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R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46
www.ijera.com 43 | P a g e
Experimental studies on PCM filled Flat Plate Solar Water
Heater without and with Fresnel lens glazing
R. Sivakumar *, V. Varun Prabu**
*Mechanical Engg. Dept., Addis Ababa Science and Technology University, Addis Ababa, Ethiopia,
**Jai Sai Ram Mech. And Tech. India Pvt. Ltd., Orissa,
ABSTRACT
Flat Plate Solar Water Heater (FPSWH) is commonly used to harvest solar energy. Solar concentration
techniques help to achieve higher temperatures of energy. The aim of this article is to compare the performance
of a Fresnel lens glazed Flat Plate Solar Water Heater with Phase Change Material (PCM) with that provided
with an ordinary glazing. The effect of solar concentration using Fresnel lens on energy storage in PCM and heat
gained by water are studied and compared with that having an ordinary glazing. Experiments showed 47%
improvements in the heat gained by water.
Keywords: Flat Plate Solar Water Heater, Fresnel lens, Phase Change Material, Solar Concentrator.
I. INTRODUCTION
Sun is the ultimate source of all forms of
energy on earth. Harvesting solar energy for
domestic and industrial uses is in practice for a long
time. Solar energy is clean, non-polluting and freely
available in nature with the only constraint that it is
diurnal and seasonal. Several models of solar water
heaters are available in market. Using Fresnel Lens
in a Flat Plate Solar Water Heater (FPSWH) can
concentrate the energy on to a small area and
thereby enables achieving higher temperature.
A Fresnel lens is a cheap and light weight
optical component. In a Fresnel lens, as much
possible optical material is removed from the non-
optical interface since the power of lens is available
only in the optical interface. Focal length of the lens
is the distance from the lens where the beam light
converges to a point.
Udawant et al [1] studied the performance
of a Fresnel Lens Solar Concentrator and reported
that the overall efficiency of the Fresnel Lens solar
concentrator is 51% and it has a good potential to
generate low pressure steam.
Gaurav A. Madhugiri and S.R. Karale [2]
reviewed the research works carried out on high
concentration solar energy using Fresnel lens and
reported that Fresnel lenses are conducive and have
a breakthrough in commercial applications in near
future.
Rajesh et al [3] evaluated the performance
of a solar desalination system with a Fresnel Lens
and reported that the performance improved with
Fresnel lens concentration and a temperature of 64o
C
was achieved in the water pre-heater tank.
Patil Divyesh Sakharam et al [4] studied a
Solar Water Heater with Fresnel lens and two axis
tracking system for design optimization, and
reported that energy consumed by the electronic
tracking system is very small when compared to the
gain in energy achieved with tracking and using
Fresnel lens.
Mohamed Salah Mahmoud et al [5]
reported that losses due to radiation are more
practically than those calculated theoretically for
heating water.
W.T. Xie et al [6] reviewed the usage of
Fresnel lens in concentrated Solar energy
applications, and reported that
Polymethylmetacrylate (PMMA) has good sunlight
resistance and transmisivity. Non-Imaging Fresnel
lens solar concentrators are suitable for collection of
solar energy while imaging Fresnel lens solar
concentrators reproduce the accurate image of the
sun. Arumugam and Seeralan [7] experimentally
studied the usage of Fresnel lens in Hybrid solar
steam generators for desalination and small laundry
system application. Radiation losses were reported
to be more because of increased temperature due to
energy concentration. Desalination yield depends on
mass flow rate. Efficiency of the system was
reported to be 25 % which could be further
improved by additional condensation steps. Heat
recovered was used for laundry system.
Valmiki et al [8] used a large Fresnel lens
with sun tracking system for concentrating sunlight
onto a solar cooker with a fixed heat receiving area.
The stove top temperature achieved was about
300o
C. The system was easy to use and efficient.
RESEARCH ARTICLE OPEN ACCESS
R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46
www.ijera.com 44 | P a g e
Christina Sierra et al [9] studied the use of
Fresnel lens for concentrating solar energy to
achieve temperatures as high as 1500 to 2000 K for
material treatment which could be completed in few
minutes.
Y. Tripanagnostopoulos et al [10]
studied the use of Fresnel lens for temperature
control in buildings within comfort range and
illumination.
Aadesh Rajkrishna [11] studied the
performance of a conventional FPSWH by placing
Fresnel lenses over a conventional glazing and
reported an improvement of instantaneous efficiency
by 20%. However comparison was not done
simultaneously with two different models. Thermal
analysis and cost analysis were done to show that the
system designed was low cost and efficient. It was
also recommended that Fresnel lens FPSWH can be
used in places where solar radiation is low.
From literature review on usage of Fresnel
lens in Solar Water Heaters, it is observed that
different studies on usage of Fresnel lens to improve
performance of water heating, desalination, cooking
etc have been carried out. However comparison of
Fresnel lens and ordinary glazing with same solar
radiation input and ambient conditions was not
observed. In this paper, the authors report the
comparison of performance using Fresnel lens and
an ordinary glazing in a FPSWH with PCM.
II. EXPERIMENTAL SET UP
Figure 1 shows the schematic diagram of
the experimental setup used. The two FPSWH
models are of dimensions 0.3 m x 0.3 m. Mild steel
box of 0.14 m depth is inserted and fitted into a box
of 0.16 m depth which is filled with 1 kg paraffin
wax PCM in pellet form and serpentine water tubes
immersed in PCM. The absorber box and absorber
surface are completely painted black. The absorber
box is provided with Styrofoam insulation of 0.02 m
thickness and an outer wooden frame cover. Water is
passed through the serpentine copper tube of ¾ inch
inner diameter with a spacing of 0.03 m pitch. The
whole assembly is kept inclined at an angle of 21o
to
ensure circulation of water by natural convection.
The Fresnel lens used is made of 80% Si. It
has a deformation temperature of 520o
C, annealing
temperature of 560o
C, melting temperature of 820o
C,
refractive index of 1.47, luminousity of 92%,
elasticity modulus of 76 kNmm-2
, tensile strength of
40 to 120 Nmm-2
, processing temperature of 1220o
C,
coefficient of linear expansion of 3.3 x 10-6
K-1
and
level 1 water resistance.
PT100 thermal sensors were used to sense
the temperature of absorber plate, paraffin wax, inlet
and outlet water temperatures. Radiation sensor and
RTD sensors were connected to a 16 channel data
logger shown in Figure 4. Holes were drilled at
suitable locations in the header tube to insert the
RTD sensors to measure the inlet and outlet
temperatures of flowing water. Experiments were
conducted with both the models simultaneously on
different days and results of data recorded on a
particular day is presented.
Figure 1 Schematic diagram of FPSWH
Figure 2 Photograph of FPSWH model with Fresnel
lens glazing
Figure 3 Photograph of FPSWH model with
ordinary glazing
R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46
www.ijera.com 45 | P a g e
Figure 4 Solarimeter and Universal data logger
III. RESULTS AND DISCUSSION
Figure 5 shows the variations in water
temperature rise achieved with time by water
circulated through the FPSWH models with Fresnel
lens and that with ordinary glazing.
Figure 5 Variations in water temperature rise with
time
Figure 6 shows the variations in wax
temperature achieved with time in FPSWH models
with Fresnel lens and that with ordinary glazing. It
is observed that the model with Fresnel lens glazing
achieved quick rise in wax temperature to it melting
point and remains for a longer duration of time
thereby acquiring latent heat of fusion and
transferring more heat to water. The region where
concentration of solar energy was more is observed
to have quick melting of PCM. On the other hand,
the model with ordinary glazing takes more time to
reach its melting point and remains only for a shorter
duration of time acquiring latent heat of fusion and
hence less heat to water. The melting of PCM is
observed to be slow and uniform. The average value
of PCM recorded with Fresnel lens is 6o
C higher
than that with ordinary glazing.
Figure 6 Variations in wax temperature with time
Figure 7 shows the variations in absorber
surface temperature achieved with time in FPSWH
models with Fresnel lens and that with ordinary
glazing. The rise in absorber surface temperature is
rapid because of solar energy concentration. Because
of melting of Paraffin wax taking place at a constant
temperature, the absorber temperature does not rise
much beyond melting temperature. Maximum
absorber temperature achieved sustains for a longer
duration of time. On the other hand, the model with
ordinary glazing takes more time to reach its
maximum temperature. The maximum temperature
achieved prolongs only for a short duration of time.
Figure 7 Variations in absorber surface temperature
with time
Figure 8 shows the variations in Average
Mean Temperature Difference in FPSWH models
with Fresnel lens and that with ordinary glazing.
The variation pattern is similar.
Figure 8 Variations in Average Mean Temperature
Difference with time
R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46
www.ijera.com 46 | P a g e
IV. CONCLUSION
Latent heat storage type Flat Plate Solar
Water Heater Models with Fresnel lens glazing and
ordinary glazing were experimentally studied and
compared. For same solar insolation on a given day,
the model with Fresnel lens glazing showed
maximum absorber temperature and sustained for
longer duration of time than that with ordinary
glazing. Similarly, maximum wax temperature was
sustained for a longer duration of time than that with
ordinary glazing. Heat gain by water is 47% more
and average PCM temperature was 60
C more in
FPSWH using Fresnel lens glazing when compared
to that with ordinary glazing.
REFERENCES
[1] Udawant R.R., K.C. Mohite, and M.G.
Takwale, Study of Performance of Fresnel
Lens Solar Concentrator, International
Journal of Energy Engineering, 6(1A),
2016, 14-22.
[2] Gaurav A. Madhugiri, and S.R. Karale,
High Solar Energy Concentration with a
Fresnel Lens - A review, International
Journal of Modern Engineering Research,
2(3), 2012, 1381-1385.
[3] Rajesh V.R., Harikrishnan K, Chaithanya
K.K., and Subi Salim, Performance
evaluation of a solar desalination system
integrated with a Fresnel lens concentrator,
International Journal of Renewable Energy
Research, 6(1), 2016, 250-253.
[4] Patil Divyesh Sakharam, Patil Nilesh
Ramesh, Ptil Bhushan Tukaram, and Patil
Satish Ramesh, Design and optimization of
solar water heating system by using Fresnel
lens with 2-axis tracking, VSRD
International Journal of Mechanical, Civil,
Automobile and Production Engineering,
IV (VIII), August 2014, 113-118.
[5] Mohamed Salah Mahmoud and Amsa Abd
El-Sattar Mohamed, Utilization of Fresnel
Lens Solar Collector in Water Heating for
desalination by humidification –
dehumidification process, Fifteenth
International Water Technology
Conference, Alexandria, Egypt, IWTC-15
2011, 1-12.
[6] W.T. Xie, Y.J. Dai, R.Z. Wang, and K.
Sumathy, Concentrated Solar Energy
applications using Fresnel lenses,
Renewable and Sustainable Energy
Reviews, 15, 2011, 2588-2606.
[7] G. Arumugam, and K. Seeralan, Hybrid
Solar Steam Generator using Fresnel lens
for Desalination and Application in small
scale laundry system, International Journal
of Advanced Research in Biology
Engineering Science and Technology,
2(11), February 2016, 1-5.
[8] M.M. Valmiki, Peiwen Li, Javier Heyer,
Matthew Morgan, Abdulla Albinali, Kamal
Alhamidi and Jeremy Wagoner, A novel
application of a Fresnel lens for a solar
stove and solar heating, 36(5), 2005, 1614-
1620.
[9] Christina Sierra, and Alfonso J. Vazquez,
High solar energy concentration with a
Fresnel lens, Journal of Material Science,
40, 2005, 1339-1343.
[10] Y. Tripanagnostopoulos, Ch. Siabekou and
J.K. Tonui, The fresnel lens concept for
solar control of buildings, International
Conference “Passive and Low Energy
Cooling for the Built Environment”, May
2005, Santorini, Greece.
[11] Aadesh Rajkrishna, Solar Geyser using spot
Fresnel lens, Fundamentals of Renewable
Energy and Applications, 6(2), 2016, 1-8.
NOMENCLATURE
I Solar Radiation (Wm-2
)
dTw Water temperature rise (o
C)
Tw Wax temperature (o
C)
Ts Absorber Surface Temperature (o
C)
AMTD Average Mean Temperature Difference (o
C)

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Experimental studies on PCM filled Flat Plate Solar Water Heater without and with Fresnel lens glazing

  • 1. R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46 www.ijera.com 43 | P a g e Experimental studies on PCM filled Flat Plate Solar Water Heater without and with Fresnel lens glazing R. Sivakumar *, V. Varun Prabu** *Mechanical Engg. Dept., Addis Ababa Science and Technology University, Addis Ababa, Ethiopia, **Jai Sai Ram Mech. And Tech. India Pvt. Ltd., Orissa, ABSTRACT Flat Plate Solar Water Heater (FPSWH) is commonly used to harvest solar energy. Solar concentration techniques help to achieve higher temperatures of energy. The aim of this article is to compare the performance of a Fresnel lens glazed Flat Plate Solar Water Heater with Phase Change Material (PCM) with that provided with an ordinary glazing. The effect of solar concentration using Fresnel lens on energy storage in PCM and heat gained by water are studied and compared with that having an ordinary glazing. Experiments showed 47% improvements in the heat gained by water. Keywords: Flat Plate Solar Water Heater, Fresnel lens, Phase Change Material, Solar Concentrator. I. INTRODUCTION Sun is the ultimate source of all forms of energy on earth. Harvesting solar energy for domestic and industrial uses is in practice for a long time. Solar energy is clean, non-polluting and freely available in nature with the only constraint that it is diurnal and seasonal. Several models of solar water heaters are available in market. Using Fresnel Lens in a Flat Plate Solar Water Heater (FPSWH) can concentrate the energy on to a small area and thereby enables achieving higher temperature. A Fresnel lens is a cheap and light weight optical component. In a Fresnel lens, as much possible optical material is removed from the non- optical interface since the power of lens is available only in the optical interface. Focal length of the lens is the distance from the lens where the beam light converges to a point. Udawant et al [1] studied the performance of a Fresnel Lens Solar Concentrator and reported that the overall efficiency of the Fresnel Lens solar concentrator is 51% and it has a good potential to generate low pressure steam. Gaurav A. Madhugiri and S.R. Karale [2] reviewed the research works carried out on high concentration solar energy using Fresnel lens and reported that Fresnel lenses are conducive and have a breakthrough in commercial applications in near future. Rajesh et al [3] evaluated the performance of a solar desalination system with a Fresnel Lens and reported that the performance improved with Fresnel lens concentration and a temperature of 64o C was achieved in the water pre-heater tank. Patil Divyesh Sakharam et al [4] studied a Solar Water Heater with Fresnel lens and two axis tracking system for design optimization, and reported that energy consumed by the electronic tracking system is very small when compared to the gain in energy achieved with tracking and using Fresnel lens. Mohamed Salah Mahmoud et al [5] reported that losses due to radiation are more practically than those calculated theoretically for heating water. W.T. Xie et al [6] reviewed the usage of Fresnel lens in concentrated Solar energy applications, and reported that Polymethylmetacrylate (PMMA) has good sunlight resistance and transmisivity. Non-Imaging Fresnel lens solar concentrators are suitable for collection of solar energy while imaging Fresnel lens solar concentrators reproduce the accurate image of the sun. Arumugam and Seeralan [7] experimentally studied the usage of Fresnel lens in Hybrid solar steam generators for desalination and small laundry system application. Radiation losses were reported to be more because of increased temperature due to energy concentration. Desalination yield depends on mass flow rate. Efficiency of the system was reported to be 25 % which could be further improved by additional condensation steps. Heat recovered was used for laundry system. Valmiki et al [8] used a large Fresnel lens with sun tracking system for concentrating sunlight onto a solar cooker with a fixed heat receiving area. The stove top temperature achieved was about 300o C. The system was easy to use and efficient. RESEARCH ARTICLE OPEN ACCESS
  • 2. R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46 www.ijera.com 44 | P a g e Christina Sierra et al [9] studied the use of Fresnel lens for concentrating solar energy to achieve temperatures as high as 1500 to 2000 K for material treatment which could be completed in few minutes. Y. Tripanagnostopoulos et al [10] studied the use of Fresnel lens for temperature control in buildings within comfort range and illumination. Aadesh Rajkrishna [11] studied the performance of a conventional FPSWH by placing Fresnel lenses over a conventional glazing and reported an improvement of instantaneous efficiency by 20%. However comparison was not done simultaneously with two different models. Thermal analysis and cost analysis were done to show that the system designed was low cost and efficient. It was also recommended that Fresnel lens FPSWH can be used in places where solar radiation is low. From literature review on usage of Fresnel lens in Solar Water Heaters, it is observed that different studies on usage of Fresnel lens to improve performance of water heating, desalination, cooking etc have been carried out. However comparison of Fresnel lens and ordinary glazing with same solar radiation input and ambient conditions was not observed. In this paper, the authors report the comparison of performance using Fresnel lens and an ordinary glazing in a FPSWH with PCM. II. EXPERIMENTAL SET UP Figure 1 shows the schematic diagram of the experimental setup used. The two FPSWH models are of dimensions 0.3 m x 0.3 m. Mild steel box of 0.14 m depth is inserted and fitted into a box of 0.16 m depth which is filled with 1 kg paraffin wax PCM in pellet form and serpentine water tubes immersed in PCM. The absorber box and absorber surface are completely painted black. The absorber box is provided with Styrofoam insulation of 0.02 m thickness and an outer wooden frame cover. Water is passed through the serpentine copper tube of ¾ inch inner diameter with a spacing of 0.03 m pitch. The whole assembly is kept inclined at an angle of 21o to ensure circulation of water by natural convection. The Fresnel lens used is made of 80% Si. It has a deformation temperature of 520o C, annealing temperature of 560o C, melting temperature of 820o C, refractive index of 1.47, luminousity of 92%, elasticity modulus of 76 kNmm-2 , tensile strength of 40 to 120 Nmm-2 , processing temperature of 1220o C, coefficient of linear expansion of 3.3 x 10-6 K-1 and level 1 water resistance. PT100 thermal sensors were used to sense the temperature of absorber plate, paraffin wax, inlet and outlet water temperatures. Radiation sensor and RTD sensors were connected to a 16 channel data logger shown in Figure 4. Holes were drilled at suitable locations in the header tube to insert the RTD sensors to measure the inlet and outlet temperatures of flowing water. Experiments were conducted with both the models simultaneously on different days and results of data recorded on a particular day is presented. Figure 1 Schematic diagram of FPSWH Figure 2 Photograph of FPSWH model with Fresnel lens glazing Figure 3 Photograph of FPSWH model with ordinary glazing
  • 3. R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46 www.ijera.com 45 | P a g e Figure 4 Solarimeter and Universal data logger III. RESULTS AND DISCUSSION Figure 5 shows the variations in water temperature rise achieved with time by water circulated through the FPSWH models with Fresnel lens and that with ordinary glazing. Figure 5 Variations in water temperature rise with time Figure 6 shows the variations in wax temperature achieved with time in FPSWH models with Fresnel lens and that with ordinary glazing. It is observed that the model with Fresnel lens glazing achieved quick rise in wax temperature to it melting point and remains for a longer duration of time thereby acquiring latent heat of fusion and transferring more heat to water. The region where concentration of solar energy was more is observed to have quick melting of PCM. On the other hand, the model with ordinary glazing takes more time to reach its melting point and remains only for a shorter duration of time acquiring latent heat of fusion and hence less heat to water. The melting of PCM is observed to be slow and uniform. The average value of PCM recorded with Fresnel lens is 6o C higher than that with ordinary glazing. Figure 6 Variations in wax temperature with time Figure 7 shows the variations in absorber surface temperature achieved with time in FPSWH models with Fresnel lens and that with ordinary glazing. The rise in absorber surface temperature is rapid because of solar energy concentration. Because of melting of Paraffin wax taking place at a constant temperature, the absorber temperature does not rise much beyond melting temperature. Maximum absorber temperature achieved sustains for a longer duration of time. On the other hand, the model with ordinary glazing takes more time to reach its maximum temperature. The maximum temperature achieved prolongs only for a short duration of time. Figure 7 Variations in absorber surface temperature with time Figure 8 shows the variations in Average Mean Temperature Difference in FPSWH models with Fresnel lens and that with ordinary glazing. The variation pattern is similar. Figure 8 Variations in Average Mean Temperature Difference with time
  • 4. R. Sivakumar. Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -5) July 2016, pp.43-46 www.ijera.com 46 | P a g e IV. CONCLUSION Latent heat storage type Flat Plate Solar Water Heater Models with Fresnel lens glazing and ordinary glazing were experimentally studied and compared. For same solar insolation on a given day, the model with Fresnel lens glazing showed maximum absorber temperature and sustained for longer duration of time than that with ordinary glazing. Similarly, maximum wax temperature was sustained for a longer duration of time than that with ordinary glazing. Heat gain by water is 47% more and average PCM temperature was 60 C more in FPSWH using Fresnel lens glazing when compared to that with ordinary glazing. REFERENCES [1] Udawant R.R., K.C. Mohite, and M.G. Takwale, Study of Performance of Fresnel Lens Solar Concentrator, International Journal of Energy Engineering, 6(1A), 2016, 14-22. [2] Gaurav A. Madhugiri, and S.R. Karale, High Solar Energy Concentration with a Fresnel Lens - A review, International Journal of Modern Engineering Research, 2(3), 2012, 1381-1385. [3] Rajesh V.R., Harikrishnan K, Chaithanya K.K., and Subi Salim, Performance evaluation of a solar desalination system integrated with a Fresnel lens concentrator, International Journal of Renewable Energy Research, 6(1), 2016, 250-253. [4] Patil Divyesh Sakharam, Patil Nilesh Ramesh, Ptil Bhushan Tukaram, and Patil Satish Ramesh, Design and optimization of solar water heating system by using Fresnel lens with 2-axis tracking, VSRD International Journal of Mechanical, Civil, Automobile and Production Engineering, IV (VIII), August 2014, 113-118. [5] Mohamed Salah Mahmoud and Amsa Abd El-Sattar Mohamed, Utilization of Fresnel Lens Solar Collector in Water Heating for desalination by humidification – dehumidification process, Fifteenth International Water Technology Conference, Alexandria, Egypt, IWTC-15 2011, 1-12. [6] W.T. Xie, Y.J. Dai, R.Z. Wang, and K. Sumathy, Concentrated Solar Energy applications using Fresnel lenses, Renewable and Sustainable Energy Reviews, 15, 2011, 2588-2606. [7] G. Arumugam, and K. Seeralan, Hybrid Solar Steam Generator using Fresnel lens for Desalination and Application in small scale laundry system, International Journal of Advanced Research in Biology Engineering Science and Technology, 2(11), February 2016, 1-5. [8] M.M. Valmiki, Peiwen Li, Javier Heyer, Matthew Morgan, Abdulla Albinali, Kamal Alhamidi and Jeremy Wagoner, A novel application of a Fresnel lens for a solar stove and solar heating, 36(5), 2005, 1614- 1620. [9] Christina Sierra, and Alfonso J. Vazquez, High solar energy concentration with a Fresnel lens, Journal of Material Science, 40, 2005, 1339-1343. [10] Y. Tripanagnostopoulos, Ch. Siabekou and J.K. Tonui, The fresnel lens concept for solar control of buildings, International Conference “Passive and Low Energy Cooling for the Built Environment”, May 2005, Santorini, Greece. [11] Aadesh Rajkrishna, Solar Geyser using spot Fresnel lens, Fundamentals of Renewable Energy and Applications, 6(2), 2016, 1-8. NOMENCLATURE I Solar Radiation (Wm-2 ) dTw Water temperature rise (o C) Tw Wax temperature (o C) Ts Absorber Surface Temperature (o C) AMTD Average Mean Temperature Difference (o C)