DETERMINATION OF THERMAL EFFICIENCY AND COOKING POWER OF PARABOLIC SOLAR CONCENTRATING SYSTEMWITH THERMAL COMPENSATOR FOR DOMESTIC APPLICATIONS

Energy and the environment have a strong relationship. The production and consumption of energy is one of the biggest causes of environmental damage on earth. Therefore, the rapid increase in the level of CO2 and other greenhouse gases are given out during burning fossil fuel rise or unsteady of fuel prices are the main purposes led to a search to more effectively utilize a different sources of renewable energy. To reduce the consequences of greenhouse gases emitted by burning fuel for energy, which course depletion of the ozone layer and global warming. Therefore, the use of solar radiation directly as a source of energy has proved in the past to be less economical and affordable. The paper was aimed at determination of the performance of a parabolic solar concentrating system with a thermal compensator for domestic applications using thermal efficiency and cooking power. The parabolic dish solar collector (PDSC) with a focal point of 6.15 m, aperture area of 5.8 m2 and rim angle (φo) of 45Owas designed and constructed for the determination of the variables. The PDSC was made of stainless steel reflector sheet in such a way that both the manufacturing and assembly method do not require complicated skilled techniques and cost. Since the PDSC is for high temperature steam generation, hot water and cooking application. A finite element stress test analysis was conducted to determine the thermal efficiency and cooking power of the system under various weather conditions. A simple manual solar tracking mechanism was employed, and the results of the system performance were also reported. The efficiency according to the finding depends on the optical properties of the materials involved, the geometry of the collector, and the various imperfections arising from the construction of the collector. The thermal efficiency and cooking power of the system were determined and obtained to be 54.4% and 543.1W respectively.


INTRODUCTION
The global energy crisis is one of the major critical issues facing the world and sustainable environment with the depletion of charcoal, coal, oil and natural gas and the increasing of energy demand.Energy demands in the world have been continuously increasing recently due to growth in population and industrialization.It is obvious that the conventional energy sources obtained from fossil Fuels are under increasing demand and there is a need to search for alternative sources to complement these energy sources (Sadik et al., 2013).Parabolic solar dish concentrators are used to achieve high thermal energy and this concentration of sunlight in form of solar radiation is achieved by reflecting or refracting the incident flux on the aperture area (reflecting surface of the concentrator) onto a smaller absorber area (receiver) (Flavia et al., 2016).
The low cost parabolic solar collector was designed for medium thermal applications, the system was made off with a spiral coil absorber for calculating its optical performance, and a mathematical and physical model of the new offset type parabolic concentrator system was presented.(Pavlović et al., 2016).A static solar concentrating collector called 3D was developed that can be used as low cost technology with the aim of production of portable hot water in rural area of India.The ray tracing software for evaluation of the system was used and optimization of the concentrator profile and geometry is carried out to improve the overall performance of the system designed Saleh (2013).
The satellite dishes of 2.405m diameter with an aluminum frames as a reflector to reduce the weight of the structure and the cost of the concentrating solar system.in the designed reported by (Kaushika and Reddy, 2000), the average temperature recorded for the system was 300 °C , when the receiver absorber was placed at the focal point.An experimental investigation of a solar parabolic dish collector with aperture area of 20m 2 , with the aim to study its performance with the modified cavity receiver was presented, and the average value of the overall heat loss coefficient for the system was found to be about 356 W/m 2 (Reddy et al., (2013).Direct steam generation achieving 90% thermal efficiency at 535°C with a parabolic dish and cavity type receiver has been reported based on experimental results using a 500 m 2 dish (Lovegrove et al., 2011).The research would try to find out a more efficient and convenient method of harnessing the available solar radiation using parabolic solar concentrator for thermal steam generation and encourage the use of friendly technology for domestic and industrial use.

Construction Materials
The parabolic dish concentrating system was constructed using locally available and affordable materials, and the specification of the materials used is shown in Table 1.In the selection of materials for the construction, the following were highly considered; local availability, low cost, easy handling during fabrication, lightness of weight for easy handling during use, ability to withstand environmental and operating conditions and non-toxic effects.
A detailed list of the materials, their specifications and quantities used for the construction of the parabolic dish collector are shown in Table 1.

Optical Design of the Solar Parabolic Thermal Concentrator
The optical design of the system was done based on the geometry of the dish concentrator.The parabola shape reflector is the meeting point in which distances from a fixed line and a fixed point are equal.Figure 1, shows a parabola, where the fixed line is called the directrix and the fixed-point F, and the focus.The line perpendicular to the directrix and passing through the focus F is called the axis of the parabola.The parabola intersects its axis at a point V called the vertex, which is exactly midway between the focus and the directrix (Fareed et al., 2012).
A mathematical equation for the parabola shape i n Cartesian and cylindrical coordinate systems was employed (Pavlovic et al., 2016), (1) Where x and y are coordinates in the aperture plane and z is the distance from the vertex measured along the line parallel with the paraboloid axis of symmetry; f is the focal length of the paraboloid i.e. distance from the vertex to the focus along the paraboloid axis of symmetry.The relationship between the focal length and the diameter of parabolic dish is called relative aperture and it defines the shape of the paraboloid and the position of the focal point.

Design Description of Solar Parabolic Concentrator
The parabolic dish solar collector or concentrator comes in twelve parts or pieces like curvilinear trapezoidal petals-shaped reflector and is assembled using bolts and nuts to tighten the parts together as shown in Figure 2, 3 and 4. Each part of trapezoidal petals-shaped reflector was made up of light steel materials, the upper surface was then fixed with stainless steel reflector sheet in order to have a high efficiency of reflecting the solar energy onto the receiver.Therefore, the components were assembled into the parabolic dish concentrating system for experimental setup with a receiver placed at the focal point for collection of reflected solar radiation from concentrating solar collector with a thermal compensator as shown in figure 5.

Determination of the Focal point of the parabolic concentrator
In determining the focal point of the dish, the mathematical method which entails using the parabola equation to calculate the required parameter adopted as shown in figure 6.Therefore, equation (2) was used for the determination of the focal point.

Determination of Concentration Ratio of the Concentrating Solar Collector
The energy utilization based on the thermal energy parameters and optical efficiency of the system considered and the concentration ratio of the collector was determined using equation (3) (Eltahir, 2013).The geometrical concentration ratio is defined as the collector aperture area , divided by the surface area of the receiver (Eltahir, 2013).

Determination of Thermal Efficiency of Concentrating Solar Collector
The efficiency is defined as the ratio of the thermal power absorbed by the heat transfer fluid to the direct normal irradiance on the aperture area (Najla et al., 2011), Therefore, the thermal efficiency was determined using equation ( 4) Where, ɳ ℎ Thermal efficiency in %, Final temperature of water measured in O C, Initial temperature of water measured in O C, Mass of water measured in kg, Specific heat capacity of water 4200J/Kg/K (Constant) and Aperture area of the collector measured in m 2 It was 0.75kg of water was boiled in 5 minutes at solar radiation of 969W/m 2 and wind speed of 0.47m/s.using pot like receiver as a cooking utensil of 70.66m 3 , containing 1000cm 3 of water.
The magnitude of the efficiency of the system by 01:00pm was calculated to be ŋ ℎ = 54.4 % Therefore, the values obtained for the thermal efficiency is line with the 56% obtained by Ibrahim (2012), and lower than the 60% obtained by Eswaramoorthy and Shanmugam (2012),

Determination of Cooking Power of the Parabolic Dish Concentrator
The cooking power, P, is defined as the rate of useful energy available during the heating period.It may be determined as a product of the change in water temperature for each interval and mass and specific heat capacity of water contained in the cooking utensil.Dividing the product by the time contained in a periodic interval yield the cooking power in Watts.
The cooking power of the parabolic dish solar collector was calculated using equation (5), given by (Funk, 2000) thus: ( ) Where, w M is the mass of the cooking utensil or boiling utensil, w C is the specific heat capacity of water, wb T is the final temperature of the water, wa T is the initial temperature of the water, is the time taken for the water to boil, b I is the intensity of direct solar irradiance on the parabolic concentrator.

Water Boiling Test
The result of the water boiling test is shown in Figure 7.The system shows that the highest temperature recorded is that of the parabolic concentrating system; the corresponding global solar radiation and wind speed were 98.7 O C, 948W/m 2 and 0.70m/s respectively at 13:00 pm on the day of experimentation.The result clearly shows the effect of the atmospheric parameters on the water temperature.It was clearly noticed that the weather was fluctuating due to the cloudy sky which tends to slow down the boiling process.
The atmospheric temperature was in constant fluctuation between 75.3 0 C to 83.5 0 C between the hours of 11:30 am to 12:30 pm with the highest ambient temperature reached at that same time.The maximum intensity of solar radiation was found between 12:00 pm to 1:00 pm.

Steam Test
The steam generation test was conducted on the second day which was having clear weather.Figure 8, shows the representation of the data in an excel graph.The atmospheric parameters were in favor of the rise in temperature with the highest temperature being attained very fast even before noon, while the atmospheric temperature was favorable.The highest solar insolation reached and recorded in this clear weather was 884W/m 2 .The graph of result in figure 8 shows that, temperature was directly resonating with the fluctuating intensity of solar radiation between the hours of 14:00pm to 14:30pm.

Cooking Test
The Cooking test result was conducted on the third day which was a little bit cloudy day that covered the intensity of solar radiation and others weather parameters for the effectiveness of the system compared to the result obtained in steam generation test.Figure 9, shows the results of the rice cooking test, which clearly shows the dependence of the cooking test on the atmospheric parameters with the temperature falling between 11:30 am to1: 00 pm.The time taken for the rice to be well cooked was a little bit longer, obviously due to the rapid in temperature fall as a result of the cloud covering the intensity of solar radiation (uncontrolled factor) (Funk, 2000).

DISCUSSION
The experimental results obtained for the boiling test was depicted in Figure 7.The Figure shows that, the temperature of water obtained by the system was continuously increasing to reach a temperature value of 100 O C as the ambient temperature continuously increased to a certain value of 43 O C and a corresponding increase in wind speed.By 13:00 pm the temperature value of the system gradually decreased to a certain value, this could be due to the gradual decrease of the intensity of solar radiation and ambient temperature as the result of cloud covered; Therefore, it is uncontrolled parameters or factors, similar results were reported by (Funk 2000) and (Serah 2014).Therefore, the maximum temperature required for water to boil was achieved, and a significant limestone was achieved compared to the temperature of 90 O C obtained by (Asere et al., 2003), and the temperature value is similar to 100 O C obtained by (Ibrahim, 2012).
Similarly, Figure 8 shows that the highest temperature recorded of the solar concentrating system during the steam generation test, corresponding global solar radiation and wind speed were 225.3 O C, 884W/m 2 and 0.40m/s respectively at 14:00 pm on the second day of experimentation.
On that day the atmospheric condition or weather was cleared around 12:30 -14:00 pm.Therefore, the atmospheric parameters were in favor of the rise in temperature with the highest temperature being attained very fast even before noon, the highest solar radiation reached and recorded in this clear weather was 884w/m 2 ., similar results was reported by (Funk, 2000).The temperature value is lower than 300 O C obtained by (Kashika and Reddy, 2000).
Figure 9 shows that, the results of temperature variation with time and corresponding global solar radiation.The result revealed that, the highest temperature recorded for cooking test, the corresponding global solar radiation and wind speed were recorded 96.4 O C, 790W/m 2 and 0.47m /s respectively.The result clearly shows the dependence of the cooking test on the atmospheric parameters with the temperature falling down between 11:30am to1: 00pm.The time taken for the rice to be well cooked was a little bit longer, obviously due to the rapid in temperature fall as a result of the cloud covered the intensity of solar radiation (uncontrolled factor) according to (Funk, 2000).The temperature of cooking material (rice) increased continuously as the ambient temperature and corresponding global solar radiation increased, while the wind speed decreased gradually.The increase of wind speed from 11:30pm to 1:00pm did not affect the increase of temperature of the cooking material, as the global solar radiation and ambient temperature were increasing.The temperature result obtained during cooking test was in lower value compared to the temperature obtained in steam and boiling test and this could be as a result of observable delay in response to the solar fluctuations., similar results was reported by (Funk, 2000).Therefore, the temperature obtained is line with 95 O C by (Gang et al., 2012),

CONCLUSION
The parabolic concentrating solar collector with thermal compensator was found to be able to produced boiling water and steam with a temperature as high as 100 O C and 225.3 O C respectively, the system can be used for some domestic applications.The thermal efficiency and cooking power were found to be 54.4%, and 543.1W respectively.The variation of temperature results obtained on some days during experimentation could be a result of both optical and thermal losses from the reflector and receiver (cooking utensil).Furthermore, the results of the tests conducted were hindered by the fluctuation of the atmospheric parameters as a result of the cloud and solar fluctuations which is one of the uncontrolled atmospheric parameter and as well as inefficiency caused by manual tracking system or mechanism.But it can be said that significant limestone was achieved.

Figure 2 :
Figure 2: Assembled of trapezoidal petal shaped reflector of parabolic dish concentrator.

Figure 5 :
Figure 5: Experimental setup of parabolic dish concentrating system with thermal compensator.

Figure 7 :
Figure 7: Results of temperature variation with time and corresponding global solar radiation of water boiling test.

Figure 8 :
Figure 8: Results of temperature variation with time and corresponding global solar radiation of steam generation test.

Figure 9 :
Figure 9: Results of temperature variation with time and corresponding global solar radiation of cooking test.

Table 2 :
List of Instruments used in the Measurement