Effect of energy matrices on life cycle cost analysis of partially covered photovoltaic compound parabolic concentrator collector active solar distillation system

Desalination 397 (2016) 75–91

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Effect of energy matrices on life cycle cost analysis of partially covered photovoltaic compound parabolic concentrator collector active solar distillation system D.B. Singh a,⁎, G.N. Tiwari b a b

Centre for Energy Studies, Indian Institute of Technology Delhi, HausKhas, New Delhi, 110016, India Bag Energy Research Society (BERS), SODHA BERS COMPLEX, Plot No. 51, Mahamana Nagar, Karaudi, Varanasi, UP, 22 10 05, India

H I G H L I G H T S • • • • •

Single and double slope PVT-CPC active solar distillation systems have been analyzed. They have been compared on the basis of energy matrices. Production cost of water and cost of electricity gain have been evaluated. Number of PVT-CPC collectors and mass flow rate has been optimized. Exergy has been calculated on the basis of entropy concept.

a r t i c l e

i n f o

Article history: Received 17 March 2016 Received in revised form 29 May 2016 Accepted 19 June 2016 Available online xxxx Keywords: Energy matrices Energy Exergy

a b s t r a c t This paper presents the life cycle cost analysis of partially covered photovoltaic thermal (PVT) compound parabolic concentrator (CPC) collector integrated solar distillation system known as PVT-CPC active solar distillation system by incorporating the effect of energy payback period. The thermal model of the system has been developed. The number of PVT-CPC collectors and mass flow rate has been optimized. The annual yield, EPF and LCCE have been found to be higher by 5%, 12.73% and 22.22% respectively for double slope than single slope PVT-CPC active solar distillation system at 0.14 m depth of water. However, production cost of water at 5% rate of interest and EPBT have been found to be lower by 10.09% and 17.98% respectively for double slope PVT-CPC active solar distillation system. It is inferred that double slope performs better than single slope PVT-CPC active solar distillation system based on annual yield if depth of water is less than 0.19 m and vice-versa. The proposed system is self sustainable and it can meet the daily requirement of potable water on commercial level as well as DC electrical power during sunshine hours. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Design and fabrication of solar distillation system is one of the attractive alternatives to meet the crisis of potable water and energy for remote areas because it is self sustainable, simple in technology, ecofriendly, more economical and easily maintainable and it can also supply DC electric power during sunshine hours if needed. Solar still can broadly be classified as passive and active. In the case of active solar still, thermal energy is fed to the basin of solar still with an aim to increase the temperature of water. It results in the creation of higher temperature difference between water surface and inner surface of glass cover. The rate of evaporation increases and higher yield is obtained. ⁎ Corresponding author. E-mail address: [email protected] (D.B. Singh).

http://dx.doi.org/10.1016/j.desal.2016.06.021 0011-9164/© 2016 Elsevier B.V. All rights reserved.

Thermal energy can be fed to the basin in many ways. However, the most recommended method is the integration of flat plate collector (FPC) to the basin of solar still. FPC can be integrated to the basin of solar still either directly [Yadav and Yadav [55], Badran and Al-Tahaineh [5], Abdel-Rehim and Lasheen [1], Tripathi and Tiwari [51], Badran et al. [6], Tiwari and Tiwari [49], Dwivedi and Tiwari [17]] or by heat exchanger [3,19,46]. Further, Lilian et al. [33] designed a solar still in which a light weight hollow drum partially submerged within the still cavity was slowly rotated. They reported an enhancement in yield by 20%– 30% as compared to conventional solar still. Rajaseenivasana et al. [39] divided the basin of solar still integrated with FPC into smaller partitions. They obtained an increase in yield by 60% in comparison to the conventional solar still. Hamadou and Abdellatif [24] heated the solar still fluid at its bottom by a circulating heat transfer fluid and reported that the relation between distilled water production and the heat

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D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

transfer fluid rate is not linear as doubling this rate increases the yield by only 9%. Estahbanati et al. [20] analyzed the effect of number of stages on productivity of multi-effect active solar still in continuous and noncontinuous mode. They concluded that a 5-stage system would produce 25% more freshwater in continuous mode compared to non-continuous mode. Calise et al. [8] studied a trigeneration system integrating photovoltaic/thermal collectors and seawater desalination. They designed it for small communities in European Mediterranean countries which are rich in renewable sources and poor in fossil fuels and water resources. Kern and Russell [29] designed PVT for the first time and reported an increase in electrical efficiency when water or air is passed below the PV module due to heat transfer from the PV module which results in the reduction of temperature of PV module. The theoretical model of PVT systems was analyzed by Hendrie [25]. Garg and Adhikari [22] investigated thermal modeling of hybrid PVT air collector integrated with compound parabolic concentrator (CPC) and found that the thermal and electrical output of the system was better with CPC. Guiqiang et al. [23] studied building integrated compound parabolic concentrator PVT systems and found that PVT-CPC collectors have lead to the reduction in the quantity of PV cells and an increase in the efficiency. Kumar and Tiwari [30] investigted the hybrid (PVT-FPC) single slope active solar still experimentally with an aim to operate the system in remote locations without grid connection. The work of Kumar and Tiwari [30] was further extended by Tiwari et al. [50] and Singh et al. [44]. They integrated two partially covered flat plate collectors in series and pump to the basin of solar still with insulated pipe. Tiwari et al. [50] presented exergoeconomic and enviroeconomic analysis and concluded that the thermal efficiency of their system was lower than the systems reported by Kumar and Tiwari [30] and Singh et al. [43]. However, exergy efficiency and overall thermal efficiency were better. Singh et al. [44] presented the experimental studies of active solar still integrated with two hybrid PVT collectors and concluded that the productivity lies between 120.29% and 883.55%. None of the above researchers have integrated N identical PVT-CPC collectors in series to basin type solar still. Hence, this paper deals with the comparative study of single and double slope PVT-CPC active solar distillation systems. The proposed system consists of N identical

PVT-CPC water collectors connected in series, DC motor driven pump and solar still. PVT-CPC water collectors are connected to solar still in closed loop with the help of pump and insulated pipes. Annual yield, energy and exergy have been evaluated for optimum mass flow rate and optimum number of collectors at 0.14 m water depth. The performance of double slope has been compared with the performance of single slope PVT-CPC active solar distillation system on the basis of energy matrices which includes EPBT, EPF and LCCE for optimum mass flow rate and optimum number of collectors at 0.14 m water depth. The production cost of water and cost of electricity gain have also been calculated. The proposed systems are unique and self-sustained to supply potable water for domestic as well as industrial applications. It can also supply DC electrical power during sunshine hours to users if needed. 2. System description Fig. 1 represents the schematic diagram of single slope PVT-CPC active solar distillation system. There are basically three components namely N identical partially (25%) covered PVT-CPC collectors, single slope solar still and pump driven by DC motor in the proposed system. Tables 1a and 1b show the detailed specification of the system. A number (N) of identical partially covered PVT-CPC water collectors are connected in series and the outlet of Nth water collector is fed to the basin of single slope active solar still. The inlet of the first water collector is connected to the outlet of pump driven by DC motor and inlet of pump is connected to the basin of single slope active solar still. Hence, N identical partially covered PVT-CPC water collectors are in closed loop with single slope active solar still through pump driven by DC motor and insulated pipes. Each of the collectors having receiver area 1 m × 1 m is integrated with a photovoltaic thermal module having area 0.25 m × 1.0 m at lower side [Chow et al. [11] and Tripathi et al. [52] (2016)] where low temperature water enters the collector. Coated aluminum has been used for the parabolic surface. The ratio of aperture area to receiver area of collector has been taken as 2. The beam radiation falling on the parabolic surface is reflected to receiver surface. The inclination of collector is 30° with horizontal surface to receive the annual maximum solar radiation. DC motor water pump is run by a portion of electrical energy generated by PV module and the remaining amount

Fig. 1. Schematic diagram of single slope active solar still integrated with N identical partially covered PVT-CPC collectors connected in series.

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91 Table 1a Specifications of single and double slope PVT-CPC active solar distillation system. Single slope active solar still

Double slope active solar still

Component

Specification Component

Specification

Length Width Inclination of glass cover Height of smaller side Material of body Material of stand Cover material Orientation Thickness of glass cover Kg

2m 1m 15o 0.2 m GRP GI Glass South 0.004 m 0.816

2m 1m 15o 0.2 m GRP GI Glass East–west 0.004 m 0.816

Length Width Inclination of glass cover Height of smaller side Material of body Material of stand Cover material Orientation Thickness of glass cover Kg

W/m-K 0.1 m 0.166

Thickness of insulation Thermal conductivity of insulation

Thickness of insulation Thermal conductivity of insulation

W/m-K

W/m-K 0.1 m 0.166 W/m-K

77

absorbed. Hence, temperature of basin liner increases. It transmits heat to water and temperature of water rises which causes temperature difference between the water surface and glass surface. Water gets evaporated and it reaches to the inner surface of glass where it gets condensed. The condensed water trickles down the inner surface of glass cover and it is collected in a trough which is fixed to the front side of solar still. The distillate is further allowed to flow down to the external jar with the help of plastic pipe. The rear wall of solar still is fitted with inlet pipe which allows saline/brackish water into the solar still. An opening provided at the bottom facilitates the flushing out of the layer of sludge that may develop as the time passes. The entire unit has been fixed on iron stand. The whole unit is oriented to face south so that the maximum radiation is achieved throughout the year. Fig. 2 shows the schematic diagram of double slope PVT-CPC active solar distillation system. It is oriented along east-west direction. Its detailed specification is presented in Tables 1a and 1b. The working principle is similar to single slope PVT-CPC active solar distillation system.

PVT-CPC collector Component Type and no of collectors Receiver Area of solar water collector

Specification

Component

Specification

Tube in plate Aperture area type ,N 1.0 m × 1.0 m Aperture area of module

Collector plate thickness 0.002

2

2m

0.5 m × 2.0

Aperture area of receiver

m 0.75 m × 2.0 m 0.25 m × 1.0

Thickness of Copper Tubes

0.00056 m

Receiver area of module

Length of each Copper Tubes

1.0 m

m Receiver area of collector 0.75 m × 1.0

Ki (Wm−1K−1) FF Thickness of insulation Angle of CPC with Horizontal Thickness of toughen glass on CPC Effective area of collector under glass Pipe diameter DC motor rating

0.166 0.8 0.1 m 30°

F' ρ τg αc

m 0.968 0.84 0.95 0.9

0.004 m

βc

0.89

0.75 m2

αp

0.8

0.0125 m 12 V, 24 W

Effective area of collector 0.25 m2 under PV module

3. Thermal modeling The following assumptions are made for the thermal modeling of single and double slope PVT-CPC active solar distillation systems. i. The partially covered PVT-CPC water collector and solar stills are in quasi steady state. ii. The ohmic losses in the solar cells are negligible. Ohmic losses are the losses due to the interconnections and bus bar in the PV module and other connecting wires. Since the electrical resistivity of the interconnections and other connecting wires (generally aluminum or copper) is very low (of the order of 10− 8 Ω − m), therefore i2r losses are negligible in comparison to the other thermal losses or heat transfers in the system. Hence, it can be neglected as it will not affect the thermal performance of the solar cell in greater extent. iii. The amount of heat loss in solar cell, glass cover, absorbing and insulating material of collector and solar stills is negligible in comparison to the other rate of heat transfer in the system. The amount of heat loss in solar cell is given by m.cp.ΔT where m is the mass of solar cell, cp is specific heat capacity at constant pressure of solar cell material (silicon) and ΔT is the temperature difference between average cell temperature and ambient temperature. The mass of solar cell (0.156 m × 0.156 m × 0.0002 m) is approximately 0.0113 kg taking density of silicon as 2.33 × 103 kg/m3. The value of cp for silicon at room temperature is 0.705 kJ/kg-K and average value of ΔT in the month of June for the proposed system is 44.87 K. Therefore, heat loss in solar cell comes out to be 0.36 kJ which is 0.0012% of the heat output from solar still as heat output from solar still is of the order of 104 kJ. Further, the amount of heat loss in glass cover is given by m.c p .ΔT where m is the mass of glass cover, c p is specific heat capacity at constant pressure of glass and ΔT is the temperature difference between inner surface and outer surface. The average temperature difference between inner and outer surfaces of glass cover is 2.84 K in the case of PVT active solar still as per Kumar et al. [31]. Mass of glass cover in solar still is 20.70 kg taking glass density as 2500 kg/m 3 . The heat consumed by glass comes out to be 49.38 kJ taking c p of glass as 0.84 kJ/kg-K whereas daily heat output of the system is of the order of 104 kJ. Therefore,

of generated energy is available for other use. Here, the function of pump is to overcome the pressure drop in collectors and piping arrangement and hence it compels water to circulate under forced mode of operation. The radiation directly absorbed by the blackened surface of the collector, the thermal energy convected from back surface of PV module and solar radiation being transmitted through non packing area of module are used to heat water passing through the pipe in the collector. The outlet of last water collector is fed to the single slope active solar still which consists of an effective basin area of 2 m × 1 m. Glassfibre reinforced plastic has been used for solar still. The top surface of the solar still is covered by a transparent glass which is inclined with horizontal at an angle of 15°. It is sealed with the help of window-putty for preventing vapor leakage to outside. The side walls and bottom are blackened from inner side to get maximum absorption of solar radiation. The solar radiation falls on the outer surface of transparent glass cover. Some portion is reflected, some is absorbed by the surface and the remaining part is transmitted to water. The water surface reflects a small part of radiation, some portion is absorbed by the water mass and the remaining amount is transmitted to basin liner where it gets Table 1b Average wind velocity for each month of year. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sept

Oct

Nov

Dec

Velocity (m/s)

2.77

3.13

3.46

3.87

4.02

4.11

3.39

2.91

2.85

2.16

1.83

2.40

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D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

Fig. 2. Schematic diagram of double slope active solar still integrated with N partially covered PVT-CPC collectors connected in series.

heat consumed by glass comes out to be 0.17% in comparison to the amount of heat output from the solar still. Similarly, heat consumed by absorbing and insulating materials can also be evaluated which will appear negligibly small. Hence, amount of heat consumed by solar cell, glass, absorbing and insulating materials can be neglected because they are not going to affect the result in greater extent. iv. Solar stills are vapor leakage proof. In the event of leakage, the steady state condition no longer exists and energy equation will become too complex due to transient condition. Hence, the vapor leakage has been neglected because it will not affect the result much and steady state condition exists. v. The level of water in the basin is constant. The maximum daily yield is 30.36 kg (Tables 2 and 3). The corresponding change in level of water is 0.015 m during 24 h. The variation in daily yield has been reported as 0.25% by Tiwari et al. [56] if water level changes by 15.38% (0.11 m to 0.13 m) in the case of active solar still. Hence, the small change in level of water in the basin can be neglected. vi. No stratification (i.e. no layered configuration) of water occurs in the basin of the solar stills. In the case of active solar

still, pump is inserted between basin of solar still and collector which circulates water throughout the system. It results in continuous stirring of water in the basin and there is a continuous mixing of water. Hence, stratification of water can be neglected. vii. The film type condensation occurs through the glass. The glass is inclined at small angle with the horizontal to facilitate the same because the component of gravitational force (mgsinθ) will act along the surface in the downward direction which will help in trickling down the condensate. Here, θ is the angle of inclination of the glass with horizontal. Also, the inner surface of glass is ensured to be clean so that droplet formation does not take place. Further, if the film type condensation is not ensured then water droplets will form at the inner surface of glass cover which will act as mirror and some portion of the solar radiation will be reflected. It will result in lesser amount of solar radiation reaching to the surface of water which will adversely affect the yield. Hence, film type condensation is ensured during the design phase. However, formation of droplets in small amount may still occur which is ignored because they are negligibly small.

Table 2 Daily, monthly and annual yield for single slope PVT-CPC active solar distillation system.

Weather condition (type a) Month

Ya

Jan 23.98 Feb 23.27 Mar 25.47 Apr 27.06 May 26.71 Jun 26.07 Jul 23.05 Aug 22.40 Sep 26.92 Oct 24.14 Nov 22.89 Dec 23.41 Annual yield (kg)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

na

ma

Yb

nb

mb

Yc

nc

mc

Yd

nd

md

Monthly yield

3 3 5 4 4 3 2 2 7 5 6 3

71.94 69.81 127.36 108.25 106.85 78.20 46.10 44.80 188.44 120.71 137.36 70.22

21.76 22.50 26.33 26.97 21.57 21.75 18.23 19.94 24.52 17.77 14.09 17.67

8 4 6 7 9 4 3 3 3 10 10 7

174.11 89.98 157.99 188.81 194.11 87.00 54.70 59.82 73.55 177.68 140.85 123.69

5.84 6.17 10.54 11.31 14.69 11.73 11.50 9.01 14.58 11.85 4.84 8.00

11 12 12 14 12 14 10 7 10 13 12 13

64.23 74.09 126.44 158.37 176.32 164.21 114.98 63.04 145.84 154.00 58.04 104.00

1.37 1.27 5.22 9.20 7.99 4.69 3.70 3.92 5.40 3.53 3.87 1.54

9 9 8 5 6 9 17 19 10 3 2 8

12.36 11.45 41.75 45.99 47.93 42.18 62.88 74.42 54.02 10.59 7.75 12.34

322.65 245.33 453.54 501.42 525.21 371.59 278.66 242.07 461.85 462.98 344.00 310.25 4519.54

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

79

Table 3 Daily, monthly and annual yield for double slope PVT-CPC active solar distillation system.

Weather condition (type a) Month

Ya

Jan 25.19 Feb 24.18 Mar 26.41 Apr 28.47 May 27.90 Jun 26.82 Jul 23.19 Aug 22.90 Sep 30.36 Oct 26.62 Nov 24.18 Dec 23.33 Annual yield (kg)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

na

ma

Yb

nb

mb

Yc

nc

mc

Yd

nd

md

Monthly yield

3 3 5 4 4 3 2 2 7 5 6 3

75.57 72.53 132.07 113.86 111.62 80.47 46.37 45.81 212.55 133.09 145.07 70.00

22.75 23.43 27.60 28.32 21.40 21.65 18.42 19.92 26.21 18.03 15.10 18.25

8 4 6 7 9 4 3 3 3 10 10 7

182.02 93.70 165.58 198.24 192.60 86.60 55.25 59.77 78.64 180.28 151.05 127.76

7.08 7.15 11.91 12.41 14.46 12.59 12.54 9.59 14.49 12.27 5.44 9.03

11 12 12 14 12 14 10 7 10 13 12 13

77.93 85.80 142.89 173.69 173.51 176.24 125.36 67.14 144.92 159.50 65.33 117.35

1.61 1.60 5.79 9.90 8.18 3.93 3.64 3.99 5.56 3.90 4.41 1.83

9 9 8 5 6 9 17 19 10 3 2 8

14.48 14.41 46.31 49.52 49.06 35.39 61.84 75.83 55.55 11.69 8.81 14.64

350.00 266.44 486.85 535.31 526.80 378.69 288.82 248.55 491.66 484.56 370.27 329.75 4757.70

3.1. Useful energy gain for N identical partially covered PVT- CPC water collectors connected in series Following Tripathi et al. [52], the rate of useful thermal output from N identical partially covered PVT-CPC water collectors connected in series can be expressed as,
Q_ uN ¼

1−K k N



ð1−K k Þ

ðA F R ðατ ÞÞ1 Ib ðt Þ þ


 1−K k N ð1−K k Þ

  ðA F R U L Þ1 T fi −T a : ð1Þ

In their set-up, PVT-CPC water collectors are in open loop. In the proposed PVT-CPC active solar distillation system, collectors are in closed loop with solar still. The water from basin of solar still enters to the inlet of first PVT-CPC water collector and outlet of Nth PVT-CPC water collector are fed to the basin of solar still. Hence, Tfi becomes equal to Tw. The temperature at the outlet of Nth PVT-CPC water collector (TfoN) is given by

T foN



 N N Ib ðt ÞðA F R ðατÞÞ1 1−K k T a ðA F R U L Þ1 1−K k þ þ T fi K Nk ð2Þ ¼ _ fCf _ fCf ð1−K k Þ ð1−K k Þ m m

where, Tfi = Tw. The temperature obtained at the outlet of Nth PVT-CPC water collector is fed to the basin of solar still. Hence, Two = TfoN. The analytical expression for the temperature dependent electrical efficiency of solar cells (ηcN) of a number (N) of PVT-CPC water collectors is given by Evans [21] and Schott [42] as ηcN

   ¼ ηo 1−βo T cN −T o

ð3Þ

where, ηo is the efficiency at standard test condition and T cN is the average solar cell temperature of Nth PVT-CPC water collector. The value of T cN has been calculated using the expression developed by Tripathi et al. [52] in which Tfi = Tw.

0

where α g ¼ ð1–Rg Þα g represents the fraction of solar flux absorbed by the glass cover and h1w = hr,wg + hc,wg + he,wg represents rate of total heat transfer coefficient from water surface to inner surface of glass cover. 3.2.2. Outer surface of glass cover    Kg  T gi –T go Ag ¼ h1g T go −T a Ag Lg

ð5Þ

where h1g = hr,g + hc,g or h1g = 5.7 + 3.8V. 3.2.3. Water mass in basin   dT w 0 Q_ uN þ α w Is ðt ÞAb þ hbw ðT b –T w ÞAb ¼ h1w T w –T gi Ab þ M w C w dt

ð6Þ

0

where α w ¼ ð1–Rg Þð1–α g Þð1–Rw Þα w which is the fraction of solar flux absorbed by water mass and Q_ is the rate of useful thermal output uN

from N identical PVT-CPC water collectors connected in series. 3.2.4. Basin liner 0

α b Is ðt ÞAb ¼ hbw ðT b –T w ÞAb þ hba ðT b −T a ÞAb

ð7Þ

0

where α b ¼ ð1–Rg Þð1–α g Þð1–Rw Þð1–α w Þα b which is the fraction of solar flux absorbed by basin liner. Using Eq. (1) and Eqs. (2) to (7), one can get the following differential equation for water temperature in basin. dT w þ aT w ¼ f ðt Þ dt

ð8Þ

3.2. Energy balance equations for single slope solar still Following Singh et al. [44], energy balance equation for single slope solar still can be written as follows. 3.2.1. Inner surface of glass cover

   Kg  0 T –T go Ag α g Is ðt ÞAg þ h1w T w –T gi Ab ¼ Lg gi

ð4Þ

Values of a and f(t) of Eq. (8) are given in Appendix A. The following assumptions have been made to get an approximate solution of differential Eq. (8). (i) The time interval (Δt ) is small i.e. (0 b t b Δt). (ii) Values of Ta, Ib(t) and Is(t) can be considered as average value between ‘0’ and‘t’ i.e. T a, Ib ðtÞ and I s ðtÞ. Hence f(t) becomes constant and its average value will be f ðtÞ . (iii) a is constant for interval Δt.

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One can get the solution of Eq. (8) with initial condition, Tw = Tw0 at t = 0, as follows. Tw ¼

 f ðt Þ  1−e−at þ T w0 e−at a

ð9Þ

After evaluating Tw from Eq. (9), one can obtain glass temperature from Eqs. (4) and (5) as follows. T gi ¼

T go

α 0g Is ðt ÞAg þ h1w T w Ab þ U c;ga T a Ag U c;ga Ag þ h1w Ab

Kg T þ h1g T a Lg gi ¼ Kg þ h1g Lg

ð10Þ

ð11Þ

  he;wg Ab T w −T gi  3600 L

3.3.2.2. For outer glass cover.    Kg  T −T goW AgW ¼ h1gW T goW −T a AgW Lg giW where h1gW = hrgW + hcgW or h1gW = 5.7 + 3.8V. 3.3.3. For basin liner

α 0b ðISE ðt Þ þ ISW ðt ÞÞ

ð12Þ

For AAar ¼ 1; Arm = 0.625 m2, Arc = 1.375 m2, Ib(t) = I(t), Ab = 1m2, and N = 2, equations derived for single slope PVT-CPC active solar distillation system reduces to expressions derived by Singh et al. [44]. They have validated the thermal model with experimental study under same assumptions.

ðMw C w Þ

Following Dwivedi and Tiwari [18], energy balance equation for double slope solar still can be written as follows. 3.3.1. Energy balances for east cover 3.3.1.1. For inner glass cover.

dT w A ¼ ðISE ðt Þ þ ISW ðt ÞÞα 0w b dt 2

uN

ð18Þ Using Eq. (1) and Eqs. (13) to (18), one can get the differential equation for water temperature (Tw) in basin. Following assumptions made in solving Eq. (8), one can get the solution of this differential equation with initial condition Tw = Two at t = 0 as  f 1 ðt Þ  1−e−a1 t þ T w0 e−a1 t : a1

T giE ¼ ð13Þ

Where h1wE = hrwgE + hcwgE + hewgE which is called total heat transfer coefficient from water surface to glass cover and αg′ represents the fraction of solar flux absorbed by the glass cover.

T goE

3.3.1.2. For outer glass cover. ð14Þ T goW

where h1gE = hrgE + hcgE or h1gE = 5.7 + 3.8V. 3.3.2. Energy balances for west cover

ð19Þ

Eq. (19) is similar to Eq. (9) obtained for single slope PVT-CPC active solar distillation system. However, constants of Eq. (19) which has been obtained for double slope PVT-CPC active solar distillation system are different. Their expressions are given in Appendix A. After evaluating Tw from Eq. (19), one can obtain glass temperature for double slope PVT-CPC active solar distillation system using Eqs. (13) to (16) as follows. A1 þ A2 T w P

ð20Þ

B1 þ B2 T w P

ð21Þ

T giW ¼

Kg T þ h1gE T a Lg giE ¼ Kg þ h1gE Lg Kg T giW þ h1gW T a Lg ¼ Kg þ h1gW Lg

ð22Þ

ð23Þ

Constants of Eqs. (20) to (23) are given in Appendix A. After evaluating glass temperature from Eqs. (20) and (21) and water temperature from Eq. (19), one can obtain hourly yield for east and west side in the case of double slope PVT-CPC active solar distillation system as follows.

3.3.2.1. For inner glass cover.  A   α 0g ISW ðt ÞAgW þ h1wW T w −T giW b þ hEW T giE −T giW AgE 2  Kg  ¼ T −T goW AgW Lg giW

ð17Þ

 A  A þ hbw ðT b −T w ÞAb −h1w T w −T giE b −h1w T w −T giE b 2 2 þ Q_

Tw ¼

3.3. Energy balance equations for double slope solar still

   Kg  T giE −T goE AgE ¼ h1gE T goE −T a AgE Lg

Ab ¼ hbw ðT b −T w ÞAb þ hba ðT b −T a ÞAb 2

3.3.4. For water mass in basin

where L is the latent heat of evaporation and can be evaluated using the expression given by Fernandez and Chargoy [57] and Toyama [58]. Above equations can be discussed for the following limiting condition.

 A   α 0g ISE ðt ÞAgE þ h1wE T w −T giE b −hEW T giE −T giW AgE 2  Kg  ¼ T −T goE AgE Lg giE

ð16Þ

where αb′ is the fraction of solar flux absorbed by basin liner.

_ ew Þ can be expressed as The hourly yield ðm _ ew ¼ m

where h1wW = hrwgE + hcwgE + hewgE which is called total heat transfer coefficient from water surface to glass cover

ð15Þ

_ ew;E ¼ m

hewE

 Ab  T w −T giE 2  3600 L

ð24Þ

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

_ ew;W ¼ m

hewW

 Ab  T w −T giW 2  3600 L

[60] ð25Þ

The hourly yield for double slope PVT-CPC active solar distillation system can be calculated by adding the hourly yield obtained from _ ew;E ) using Eq. (24) and hourly yield obtained from west east side (m _ ew;W Þ using Eq. (25). side (m 4. Analysis 4.1. Energy analysis First law of thermodynamics has been used for the energy analysis. The sum of annual thermal energy obtained from solar still and the equivalent annual thermal energy obtained from N identical PVT-CPC water collectors connected in series gives the overall annual energy. Hence, the overall thermal energy (Eout) of PVT-CPC active solar distillation system can be expressed as Eout ¼

81

ðMew  LÞ ðPm –Pu Þ þ : 3600 0:38

ð26Þ

Here, Mew is annual yield from solar still, Pm is annual power generated from photovoltaic module, Pu is annual power utilized by pump and L is latent heat. The value of latent heat has been taken as 2400 kJ/kg-K. The difference of Pm and Pu used in Eq. (26) represents net electrical energy for the whole year. Electrical energy is high grade energy. Hence, the factor 0.38 has been used for converting electrical energy into equivalent thermal energy. This factor corresponds to power generation efficiency for a conventional power plant [26]. The _ e Þ can be expression for hourly electrical energy/electrical exergy ðEx

 P w ¼ exp 25:317−

5144 and ðT w þ 273Þ

" P gi ¼ exp 25:317− 

5144  T gi þ 273

#

The daily thermal exergy for clear days (condition (a)) can be calculated by adding hourly exergy obtained from Eq. (28) for 10 h as the beam intensity exists for 10 h only and the same process has been adopted to calculate the daily thermal exergy for other climatic conditions (b), (c), and (d). The monthly thermal exergy for clear days (condition (a)) can be evaluated by multiplying daily thermal exergy with the corresponding number of clear days and the same process has been adopted to calculate the monthly exergy for other climatic conditions (b), (c), and (d). The sum of the thermal exergy in the climatic conditions (a), (b), (c), and (d) gives the total thermal exergy for each month. The annual thermal exergy can be calculated by adding monthly thermal exergy for 12 month. Following Eq. (28), the expression of hourly exergy gain for double slope active solar still can be written as A Hourlyexergygain ¼ hewgE  b 2 " ( )#   ðT w þ 273Þ   T w −T giE −ðT a þ 273Þ  ln  T giE þ 273 A þ hewgW  b 2 " ( )#   ðT w þ 273Þ  :  T w −T giW −ðT a þ 273Þ  ln  T giW þ 273 ð30Þ

written as N   _ e ¼ Am I b ðt Þ ∑ ατ g η : Ex cN

ð27Þ

1

The daily electrical exergy can be calculated by adding hourly electrical exergy for 10 h as beam intensity exists for 10 h only. The monthly electrical exergy can be evaluated by multiplying daily electrical exergy with number of clear days and addition of monthly electrical exergy for 12 moth will give annual electrical exergy (Pm) used in Eq. (26). 4.2. Exergy analysis

written as "

( )#   ðT w þ 273Þ  T w −T gi −ðT a þ 273Þ  ln  T gi þ 273

where; he;wg ¼ 16:273  10−3 hc;wg



P w −P gi T w −T gi

 

 T w −T gi þ



ð28Þ

ð29Þ

[59]

hc;wg ¼ 0:884

Gex;annual ¼ Exout þ ðP m −P u Þ:

ð31Þ

Here, Exout is annual thermal exergy output obtained from active solar still, Pm is annual electrical exergy obtained from N identical PVT-CPC water collectors connected in series and Pu is power required to drive the pump. 4.3. Energy matrices

Second law of thermodynamics has been used for exergy analysis. The term exergy analysis on the basis of entropy concept has been used by Jafarkazemi and Ahmadifard [28] for exergetic evaluation of flat plate collectors. Following Nag [34], the hourly output thermal _ out ðWÞ for single slope active solar distillation system can be exergy Ex

_ out ¼ Ab h Ex ewg

The value of hewgE and hewgW can be evaluated using Eq. (29). The overall annual exergy gain (Gex,annual) for single slope and double slope PVT-CPC active solar distillation systems can be written as

 P w −P gi T w

268:9  103 −P w

Analysis of energy matrices means to evaluate energy payback time, energy production factor and life cycle conversion efficiency. These parameters are important for renewable technologies as the use of technology does not make any sense if the energy produced by them during the whole life time is less than the energy used in their manufacturing [61]. 4.3.1. Energy payback time (EPBT) The time period needed to recover the total energy exhausted in preparing the materials (embodied energy) required for fabrication of PVTCPC active solar distillation system is known as EPBT. Following Tiwari and Mishra (2012), it can be written as EPBTbased on energy ¼

Embodiedenrgy ðEin Þ Annualenergyoutput ðEout Þ

ð32Þ

EPBTbased on exergy ¼

Embodiedenrgy ðEin Þ : Annualexergyoutput ðGex; annualÞ

ð33Þ

ð13Þ

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Here, embodied energy means the amount of energy used to manufacture the material required for PVT-CPC active solar distillation system. Table 6 shows the calculation of embodied energy for single slope and double slope PVT-CPC active solar distillation systems. The overall annual energy output can be evaluated using Eq. (26). Tables 2 and 3 represent the calculation of annual yield for single slope and double slope PVT-CPC active solar distillation system. The value of latent heat has been taken as 2400 kJ/kg. The numerical value of EPBT for single slope and double slope PVT-CPC active solar distillation system should be as low as possible to make them cost effective. It means lower the value of EPBT, better is the system. EPBT for single slope and double slope PVT-CPC active solar distillation system has been evaluated using Eqs. (32) and (33) and they have been presented in Table 6. 4.3.2. Energy production factor (EPF) It represents the overall performance of the PVT-CPC active solar distillation system. It is the reciprocal of EPBT and its ideal value on annual basis is 1. Following Tiwari and Mishra (2012), EPF for PVT-CPC active solar distillation system on annual basis can be written as

EPF based on energy ¼

Eout Ein

ð34Þ

EPF based on exergy ¼

Gex;annual : Ein

ð35Þ

Here, Eout, Ein and Gex, annual are respectively overall annual energy output, embodied energy and overall annual exergy gain for PVT-CPC active solar distillation system. The overall annual energy output and overall annual exergy gain can be evaluated using Eq. (26) and (31) respectively. EPF for single slope and double slope PVT-CPC active solar distillation systems have been evaluated using Eqs. (34) and (35) and presented in Table 6. 4.3.3. Life cycle conversion efficiency (LCCE) It represents the net output of PVT-CPC active solar distillation system with respect to solar radiation falling on it for the entire life time. The ideal value of LCCE for PVT-CPC active solar distillation system is one. Higher the value of LCCE, better will be the system. Following Tiwari and Mishra (2012), LCCE for PVT-CPC active solar distillation system can be written as

LCCEbased on energy ¼

Eout  n−Ein Esol  n

ð36Þ

LCCEbased on exergy ¼

Gex;annual  n−Ein : ðAnnualsolarexergyÞ  n

ð37Þ

Here, Esol,n,Eout,Ein and Gex,annual are respectively annual solar energy, life, overall annual energy output, embodied energy and overall annual exergy gain for PVT-CPC active solar distillation system. Figs. 15 and 16 represent the variation of monthly solar energy for single and double slope PVT-CPC active solar distillation system. The annual solar energy (Esol) for single slope and double slope PVT-CPC active solar distillation systems can be calculated by adding monthly solar energy for 12 month. Annual solar exergy can be calculated by multiplying Esol with 0.93 which is obtained from expression given by Petela [38]. LCCE based on energy for single slope and double PVT-CPC active solar distillation system has been evaluated using Eq. (36) and presented in Table 7. LCCE based on exergy for single slope and double PVT-CPC active solar distillation system has been evaluated using Eq. (37) and presented in Table 7.

4.4. production cost of water and electricity Following Kumar and Tiwari [62] and Singh et al. [44], the production cost of water in Rs./kg (Cwp) and cost of electricity generation in Rs./kWh (Ce) can be written as UAC−Re Mw

ð38Þ

UAC−Rw : Ee

ð39Þ

C wp ¼

Ce ¼

Here, UAC, Re, Mw, Rw and Ee represent uniform end-of-year annual cost, revenue earned from electricity, annual yield, revenue earned from water and net annual electricity gain from PVT-CPC active solar distillation system respectively. If the value of (UAC-Rw) obtained is negative, then it can be taken as zero as negative cost does not make any sense. In this case, value of Ce becomes zero which will mean that we are getting electricity at no cost. Also, negative value of (UAC-Rw) represents that revenue obtained from water alone is capable of overcoming the cost of system. The present value method has been used to calculate the value of UAC for a given initial investment of PVT-CPC active solar distillation system. Table 5 shows the cost of different components of the system. The salvage value is based on the current price of different scrap materials in Indian local market. Following Tiwari [47], the uniform end-of-year annual cost for a given initial investment of PVT-CPC active solar distillation systems can be written as UAC ¼ P s  F CR;i;n þ M  F CR;i;n −Ss  F SR;i;n :

ð40Þ

Here, Ps, Ss and M are the net present cost, salvage value and maintenance cost of PVT-CPC active solar distillation system respectively. The first term of Eq. (40) corresponds to the part of UAC coming from net present cost, the second term represents the part of UAC corresponding to present value of maintenance cost and third term represent the part of UAC that comes from salvage value. The maintenance cost (M) is the product of the net present cost (Ps) and maintenance cost factor which is generally taken as 0.1. The capital recovery factor (FCR,i,n)and sinking fund factor (FSR,i,n) are given by F CR;i;n ¼

i  ð1 þ iÞn i and F SR;i;n ¼ ð1 þ iÞn −1 ð1 þ iÞn −1

where i and n are the rate of interest and life of the system. The capital recovery factor and sinking fund factor [47] have been used to convert the present cost and future cost into uniform end-of-year annual cost respectively. Net present cost (Ps) for the 50 years life span of PVTCPC active solar distillation system can be expressed as Ps ¼ P þ Pp þ

Pp ð1 þ iÞ10

þ

Pp ð1 þ iÞ20

þ

Pp ð1 þ iÞ30

þ

Pp ð1 þ iÞ40

:

Here, P and Pp are the initial cost of the system and the cost of the pump respectively. The life of DC water pump is 10 years and it has been assumed that the cost of the pump remains same on each purchase after adjusting its salvage value. The initial cost of the system can be calculated as P = Csolar still + CPVT + CCPC + Cfab. Here, Csolar still is the cost of solar still, CPVT represent the cost of photovoltaic module, CCPC represent the cost of N identical compound parabolic concentrator water collector and Cfab represent the fabrication cost which includes the cost of piping and labor. 5. Methodology The following methodology has been adopted for the evaluation of energy matrices of PVT-CPC active solar distillation systems.

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83

5.1. Step I Solar radiation on a horizontal surface, ambient air temperature and number of days for the weather conditions (a), (b), (c) and (d) have been taken from Indian Metrological Department (IMD), Pune, India. Liu and Jordan formula has been used to evaluate solar radiation for inclined surface at 30° north latitude with the help of MATLAB. The hourly variation of solar and beam radiation on horizontal surface and ambient air temperature have been shown in Figs. 3, 4 and 5 respectively. 5.2. Step II Eqs. (2) and (3) have been used to calculate TfoN and ηcN. Water temperature in basin, glass temperature and evaporative heat transfer coefficient for single slope PVT-CPC active solar distillation system have been evaluated using Eqs. (9), (10) and (29) respectively. Then, yield for single slope PVT-CPC active solar distillation system has been calculated using Eq. (12). Similarly, Water temperature in basin, glass temperature for east side, glass temperature for west side and evaporative heat transfer coefficient for double slope PVT-CPC active solar distillation system have been evaluated using Eqs. (19), (20), (21) and (29) respectively. Then, yield for east side and west side of double slope PVTCPC active solar distillation system have been calculated using Eqs. (24) and (25) respectively. The addition of yield of east side and west side gives the total yield for double slope PVT-CPC active solar distillation system. 5.3. Step III Overall thermal energy and overall exergy have been evaluated using Eqs. (26) and (31) respectively for PVT-CPC active solar distillation system. Then, Eqs. (32) to (37) have been used to calculate energy matrices for single and double slope PVT-CPC active solar distillation systems. 5.4. Step IV UAC has been evaluated using Eq. (40). Further, production cost of water and cost of electricity gain have been evaluated using Eqs. (38) and (39) respectively. 6. Results and discussion All relevant equations and climatic data namely solar radiation, ambient temperature and average velocity have been fed to MATLAB. Beam radiation on horizontal surface, total radiation on horizontal surface and ambient temperature are represented by Figs. 3, 4 and 5 respectively. The output obtained is shown in Figs. 6 to 16 and Tables 2 to 7. Figs. 6

Fig. 3. Hourly variation of beam radiation (Ib) for each month of year.

Fig. 4. Hourly variation of solar intensity (W/m2) for each month of year.

and 7 show the variation of maximum temperature of fluid respectively in the collector of single slope and double slope PVT-CPC active solar distillation systems at given mass flow rate for a typical day in months of june. It has been observed that rise in maximum temperature of fluid decrease with the increase in mass flow rate. The rise in maximum temperature of fluid in collector is significant up to 0.04 kg/s and beyoud this value the gap between curves is vergy small which suggest that rise in value of maximum temperature at a given number of collectors is very small. If mass flow rate is continued to increase, then curves will overlap with each other. Hence, it can be concluded from Figs. 6 and 7 that the rise in temperature of water is vey small beyound 0.04 kg/s mass flow rate. It means that 0.04 kg/s is the optimum value of mass flow rate. At the mass flow rate beyond 0.04 kg/s, the rise in temperaute of water has been found to be very small because water gets lesser time to gain heat in PVT-CPC water collector. Figs. 6 and 7 also represent the effect of mass flow rate on maximum outlet water temperature. It has been observed that maximum outlet water temperature at Nth collector decreases with the increase of mass flow rate. It occurs mainly due to the fact that the rate of heat transfer from absorber plate to water increases with the increase in mass flow rate. Further, a drop of aproximately 40 °C of maximum outlet water temperature with increase of mass flow rate from 0.01 to 0.04 kg/s has been observed for a given seventh collector. In this case, other fluids having boiling temperature higher than water can be used along with heat exchanger to get higher yield with more number of collectors connected in series. Also, the temperature of water becomes more than

Fig. 5. Hourly variation of ambient temperature (Ta) for each month of year.

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Fig. 6. Variation of maximum temperature of water in the collector (TfoNs,max) of single slope PVT-CPC active solar distillation system for a typical day in the month of June.

Fig. 8. Hourly variation of yield of single and double slope PVT-CPC active solar distillation system for a typical day in the month of June and January.

100 °C, if number of PVT-CPC water collectors are more than 7 at the mass flow rate of 0.04 kg/s. Further, it has been noted that the rise in water temperature decreases with the increase in numbers of water collector due to higher heat losses as expected. Hence, optimum number of PVT-CPC water collectors has been found to be seven. Fig. 8 shows the variation of yield with mass flow rate at N = 7 for single and double slope PVT-CPC active solar distillation system for a typical day in the month of June and January. As mass flow rate increase, yield decreases which is as per expectation. It occurs because temperature at the outlet of Nth collector becomes lower with the increse in mass flow rate which contributes a lesser increase in temperaure of water in the basin as outlet of Nth water collector is fed to the basin of solar still. A lower temperaure difference is created between water temperature and glass cover temperaure due to lesser rise in water temperature. It results in lower evaporation and hence lower yield is obtained. It has been noted from Fig. 9 that the yield first increases with the increase in depth of water and then becomes almost constant. The daily yield is the sum of yield obtained in day time and yield obtained at night. The yield in day time decreases with the increase in depth as expected. It happens because of lesser rise in water temperature in the basin at higher depth of water. The yield at night depends on sensible heat contained by water mass which increase with the increase in depth of water and hence yield at night increases with the increase in depth of water. Further, increase in yield at night is more than the decrease in yield in day time with the increase in depth. Hence, daily yield increases with the increase in depth in the case of PVT-CPC active solar distillation system. However, the daily yield becomes almost constant after initial rise. It happens because further rise in water temperature is not possible at higher depth of water and increase in yield at night due to sensible heat contained by water mass is balanced by the

decrease in yield in day time. Hence, daily yield increase initially with the increase in depth of water and then it becomes almost constant. It has been observed from Fig. 10 that double slope performs better than single slope PVT-CPC active solar distillation system on the basis of yield if depth of water in basin is lower than 0.19 m and vice-versa. It happens because rise in temperature of water is higher at lower depth of water and moderate solar intensity exists for a longer period in the case of double slope PVT-CPC active solar distillation system. So, a moderate difference of water temperature and glass temperature exists for a longer period in the case of double slope PVT-CPC active solar distillation system. However, in the case of single slope PVT-CPC active solar distillation system, difference of water temperature and glass temperature is higher but it exists for a shorter period. Hence, higher daily yield is obtained for double slope PVT-CPC active solar distillation system at lower depth of water in the basin. At higher depth, the rise in temperature is lesser in the day time, but the sensible heat of water mass will be higher for single slope PVT-CPC active solar distillation system. So, daily yield for single slope is higher than double slope PVT-CPC active solar distillation system at higher depth of water. It can be noted from Fig. 10 that the daily yield increases with the increase in number of collectors due to higher heat gain as expected. However, the number of collectors cannot be taken more than 7 for the proposed system as maximum temperature of water at the outlet of Nth PVT-CPC collector becomes more than 100 °C. In such cases, another fluid having higher boiling point can be used along with heat exchanger so that heat gain can be transferred to the water in basin. The solar cell temperature and electrical exergy have been found to increase first and then to decrease as evident from Figs. 12 and 13 respectively. They occur due to similar variation in beam radiation. Figs. 12 and 13 also show that electrical efficiency decreases with the

Fig. 7. Variation of maximum temperature of water in the collector (TfoNd,max) of double slope PVT-CPC active solar distillation system for a typical day in the month of June.

Fig. 9. Variation of daily yield with depth of water for single slope and double slope PVTCPC active solar distillation system for a typical day in the month of June and January.

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

Fig. 10. Variation of cumulative (Jun and Jan) daily yield for single and double slope PVTCPC active solar distillation system.

85

Fig. 12. Hourly variation of electrical efficiency of module and average solar cell temperature for a typical day in the month of June.

increase in average solar cell temperature. It happens due to higher thermal energy losses at higher temperature and more collisions between electrons in depletion layer of solar cell at higher operating temperature. At lower temperature, loss in thermal energy and collisions between electrons in depletion layer of solar cell are lower and hence electrical efficiency increase with the decrease in average solar cell temperature. Tables 2 and 3 show the calculation of daily, monthly and annual yield for single and double slope PVT-CPC active solar distillation sys_ f ¼ 0:04 kg=s. The monthly tems at 0.14 m water depth, N = 7 and m yield for single slope and double slope PVT-CPC active solar distillation system is highest in May and April respectively. They happen because the monthly yield depends on daily yield and number of clear days. Further, daily yield depends on hourly yield which depends on heat transfer coefficient and temperature difference between water temperature and glass cover temperature. The evaporative heat transfer coefficient and temperature difference between water temperature and glass cover temperature are governed by solar intensity. The minimum value of monthly yield occurs in August for both single and double slope PVT-CPC active solar distillation systems. It happens due to lesser number of clear days due to rainy season. Tables 4 and 5 show the calculation of daily, monthly and annual thermal exergy for single and double slope PVT-CPC active solar distillation systems at 0.14 m water _ f ¼ 0:04 kg=s. Fig. 14. represents the variation of depth, N = 7 and m monthly electrical exergy of PVT for single and double slope PVT-CPC active solar distillation system. The electrical exergy of PVT is approximately same for both single and double slope PVT-CPC active solar distillation system as expected. It happens because PVT-CPC water collectors are south oriented in both cases. Figs. 15 and 16 show the

variation of monthly solar energy for single and double slope PVT-CPC active solar distillation system. Table 6 represents the calculation for embodied energy (Ein), energy payback time (EPBT) and energy production factor (EPF) for single slope and double slope PVT-CPC active solar distillation systems at 0.14 m _ f ¼ 0:04 kg=s. The embodied energy for sinwater depth, N = 7 and m gle slope is higher than double slope PVT-CPC active solar distillation system for same basin area because of the requirement of higher amount of material for single slope PVT-CPC active solar distillation system due to its geometrical shape. The value of EPBT based on energy for double slope is 7.5% lower than single slope PVT-CPC active solar distillation system because embodied energy of double slope is lower by 2.83% and annual energy of double slope is higher by 4.2% than single slope PVT-CPC active solar distillation system. The value of EPBT based on exergy for double slope is 17.98% lower than single slope PVT-CPC active solar distillation system because embodied energy of double slope is lower by 2.83% and annual exergy of double slope is higher by 12.79% than single slope PVT-CPC active solar distillation system. EPF based on energy for double slope is higher by 5.12% than single slope PVT-CPC active solar distillation system because annual energy of double slope is higher by 4.2% and embodied energy of double slope is lower by 2.83% than single slope PVT-CPC active solar distillation system. EPF based on exergy for double slope is higher by 12.72% than single slope PVT-CPC active solar distillation system because annual exergy of double slope is higher by 12.79% and embodied energy of double slope is lower by 2.83% than single slope PVT-CPC active solar distillation system.

Fig. 11. Variation of daily yield of single and double slope PVT-CPC active solar distillation system for a typical day in the month of June and Jan.

Fig. 13. Hourly variation of electrical efficiency and exergy of module for a typical day in the month of June.

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Fig. 14. Variation of monthly electrical exergy of PVT for single and double slope PVT-CPC active solar distillation system.

Table 7 represents the calculation of life cycle conversion efficiency (LCCE) for single slope and double slope PVT-CPC active solar distilla_ f ¼ 0:04 kg=s. It has tion system at 0.14 m water depth, N = 7 and m been observed that LCCE based on energy for double slope is 5.55% higher than single slope PVT-CPC active solar distillation system because overall annual energy is higher by 4.2%, embodied energy is lower by 2.83% and solar energy is lower by 1.56% for double slope than single slope PVT-CPC active solar distillation system. So, it is clear from Eq. (36) that the numerator is higher by 4.57% and denominator is lower by 1.56% for double slope than single slope PVT-CPC active solar distillation system and hence the ratio which represent LCCE based on energy is 5.55% higher. LCCE based on exergy for double slope is 22.22% higher than single slope PVT-CPC active solar distillation system because overall annual exergy is higher by 12.79%, embodied energy is lower by 2.83% and solar energy is lower by 1.56% for double slope than single slope PVT-CPC active solar distillation system. So, it is clear from Eq. (37) that the numerator is higher by 21.48% and denominator is lower by 1.56% for double slope than single slope PVTCPC active solar distillation system and hence the ratio which represent LCCE based on exergy is 22.22% higher. Table 8 represents the capital investment for single and double slope PVT-CPC active solar distillation systems. UAC for single and double slope PVT-CPC active solar distillation systems have been evaluated using Eq. (40) and presented in Table 9. The minimum value of UAC has been found corresponding to 2% rate of interest as expected. The production cost of water and cost of electricity gain have been calculated using Eqs. (38) and (39) respectively for single and double slope PVT-CPC active solar distillation systems. They have been presented in Table 10. The production cost of water for single slope PVT-CPC active solar distillation system has been found to vary from Rs. 0.51 per kg to Rs. 2.42 per kg and for double slope PVT-CPC active solar distillation system, it has been found to vary from Rs. 0.47 per kg to Rs. 2.21 per kg. It

Fig. 15. Variation of monthly solar energy for single slope PVT-CPC active solar distillation system.

Fig. 16. Variation of monthly solar energy for double slope PVT-CPC active solar distillation system.

has been observed that the production cost of water obtained from double slope is lower than single slope PVT-CPC active solar distillation system. It happens because yield of double slope at 0.14 m depth of water is higher and UAC is lower than single slope PVT-CPC active solar distillation system. It has also been observed from Table 10 that electricity is gained at no cost from both single slope and double slope PVT-CPC active solar distillation systems because revenue obtained from distilled water overcome the total cost (UAC) of systems in both cases. 7. Conclusions The theoretical analysis for energy matrices based on exergy as well as energy and production cost of water for single slope and double slope PVT-CPC active solar distillation systems has been performed. The annual exergy and energy have been evaluated at 0.14 m depth of water, optimum number of collectors and mass flow rate considering four weather condition namely type a, type b, type c and type d. The double slope gives better performance than single slope PVT-CPC active solar distillation system at optimum number of collectors and mass flow rate if depth of water is less than 0.19 m and vice-versa. The value of energy matrices, exergy and energy at 0.14 m depth of water for double slope is better than single slope PVT-CPC active solar distillation system. EPBT based on exergy and energy are lower by 17.98% and 7.5% respectively for double slope than single slope PVT-CPC active solar distillation system. EPF based on exergy and energy have been found to be higher by 12.72% and 5.12% respectively for double slope than single slope PVT-CPC active solar distillation system. LCCE based on exergy and energy have been found to be higher by 22.22% and 5.55% respectively for double slope than single slope PVT-CPC active solar distillation system. The production cost of water in Rs./kg and cost of electricity gain in Rs./kWh have been calculated for both systems. Nomenclature area of receiver covered by PV module (m2) Arm area of receiver covered by glass (m2) Arc area of aperture covered by PV module (m2) Aam area of aperture covered by glass (m2) Aac area of glass cover (m2) Ag area of east glass cover (m2) AgE area of basin (m2) Ab area of west glass cover (m2) AgW L latent heat (J/kg) thickness of glass cover (m) Lg thermal conductivity of glass (W/m-K) Kg beam radiation (W/m2) Ib(t) ambient temperature (°C) Ta thickness of insulation (m) Li thermal conductivity of insulation (W/m-K) Ki

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87

Table 4 Daily, monthly and annual thermal exergy for single slope PVT-CPC active solar distillation system. Weather condition (type a) Month

Exa

Jan 2.53 Feb 2.23 Mar 2.50 Apr 2.31 May 2.09 Jun 2.05 Jul 1.78 Aug 1.87 Sep 2.55 Oct 2.36 Nov 2.29 Dec 2.30 Annual exergy (kWh)

αc _ f m τg Cf/Cw βo Lr La Lrc Lrm Lac Lam ηc ηm ηcN br bo (ατ)eff F′ Tc Tp Lp Kp Tfi Tf PF1 PF2 PF3 PFc β ηo

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

na

Exma

Exb

nb

Exmb

Exc

nc

Exmc

Exd

nd

Exmd

Monthly Exergy

3 3 5 4 4 3 2 2 7 5 6 3

7.60 6.69 12.48 9.23 8.38 6.15 3.56 3.74 17.85 11.81 13.73 6.89

2.14 2.10 0.53 2.32 1.40 1.48 1.19 1.54 2.11 0.68 0.98 1.51

8 4 6 7 9 4 3 3 3 10 10 7

17.15 8.40 3.21 16.21 12.60 5.92 3.57 4.62 6.32 6.83 9.78 10.58

0.46 0.27 0.53 0.50 0.70 0.50 0.54 0.39 0.82 0.68 0.18 0.43

11 12 12 14 12 14 10 7 10 13 12 13

5.11 3.19 6.42 6.94 8.39 7.03 5.36 2.76 8.20 8.88 2.11 5.54

0.03 0.02 0.17 0.35 0.24 0.10 0.07 0.09 0.15 0.09 0.12 0.03

9 9 8 5 6 9 17 19 10 3 2 8

0.26 0.21 1.36 1.75 1.43 0.92 1.27 1.80 1.48 0.27 0.25 0.26

30.11 18.49 23.47 34.13 30.80 20.02 13.76 12.92 33.86 27.78 25.86 23.28 294.48

TfoN

absorptivity of the solar cell mass flow rate of water (kg/s) transmissivity of the glass (fraction) specific heat of water (J/kg-K) temperature coefficient of efficiency (K−1) total length of receiver area (m) total length of aperture area (m) length of receiver covered by glass length of receiver covered by PV module length of aperture covered by glass length of aperture covered by PV module solar cell efficiency PV module efficiency temperature dependent electrical efficiency of solar cells of a number (N) of PVT-CPC water collectors breath of receiver (m) breath of aperture (m) product of effective absorptivity and transmittivity collector efficiency factor solar cell temperature (°C) absorption plate temperature (°C) thickness of absorption plate (m) thermal conductivity of absorption plate (W/m-K) fluid temperature at collector inlet (°C) temperature of fluid in collector (°C) penalty factor due to the glass covers of module penalty factor due to plate below the module penalty factor due to the absorption plate for the glazed portion penalty factor due to the glass covers for the glazed portion packing factor of the module efficiency at standard test condition

outlet water temperature at the end of Nth PVT–CPC water collector (°C) heat transfer coefficient for space between the glazing and absorption plate (W/m2-K) heat transfer coefficient from bottom of PVT to ambient (W/ m2-K) heat transfer coefficient from top of PVT to ambient (W/m2K) overall heat transfer coefficient from cell to ambient (W/m2K) overall heat transfer coefficient from cell to plate (W/m2-K) heat transfer coefficient from blackened plate to fluid (W/m2K) overall heat transfer coefficient from plate to ambient (W/ m2-K) overall heat transfer coefficient from module to ambient (W/ m2-K) overall heat transfer coefficient from glassing to ambient (W/ m2-K) selling price of water (Rs.) selling price of electricity (Rs.) capital recovery factor (fraction) sinking fund factor (fraction) uniform end-of-year annual cost (Rs.) salvage value (Rs.) net present cost (Rs.) annual power generated from photovoltaic module (kWh) annual power utilized by pump (kWh) emissivity absorptivity hourly exergy (W) solar intensity (W/m2)

hi h′i ho Utca Utcp hpf Utpa ULm ULc (SP)w (SP)e FCR,i,n FSR,i,n UAC Ss Ps Pm Pu є α′ _ Ex Is(t)

Table 5 Daily, monthly and annual thermal exergy for double slope PVT-CPC active solar distillation system. Weather condition (type a) Month

Exa

Jan 2.97 Feb 2.60 Mar 2.83 Apr 2.87 May 2.64 Jun 2.48 Jul 2.08 Aug 2.19 Sep 3.51 Oct 3.08 Nov 2.80 Dec 2.54 Annual exergy (kWh)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

na

Exma

Exb

nb

Exmb

Exc

nc

Exmc

Exd

nd

Exmd

Monthly Exergy

3 3 5 4 4 3 2 2 7 5 6 3

8.91 7.80 14.13 11.49 10.58 7.45 4.16 4.38 24.54 15.41 16.79 7.61

2.48 2.43 3.04 2.90 1.61 1.69 1.33 1.74 2.68 1.54 1.07 1.68

8 4 6 7 9 4 3 3 3 10 10 7

19.84 9.71 18.23 20.31 14.49 6.78 3.99 5.23 8.05 15.39 10.73 11.76

0.33 0.30 0.59 0.54 0.75 0.53 0.58 0.41 0.87 0.73 0.19 0.46

11 12 12 14 12 14 10 7 10 13 12 13

3.62 3.60 7.09 7.51 9.03 7.45 5.78 2.87 8.73 9.54 2.26 6.02

0.03 0.03 0.18 0.37 0.24 0.08 0.07 0.09 0.15 0.09 0.13 0.04

9 9 8 5 6 9 17 19 10 3 2 8

0.28 0.25 1.45 1.86 1.44 0.68 1.20 1.77 1.45 0.28 0.27 0.29

32.66 21.36 40.90 41.17 35.54 22.37 15.13 14.26 42.78 40.62 30.04 25.69 362.50

88

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

Table 6 Embodied energy (Ein), energy payback time (EPBT) and energy production factor (EPF) for single slope and double slope PVT-CPC active solar distillation system.

Name of component Single slope solar still CPC collector (N = 7) PV (glass to glass) (N = 7) Others

Single slope PVT-CPC active solar distillation system

Double slope PVT-CPC active solar distillation system

Embodied energy (kWh)

Embodied energy (kWh)

1737.79

1483.90

5738.98

5738.98

1714.20

1714.20

20

20

Table 8 Capital investment for single and double slope PVT-CPC active solar distillation systems.

S.N. Parameter 1 2 3 4 5

Cost of solar Still 23,143 Cost of PVT-CPC collector @ 10,500 each 73,500 Cost of motor and pump 1000 Fabrication cost 6000 Salvage value of the system after 50 years, if inflation 68,681 remains @ 4% in India, [using present value of scrap material sold in Indian market]

hewg Single slope PVT-CPC active solar distillation system Total embodied energy = 9210.97 kWh Annual yield = 4519.54 kg Annual energy available from solar still = 3389.00 kWh Annual exergy available from solar still = 437.35 kWh Energy payback time (EPBT) based on energy = 2.72 years Energy payback time (EPBT) based on exergy = 21.06 years Energy production factor (EPF) based on energy = 0.37 per year Energy production factor (EPF) based on exergy = 0.048 per year Double slope PVT-CPC active solar distillation system Total embodied energy = 8957.08 kWh Annual yield = 4757.70 kg Annual energy available from solar still = 3537.67 kWh Annual exergy available from solar still = 501.53 kWh Energy payback time (EPBT) based on energy = 2.53 years Energy payback time (EPBT) based on exergy = 17.85 years Energy production factor (EPF) based on energy = 0.39 per year Energy production factor (EPF) based on exergy = 0.055 per year

ISE(t) ISW(t) TgiE TgiW hrwg hcwg

solar intensity on east glass cover (W/m2) solar intensity on west glass cover (W/m2) glass temperature at inner surface of east glass cover (°C) glass temperature at inner surface of west glass cover (°C) radiative heat transfer coefficient from water to inner surface of glass cover (W/m2-K) convective heat transfer coefficient from water to inner surface of glass cover (W/m2-K)

Table 7 Life cycle conversion efficiency (LCCE) for single slope and double slope PVT-CPC active solar distillation system.

Life ( year ) Energy output (Eout) in kWh Embodied energy (Ei) in kWh Solar energy for life time (Esol) in kWh Life cycle conversion efficiency (LCCE) based on energy Exergy output (Gex) in kWh Solar exergy for life time (Esol) in kWh Life cycle conversion efficiency (LCCE) based on exergy

Single slope PVT-CPC active solar distillation system

Double slope PVT-CPC active solar distillation system

50 169,450.00

50 176,883.50

9210.97

8957.08

956,145.5 0.17

941,422.5 0.18

21,867.5

25,076.5

889,215.31

875,522.92

0.014

0.018

hewgE hewgW M Mw _ ew;E m _ ew;W m Mew a b c d Q_

Cost (Rs.) Cost (Rs.) of SS of DS

uN

n i Gex,annual ln SS DS t R r Ts Tw Ta Two T CN Tgi Eout Y m Ex Exm N Ein EPF EPBT LCCE Cwp Ce Csolar still CPVT CCPC Cfab Ee θ

19,183 73,500 1000 6000 65,867

evaporative heat transfer coefficient from water to inner surface of glass cover (W/m2-K) evaporative heat transfer coefficient for east side (W/m2-K) evaporative heat transfer coefficient for west side (W/m2-K) maintenamce cost of PVT-CPC active solar distillation system mass of water in basin (kg) hourly yield from east cover of double slope PVT-CPC active solar distillation system (kg) hourly yield from west cover of double slope PVT-CPC active solar distillation system (kg) annual yield from PVT-CPC active solar distillation system (kg) clear days (blue sky) hazy days (fully) hazy and cloudy days (partially) cloudy days (fully) the rate of useful thermal output from N identical partially (25%) covered PVT-CPC water collectors connected in series (kWh) life of PVT-CPC active solar distillation system (year) rate of interet (%) annual exergy gain (kWh) natural logarithm single slope PVT-CPC active solar distillation system double slope PVT-CPC active solar distillation system time, h reflectivity resistance temperature of sun, °C temperature of water in basin, °C ambient temperature, °C water temperature at t = 0, °C average solar cell temperature glass temperature at inner surface, °C overall annual energy available from PVT-CPC solar distillation system (kWh) daily yield (kg) monthly yield (kg) daily exergy (kWh) monthly exergy (kWh) number of PVT-CPC water collector embodied energy (kWh) energy production factor (fraction) energy payback time (yr) life cycle conversion efficiency production cost of water (Rs./kg) cost of electricity gain (Rs./kWh) cost of solar still cost of PVT cost of CPC fabrication cost which includes the cost of piping and labor annual electricity gain (kWh) angle of inclination of glass cover with horizontal

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

89

Table 9 Uniform-end-of-year annual cost for single slope and double slope PVT-CPC active solar distillation system. n

i

Ps

M

Ss

FCR,i,n

FSR,i,n

UAC

System

(Yr.)

(%)

(Rs.)

@ 10%

(Rs)

(Fraction)

(Fraction)

(Rs.)

PVT-CPC-SS

50 50 50 50 50 50

2 5 10 2 5 10

103,643 103,643 103,643 99,683 99,683 99,683

10,364.3 10,364.3 10,364.3 9968.3 9968.3 9968.3

68,681 68,681 68,681 65,867 65,867 65,867

0.031823 0.054777 0.100859 0.031823 0.054777 0.100859

0.01182 0.00478 0.00086 0.01182 0.00478 0.00086

2816.048 5916.877 11,439.67 2710.697 5691.711 11,002.75

PVT-CPC-DS

Subscript

g w E W in out eff

Arm ¼ br Lrm ; Aam ¼ bo Lam ; Ac F Rc ¼

glass water east west incoming outgoing effective

Am F Rm ¼



 Ac F Rc U Lc ðA F R U L Þ1 ¼ Ac F Rc U Lc þ Am F Rm U Lm þ Am F Rm U Lm 1− _ f cf m

Expressions for Kk, (A FR(ατ))1 and (A FRUL)1 used in Eq. (1) are as follows 

1 Lg þ ho K g

−1

 ; U tcp ¼

1 Lg þ hi K g

−1

;



1 1 ¼ þ U tca U tcp

−1

"

1 1 L þ 0þ þ i hi hpf K i

ðA F R U L Þm1 ¼ Am F Rm U Lm

#−1

Km ¼

;

 Am F Rm U Lm 1− _ f cf m

Expressions for a and f(t) used in Eq. (8) and expressions of heat transfer coefficients used in Eqs. (10) to (12) are as follows.

0

hi ¼ 2:8 þ 3V 0 ; Wm−2 K −1 ; hpf U L2 U tcp U tca ; U L2 ¼ U L1 þ U tpa ; U Lm ¼ 0 ; U Lc U tcp þ U tca F hpf þ U L2 hpf U tpa ¼ 0 ; F hpf þ U tpa

a¼

U L1 ¼

PF 1 ¼

 ðA F R U L Þ1 1− _ f cf m

KK ¼

ðA F R ðατ ÞÞm1 ¼ PF 2 ðατÞmeff Am F Rm

ho ¼ 5:7 þ 3:8V; Wm−2 K −1 ; V ¼ 1 ms−1 ; hi ¼ 5:7; Wm−2 K −1 ;

U tpa



 _ f cf m − F 0 U Lm Am ; 1− exp _ f cf U Lm m



 Ac F Rc U Lc ; ðA F R ðατ ÞÞ1 ¼ Ac F Rc ðατ Þceff þ PF 2 ðατÞmeff Am F Rm 1− _ f cf m

Appendix A

U tca ¼



 _ f cf m −F 0 U Lc Ac ; 1− exp _ f cf U Lc m


 i 1 h _ f C f 1−K Nk þ U s Ab ; m Mw C w


 1−K k N 1 f ðt Þ ¼ ½α A Is ðt Þ þ ðA F R ðατ ÞÞ1 Ib ðt Þ ð1−K k Þ Mw
C w eff b 0 1 N 1−K k ðA F R U L Þ1 þ U s Ab AT a ; þ@ ð1−K k Þ

hpf hpf U tcp ; PF 2 ¼ 0 ; PF c ¼ 0 ; U tcp þ U tca F hpf þ U L2 F hpf þ U tpa

  Aam Aam ðατ Þ1eff ¼ ρ α c −ηc τ g βc ; ðατÞ2eff ¼ ρα p τ2g ð1−βc Þ ; Arm Arm

α 0eff ¼ α 0w þ h1 α 0b þ h1 α 0g ;

h i Aac ðατ Þmeff ¼ ðατÞ1eff þ PF 1 ðατÞ2eff ; ðατÞceff ¼ PF c :ρα p τ g ; Arc

h1 ¼

0

hbw h1w Ag 0 ;h ¼ ; h1w ¼ hrwg þ hcwg þ hewg ; hbw þ hba 1 U c;ga Ag þ h1w Ab

Table 10 _ f ¼ 0:04 Production cost of water and cost of electricity gain for single slope and double slope PVT-CPC active solar distillation systems for at 0.14 m depth of water, n = 50 yr, N = 7 and m kg/s. i

UAC

Mw

(SP)w

(SP)e

Rw

Ee

Re

(UAC-Re)

(UAC-Rw)

Cwp

Ce

System

(%)

(Rs.)

(kg)

(Rs./kg)

(Rs./kWh)

(Rs.)

(kWh)

(Rs.)

(Rs.)

(Rs.)

(Rs./kg)

(Rs./kWh)

SS

2 5 10 2 5 10

2816.05 5916.88 11,439.7 2710.7 5691.71 11,002.8

4519.54 4519.54 4519.54 4757.7 4757.7 4757.7

5 5 5 5 5 5

4 4 4 4 4 4

22,597.7 22,597.7 22,597.7 23,788.5 23,788.5 23,788.5

123.35 123.35 123.35 123.51 123.51 123.51

1749.4 1749.4 1749.4 2006.12 2006.12 2006.12

1066.648 4167.477 9690.27 704.577 3685.591 8996.63

0 0 0 0 0 0

0.51 1.20 2.42 0.47 1.09 2.21

0 0 0 0 0 0

DS

90

D.B. Singh, G.N. Tiwari / Desalination 397 (2016) 75–91

he;wg ¼ 16:273  10−3 hc;wg

hc;wg ¼ 0:884

 



P w −P gi ; T w −T gi

   P w −P gi ðT w þ 273Þ ; T w −T gi þ 268:9  103 −P w

 P w ¼ exp 25:317−

5144 ; T w þ 273

 P gi ¼ exp 25:317−

5144 ; T gi þ 273

hrwg


h  2 i ¼ 0:82  5:67  10−8 ðT w þ 273Þ2 þ T gi þ 273    T w þ T gi þ 546 ;

Us ¼ Ut þ Ub; Ub ¼

U c;ga

h1w U c;ga Ag hba hbw ; Ut ¼ ; hbw þ hba U c;ga Ag þ h1w Ab

Kg  −1 h1g lg L 1 ¼ ; hba ¼ i þ ; Kg K i hcb þ hrb þh1g lg

hcb þ hrb ¼ 5:7 Wm−2 K −1 ; hbw ¼ 250 Wm−2 K −1 ; Expressions for a1 and f 1 ðtÞ used in Eq. (19) and expressions of different terms used in Eqs. (20) to (25) are as follows. 
 1 h1wEðP−A2 ÞAb h1wW ðP−B2 ÞAb _ f C f 1−K Nk þ U b Ab þ m a1 ¼ þ ; 2P 2P Mw C w

f ðt Þ ¼ 1

0    1 α ½ w þ h1 α 0b Ab I SE ðt Þ þ ISW ðt Þ 2 Mw C w
  0
1 1−K k N 1−K k N  @ þ ðA F R ðατÞÞ1 Ib ðt Þ þ ðA F R U L Þ1 þ U Ab AT a ð1−K k Þ ð1−K k Þ b

 h1wE A1 þ h1wW B1 Ab þ ; P 2

A1 ¼ R1 U 1 AgE þ R2 hEW AgW A2 ¼ h1WE U 2

Ab A þ hEW h1WW b 2 2 2

P¼

U1 ¼

U2 ¼

B1 ¼

B2 ¼

U1U2−

h1wE

!

hEW A h1WW b AgW AgE 2

Ab þ hEW AgE þ U c;gaE AgE 2 AgW

h1wW

Ab þ hEW AgW þ U c;gaW AgW 2 AgE

ðR2 P þ A1 hEW ÞAgW U 2 AgE Ph1wW

Ab þ hEW AgW A2 2 U 2 AgE

R1 ¼ α 0g ISE ðt Þ þ U c;gaE T a R2 ¼ α 0g ISW ðt Þ þ U c;gaW T a

h

i hEW ¼ 0:034  5:67  10−8 T 2giE þ 273 þ T 2giW þ 273 h i  T giE þ T giW þ 546

U c;gaE

Kg Kg h1gE h1gW lg lg ¼ ; U c;gaW ¼ ; Kg Kg þh1gE þh1gW lg lg

h1gE ¼ 5:7 þ 3:8V; h1gW ¼ 5:7 þ 3:8V; h1wE ¼ hrwgE þ hcwgE þ hewgE h1wW ¼ hrwgW þ hcwgW þ hewgW he;wgE ¼ 16:273  10−3 hc;wgE

hc;wgE ¼ 0:884

 

hc;wgW ¼ 0:884



P w −P giE ; T w −T giE

   P w −P gi E ðT w þ 273Þ ; T w −T giE þ 268:9  103 −P w

     P w −P giW ðT w þ 273Þ ; T w −T giW þ 268:9  103 −P w

 P w ¼ exp 25:317−

5144 ; T w þ 273

 P giE ¼ exp 25:317−

5144 ; T gi E þ 273

 P giW ¼ exp 25:317−

5144 ; T giW þ 273


h  2 i hrwgE ¼ 0:82  5:67  10−8 ðT w þ 273Þ2 þ T giE þ 273    T w þ T giE þ 546 ;
h  2 i hrwgW ¼ 0:82  5:67  10−8 ðT w þ 273Þ2 þ T giW þ 273    T w þ T giW þ 546 ;

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