial water heating systems using parabolic trough solar
collectors. This model aims to optimize the size of the collector aperture area
and thermal storage tank by considering sudden changes in solar radiation such
as passing cloud.
The objective of this work is to investigate the viability of the available
PTC for solar cooking application. For this purpose, the parameters like the
mass flow rate, solar radiation, concentration ratio and heat removal factor
have been considered and addressed, for various inlet fluid temperatures. The
required mass flow rate and HTF is thus finally identified for an ongoing solar
cooking research.
THERMAL ANALYSISPARABOLIC TROUGH COLLECTOR
A PTC generally includes the receiver tube, the concentrator and collector structure. The receiver is the element of the system where solar radiation is absorbed and converted into thermal energy. The receiver is covered by a glass tube to reduce thermal radiation as well as convection heat loss to the free air which moves around the receiver. The heat loss from the receiver is further reduced by evacuating the air from the space between the receiver and the glass cover.
A prototype PTC model has been developed, installed and experimented at the Institute for Energy Studies, Anna University, Chennai. The PTC model uses mirrored surfaces curved in a parabolic shape that linearly extend into a trough shape. The mirror is made of a glass (Saint Gobain make) with a thickness of 6 mm. In general, the concentrating collectors are found to have less heat gain values, because they use only direct irradiation. This disadvantage is compensated by the tracking device. The PTC rotates around the horizontal NS axis and a single axis tracking is adopted in the EW direction to track the sun to obtain the maximum energy incidence. The technical specifications of the prototype PTC are tabulated and given in Table 1.
The performance analysis of the existing PTC is carried out by considering
its aperture width W_{a}, length L and rim angle φ_{r}
(Fig. 1). The absorber tube has an inner diameter D_{i}
and an outer diameter D_{o} and it has a concentric glass cover inner
diameter D_{ci} and outer diameter D_{co} around it. The HTF
being heated in the collector has a mass flow rate
a specific heat C_{p}, an inlet temperature T_{fi} and an outlet
temperature T_{fo}. For a particular set of HTF inlet temperatures under
constant insolation, the corresponding HTF outlet temperatures, the heat gained
by the HTF and the efficiency of the PTC were obtained.
Table 1: 
PTC specifications 


Fig. 1: 
Cross sectional view of the PTC 
The graphs are plotted for the above parameters by varying the mass flow rate,
the heat removal factor of the fluid, the solar insolation and the concentration
ratio. The efficiency of the PTC is also obtained for different HTFs.
The concentration ratio of the collector is given by Eq. 1:
The performance analysis of the PTC is, in many respects, similar to the analysis of a liquid flatplate collector. Figure 1 shows the elementary slice dx of the absorber tube, at a distance x from the inlet. The steady state Eq. 2 describes the energy balance of an elementary slice dx:
Where:
dq_{u} 
= 
Useful heat gain rate for a length dx 
ρ 
= 
Specular reflectivity of the concentrator surface 
γ 
= 
Intercept factor 
(τα)_{b} 
= 
Average value of the transmissivity  absorptivity product for beam radiation 
U_{l} 
= 
Overall loss coefficient 
T_{p} 
= 
Local temperature of the absorber tube 
T_{a} 
= 
Ambient temperature 
The first term on the right hand side in Eq. (2) represents
the incident beam radiation absorbed in the absorber tube after reflection and
the second term represents the absorbed incident beam radiation which falls
directly on the absorber tube. The second term is small in comparison with the
first, but cannot be ignored when the concentration ratio is small. The third
term represents the loss by convection and reradiation.
The absorbed solar flux S is given in Eq. 3:
The substitution of Eq. 3 in 2 gives the
expression for useful heat gain rate for a length dx, as given in Eq.
4:
The useful heat gain rate, dq_{u} can also be written as:
Where:
h_{f} 
= 
heat transfer coefficient on the inside surface of the tube 
T_{f} 
= 
local fluid temperature 
The useful heat gain rate Eq. 7 is obtained by combining
Eq. 4 and 5, so as to eliminate the absorber
tube temperature T_{p}:
where, F' is the collector efficiency factor, given in Eq. 8:
Equation 9 is obtained by the combination of Eq.
6 and 7:
Equation 10 is formed by integrating and using the inlet
condition at x = 0, T_{f} = T_{fi} in Eq. 9:
Equation 11 is formed by substituting T_{f} = T_{fo}
and x = L in Eq. 10 and then subtracting both sides of the
resulting equation from unity:
Thus, the useful heat gain rate is given in Eq. 12:
Equation 13 is obtained by introducing Eq.
11 in Eq. 12:
Equation 14 is obtained by introducing a heat removal factor
in Eq. 13:
where F_{R} is the heat removal factor, given in Eq. 15:
Equation 15 is the equivalent of the HottelWhillierBliss
equation for a flatplate collector.
The instantaneous collector efficiency(η_{i}) is given in Eq. 16:
The instantaneous efficiency (η_{ib}) as shown in Eq. 17 is also calculated on the basis of the beam radiation by neglecting the ground reflected radiation, in which case:
The efficiency of the collector (η) with respect to the concentration ratio is given by Eq. 18:
RESULTS AND DISCUSSION
In order to have a numerical appreciation of the results, the PTC parameters given in Table 1 are utilized to determine the thermal behavior of the prototype PTC. The effect of the mass flow rate, the efficiency, the useful energy, the concentration ratio of the collector and the heat removal factor are studied and the results are discussed.
When the HTF inlet temperature increases, the temperature of the absorber tube
surface also increases. As a result, the losses due to radiation and convection
to the surroundings also increase, resulting in a decrease in efficiency. It
is clear from Fig. 2a that the value of efficiency for various
mass flow rates decreases significantly with the HTF inlet temperature. This
is due to the less heat transfer coefficient for a less mass flow rate and thus,
the efficiency of the collector is also less.
The efficiency of the PTC for different heat transfer fluids is calculated
and plotted in Fig. 2b. When the inlet temperature of the
HTF increases, the efficiency of the PTC decreases. This is due to the less
useful heat gain from the PTC. The useful heat gain from the collector is the
maximum, when water is used as the HTF. The efficiency of the PTC is less when
castor oil is used as the HTF. This is due to water having more specific heat
than castor oil that reflects in the PTC efficiency variation.
The energy of the solar insolation value reaching the earth’s surface
varies from place to place and also from time to time. The useful heat gain
of the HTF is evaluated for various solar insolation values and depicted in
Fig. 2c. It is seen that as the solar insolation increases,
the useful heat gained by the HTF also increases.

Fig. 2a: 
Efficiency vs. inlet fluid temperature for various mass flow
rates 

Fig. 2b: 
Efficiency vs. inlet fluid temperature for various heat transfer
fluids 

Fig. 2c: 
Useful energy vs. inlet fluid temperature for various solar
insolation values 

Fig. 2d: 
Useful energy vs. inlet fluid temperature for various heat
removal factors 
Figure 2d shows the variation of the useful heat energy
with the the heat removal factor increases (this can be achieved by increasing
the mass flow rate) the useful energy gained by the collector also increases.
The effect of increasing the concentration ratio by decreasing the size of
the absorber tube is shown in Fig. 2e. It is evident that
the useful energy increases as the concentration ratio increases. This is because
when the concentration ratio is high, the losses from the PTC absorber tube
decrease and thus the collection of useful energy increases.

Fig. 2e: 
Useful energy vs. inlet fluid temperature for various concentration
ratios 

Fig. 3: 
Proposed experimental setup 
In the proposed work, the solar cooking system using DMannitol as the phase
change storage medium (Kumaresan et al., 2011)
is under investigation and Fig. 3 shows the planned setup
of the test field. This system consists of a PTC, Thermal Energy Storage (TES)
tank and the cooking unit which is kept inside the room. Therminol 55 is considered
as the HTF to transfer the heat between the PTC and the indoor cooking unit.
The PTC provides heated oil to the TES tank. The stored heat thus could be retrieved
by the HTF, even during off sunshine hours. The PTC considered in the proposed
study is designed and fabricated, based on the local available technologies
and raw materials in Chennai, India.
CONCLUSION
The aim of the proposed work is to present a novel system, in which the solar parabolic trough collector has been introduced to the thermal energy storage system, integrated with a residential type cooking unit. For this purpose the thermal analysis of the available PTC by considering the mass flow rate, efficiency, useful energy, the concentration ratio of the collector and the heat removal factor are theoretically studied and the results are presented in this proposed work. The results showed that most of the performance parameters, such as thermal efficiency and useful heat gain rate increase as the solar insolation increases. The thermal efficiency of the PTC is also found to increase when the mass flow rate and concentration ratio increase for a given value of the solar intensity. The system performance is compared for different heat transfer fluids. These theoretical results are well considered as input parameters for further development of the experimental work.
NOMENCLATURE
C_{P} 
: 
Specific heat of fluid (J kg^{1} K^{1}) 
I 
: 
Solar intensity (W m^{2}) 
S 
: 
Absorbed solar flux (W m^{2}) 
m 
: 
Mass flow rate of fluid (kg sec^{1}) 
Q 
: 
Useful heat gain (W) 
T 
: 
Temperature (°C) 
U_{l} 
: 
Overall loss coefficient (W K^{1} m^{2}) 
E_{o} 
: 
Energy output (W) 
k 
: 
Thermal conductivity (W K^{1} m^{1}) 
W 
: 
Width of collector (m) 
L 
: 
Length of collector (m) 
D 
: 
Diameter (m) 
F_{R} 
: 
Heat removal factor 
F’ 
: 
Efficiency factor 
Re 
: 
Reynolds number 
Pr 
: 
Prandtl number 
C 
: 
Concentration ratio 
Greek letters:
α 
: 
Absorptivity 
E 
: 
Emissivity 
H 
: 
Efficiency 
P 
: 
Reflectivity 
σ 
: 
Stefan’s Constant 
γ 
: 
Intercept Factor 
Subscripts:
a 
: 
Ambient 
I 
: 
Inlet 
u 
: 
Useful 
b 
: 
Beam radiation 
d 
: 
Diffuse radiation 
o 
: 
Outlet 
f 
: 
Fluid 
m 
: 
Mean 