Energy, exergy and cost analyses of N identical evacuated tubular collectors integrated basin type solar stills: A comparative study

Solar Energy 155 (2017) 829–846

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Energy, exergy and cost analyses of N identical evacuated tubular collectors integrated basin type solar stills: A comparative study 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

a r t i c l e

i n f o

Article history: Received 20 February 2017 Received in revised form 2 July 2017 Accepted 6 July 2017

Keywords: Energy Exergy Cost ETC Solar still

a b s t r a c t This paper deals with the comparative study of basin type solar stills incorporated with N identical evacuated tubular collectors on the basis of overall energy and exergy for the same basin area under similar climatic condition. In this work, the optimum number of collectors and mass flow rate has been computed followed by the evaluation of annual production of potable water, energy, exergy and production cost of potable water for the proposed systems at 0.14 m water depth for the complex climatic condition of New Delhi. It is inferred that the value of annual energy is higher by 6.85%; annual exergy is higher by 12.30% and production cost of potable water is lower by 15.19% for double slope solar still integrated with N identical evacuated tubular collectors than similar single slope set up. The proposed systems can be used on commercial scale for providing potable water. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The contemporary problem of potable water crisis in remote areas can be curtailed with the help of proposed active solar still in which a number of evacuated tubular collectors have been used for providing external heat to the basin. The main advantage of using evacuated tubular collectors is that the loss due convection does not take place as vacuum is present in between tubes. Rai and Tiwari (1983) investigated active solar still in forced mode theoretically for the first time and concluded that the daily yield of active solar still was higher by 24% than conventional solar still. In unison, Zaki et al. (1983) studied the active solar still under natural circulation mode for the first time and concluded that the maximum enhancement in distillate output was 33% higher in comparison to conventional solar still. Solar still can be integrated with a number of series connected flat plate collectors (FPC) to form a closed loop so that hot water can be discharged either directly or indirectly by providing heat exchanger in the basin. Single slope solar still (SS) included with inverted absorber asymmetric line-axis compound parabolic concentrator collector (CPC) was investigated by Yadav and Yadav (2004) and they concluded that the production of potable water was improved as compared to conventional solar still because solar energy was provided to solar still both from top and bottom concurrently ensuing in enhanced ⇑ Corresponding author. E-mail address: [email protected] (D.B. Singh). http://dx.doi.org/10.1016/j.solener.2017.07.018 0038-092X/Ó 2017 Elsevier Ltd. All rights reserved.

temperature difference between water surface and glass cover. An experimental investigation of solar still having mirrors at interior walls and coupled with FPC was done by Badran and Al-Tahaineh (2004). They observed an enhancement in distillate output by 36% as compared to conventional solar still. It happened due to enhanced temperature difference between water surface and inner surface of glass cover. Abdel-Rehim and Lasheen, 2007 studied basin type SS by integrating solar parabolic trough collector and heat exchanger. Oil was used as working fluid in collector. The amount of distillate output obtained from such system was 18% higher as compared to conventional solar still because of the attainment of higher water temperature in basin as water received solar energy from top and also through heat exchanger in basin. Tripathi and Tiwari (2005) explored experimentally basin type SS included with two collectors and operating in forced mode. They concluded that higher production of potable water was obtained during offsunshine hours due to heat storage effect at higher depth. Badran et al. (2005) explored basin type solar still (double slope) which was included with FPC and operating in forced mode. They concluded that the production of potable water was higher by 52% as compared to conventional solar still. Taghvaei et al. (2014) studied experimentally SS coupled with FPC to assess the long term performance (continuous 10 days) and recommended a higher depth of water for practical application as the amount of potable water production and efficiency were found to be higher at higher depth due to heat storage effect.

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Nomenclature area of basin, m2 area of glass cover, m2 clear day (blue sky) hazy day (fully) hazy and cloudy (partially) specific heat capacity, J/kg-K cost of solar still, Rs. cost of ETC, Rs. fabrication cost, Rs. production cost of water, Rs./kg cloudy day (fully) single slope solar still evacuated tubular collector annual energy output, kWh fill factor, dimensionless capital recover factor, fraction sinking fund factor, fraction collector efficiency factor, dimensionless hourly exergy gain, kWh hcwg convective heat transfer coefficient from water to inner surface of glass cover, W/m2-K evaporative heat transfer coefficient from water surhewg face to inner surface of glass cover, W/m2-K hc convective heat transfer coefficient, W/m2-K hba heat transfer coefficient from blackened surface to ambient, W/m2 K hbw heat transfer coefficient from blackened surface to water mass, W/m2-K h heat transfer coefficient, W/m2-K hrwg radiative heat transfer coefficient from water surface to inner surface of glass cover, W/m2-K hr radiative heat transfer coefficient, W/m2-K total heat transfer coefficient from outer surface of h1w glass cover to ambient, W/m2-K h1g total heat transfer coefficient from water surface to inner glass cover, W/m2-K IðtÞ solar intensity on collector, W/m2 IS ðtÞ solar intensity on glass cover, W/m2 ISE ðtÞ solar intensity on east glass cover, W/m2 ISW ðtÞ solar intensity on west glass cover, W/m2 i rate of interest K thermal conductivity, W/m-K Lg thickness, m L latent heat, J/kg L0 length, m _f m mass flow rate of fluid/water, kg/s _ ew m mass of distillate from single slope solar still, kg M maintenance cost M ew annual production of potable water N-ETC-SS single slope solar still included with N identical ETC N-ETC-DS double slope solar still included with N identical ETC n0 number of days Ab Ag a b c C C solar still C ETC C fab C wp d SS ETC Eout FF F CR;i;n F SR;i;n F0 G_ ex

El-Sebaii et al. (2009) compared the performance of single basin active solar still theoretically between with and without a sensible storage material (sand) and reported that daily productivity of the solar still with storage was 23.8% higher than that when it was used without storage. An experimental study regarding the performance of various designs of active solar still was done by Arslan (2012) under closed cycle mode and he obtained highest overall daily efficiency for the circular box active solar still design. In a variation, Lilian et al. (2014) studied a slowly rotating lightweight hollow drum partially submerged in solar still cavity and

n N0 N PF c

Ta T gi T Two Tw UL UAC V

life of N-ETC-SS/N-ETC-DS, year number of sunshine hours number of collectors penalty factor due to the glass covers for the glazed portion penalty factor first, dimensionless penalty factor second, dimensionless cost of pump, Rs. net present cost useful energy gain for N identical collector connected in series, kWh inner radius of outer glass tube of evacuated coaxial glass tube, m outer radius of inner glass tube of evacuated coaxial glass tube, m outer radius of outer glass tube of evacuated coaxial glass tube, m radius of copper tube in ETC reflectivity ratio of daily diffuse to daily global irradiation outlet water temperature at the end of Nth water collector, °C ambient air temperature, °C glass temperature at inner surface of glass cover, °C time, h water temperature at t = 0, °C water temperature, °C overall heat transfer coefficient uniform end-of-year annual cost, Rs. velocity of air, m/s

Subscript E W SS DS eff en ex f g in out w

east west single slope active solar still double slope active solar still effective energy exergy fluid glass incoming outgoing water

PF 1 PF 2 Pp Ps Q_ u;N Ro1 Ri2 Ro2 r0 R0 r T foN

Greek letters a absorptivity (fraction) g efficiency, % product of effective absorptivity and transmissivity ðasÞeff r Stefan-Boltzmann constant, W/m2-K4 s transmissivity

reported an improvement of 20–30% in the production of potable water as compared to conventional solar still. However, the production of potable water becomes 60% higher than the conventional solar still if the basin of an FPC integrated solar still is partitioned as reported by Rajaseenivasana et al. (2014). A considerable enhancement in productivity is also obtained if thermal energy is supplied to solar still by circulating heat transfer fluid at its bottom. Hamadou and Abdellatif (2014) reported that doubling the heat transfer fluid rate effected a 9% enhancement in the production of potable water. The relation between production

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of potable water and the heat transfer fluid rate is thus non-linear. A novel tri-generation system employing PVT collectors was designed by Calise et al. (2014) for seawater desalination in European Mediterranean countries, known to have abundant renewable sources but deprived of fossil fuels and water resources. Ibrahim et al. (2015) investigated experimentally the performance of modified solar still consisting of external air cooled condenser and reported an enhancement of 16.2% and 29.7% in the production of potable water and thermal efficiency respectively for the proposed system over conventional solar still. Active solar distillation system can be made self-sustainable so that it can operate even in remote areas having abundant sunlight but electrical power is not available and the system can generate electrical energy too if need arises. It can be done by including a photovoltaic (PV) panel with FPC coupled to the basin of solar still. The integration of PV panel to collector was proposed by Kern and Russell (1978) and it was reported that electrical efficiency was enhanced if fluid was allowed to pass below the panel. A theoretical study of such system was done by Hendrie (1979). In continuation of this approach, an experimental study of SS by incorporating two series connected FPCs (one partially covered with PV) was done by Kumar and Tiwari (2008, 2009a, 2009b, 2010) and Kumar et al. (2010) and an enhancement in production of potable water by more than 3.5 times over conventional solar distillation system was reported. They developed empirical relation for heat transfer coefficient and also reported that the payback period of active solar distillation system lied in the range of 3.9– 23.9 years. It was extended for double slope active solar still by Singh et al. (2011). Further, Tiwari et al. (2015) and Singh et al. (2016) extended their work by partially covering both series connected identical FPCs with PV panels. They performed experimental investigation and reported that though the exergy efficiency and overall thermal efficiency values of the system where both the FPCs are partially covered with PV panels are better, the thermal efficiency is lower than the system reported by Kumar and Tiwari (2010) and Singh et al. (2011). Also, value of annual productivity varies from 120.29% to 883.55% indicating that the proposed system was feasible. The optimum number of collectors on the basis of exergy efficiency was found to be 4 for 50 kg water mass in the basin of active solar still coupled with a number of PVTFPCs as reported by Gaur and Tiwari (2010). Eltawil and Omara (2014) studied a solar distillation system consisting of SS, FPC, spraying unit, perforated tubes, solar air collector and PV panel to improve the production of potable water and supply electrical power. They reported an enhancement in the production of potable water by 51–148% over conventional solar still depending on the type of modification. Saeedi et al. (2015) performed optimization of PVT solar still on the basis of energy efficiency using simulation technique and reported optimum mass flow rate and number of collectors as 0.044 kg/s and 7 respectively. Singh and Tiwari (2016, 2017a, 2017b) performed theoretical study on basin type solar stills included with N identical PVT-CPC collectors for New Delhi climatic condition and reported that the performance of double slope was better than the similar single slope set up at 0.14 m water depth under optimized condition due to higher energy, exergy and lower embodied energy for double slope set up. They also reported that the performance of single slope was better than double slope PVT-CPC active solar still on the basis of average daily productivity, thermal and overall thermal efficiencies if depth of water in the basin is higher than 0.31 m and vice versa. Singh et al. (2013) investigated the performance of SS augmented with evacuated tubes in natural mode in which one end of all tubes were inserted into the basin and concluded that overall energy and exergy efficiencies has lied in the range of 5.1–54.4% and 0.15–8.25% respectively during the sunshine hours at 0.03 m water depth for a typical day in the month

of summer. Further, Kumar et al. (2014) investigated SS augmented with evacuated tubes in forced mode in which one end of all tubes were inserted into the basin and concluded that the daily yield was 3.47 kg at 0.01 m water depth and 0.006 kg/s mass flow rate for climatic condition of New Delhi. The subsisting research shows that basin type solar stills incorporated with N identical evacuated tubular collectors (ETC) have not been analyzed by any researchers. Recently, Mishra et al. (2015) have reported the development of characteristic equation for N identical ETC connected in series. Hence, this paper presents the comparative study of single and double slope solar stills integrated with N identical evacuated tubular collectors. In the proposed system, N identical ETC form a closed loop with single slope solar still as outlet of Nth ETC is discharged to the basin and 1st ETC is fed with water from basin with the help of pump. The proposed system is different from the system of earlier researcher in two ways. Firstly, a number (N) of identical FPC/ CPC have been replaced by N identical ETC. Secondly, a number (N) of ETC have been connected in series instead of inserting one end of all collectors to the basin as reported by Singh et al. (2013) and Kumar et al. (2014). The objective of the proposed investigation can be stated as follows. (i) To find optimum number of collectors and mass flow rate for single and double slope solar stills incorporated with N identical evacuated tubular collectors. (ii) To compute hourly, daily and annual production of potable water (yield), energy and exergy of the proposed systems at 0.14 m water depth, optimum number of collectors and mass flow rate for New Delhi climatic condition. (iii) To compute the cost of potable water for both the proposed systems (iv) To compare single and double slope solar stills incorporated with N identical evacuated tubular collectors for the same basin area under similar climatic condition on the basis of annual energy, annual exergy and cost of potable water. 2. System description Fig. 1 shows the cross sectional view of evacuated tubular collector (ETC), Fig. 2 shows the schematic diagram of N identical evacuated tubular collectors integrated single slope solar still (N-ETC-SS), Fig. 3 shows the schematic diagram of N identical evacuated tubular collectors integrated double slope solar still (N-ETC-DS) and Table 1 represents the exhaustive specification of proposed systems. Generally, collectors are connected in parallel to get higher discharge at lower temperature and they are connected in series to get lower discharge at higher temperature. Here, our aim is to increase the temperature of water in the basin which can be achieved by connecting collectors in series. Hence, they have been connected in series in the proposed system. There are N numbers of identical ETC in the proposed system. Each ETC consists of an inner copper tube through which water

Inner glass tube

Outer glass tube

Heat transfer fluid Vacuum U tube Fig. 1. Cross sectional view of evacuated tubular collector (ETC).

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

Fig. 2. Schematic diagram of N-ETC-SS.

Fig. 3. Schematic diagram of N-ETC-DS.

is allowed to flow and outer evacuated coaxial glass tube. The inner surface of evacuated coaxial glass tube is coated. The evacuated coaxial glass tube consists of two tubes and an evacuated space is provided between two glass tubes to minimize the heat loss by convection. The radius of inner copper tube is 0.0125 m. The inner radius of inner glass tube of evacuated coaxial glass tube is 0.0165 m. The outer radius of outer glass tube of evacuated coaxial glass tube is 0.024 m. The thickness of inner/outer glass tube of evacuated coaxial glass tube is 0.002 m. The inner copper tube is covered by copper plate to facilitate the transfer of heat to water flowing through the inner copper tube. The outlet of first ETC is connected to the inlet of second ETC; the outlet of second ETC is connected to the inlet of third ETC and so on. This type of arrangement of collectors is called series connection and it has been taken because our aim is to increase the temperature of water in the basin to get higher distillate. The

hot water available at the outlet of Nth ETC is discharged to basin and inlet of 1st ETC is fed with water from basin with the help of pump resulting in the formation of closed loop. An inclination of 30° has been provided to all series connected ETC in the proposed system with an aim to obtain yearly maximum solar radiation. DC motor pump can be run either by grid supply or photovoltaic module. The function of pump is to overcome the pressure drop so that water circulates through water collectors and basin of solar still. Water while passing through pipes of water collector receives heat and gets heated and this heated water is discharged to the basin. The single slope active solar still has an effective basin area of 2 m  1 m and it is made up of glass reinforced plastic (GRP). It is oriented toward south to get maximum annual solar intensity. A transparent glass inclined at an angle of 15° with the horizontal has been taken as condensing cover of the solar still. It is sealed with the help of window-putty. The inner surfaces of bottom and

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846 Table 1 Specifications of N-ETC-SS and N-ETC-DS. 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 Thickness of insulation Ki

2m 1m 15° 0.2 m GRP GI Glass South 0.004 m 0.816 W/m-K 0.1 m 0.166 W/m-K

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

2m 1m 15° 0.2 m GRP GI Glass East-west 0.004 m 0.816 W/m-K 0.1 m 0.166 W/m-K

Evacuated tubular collector Component

Specification

Component

Specification

Type and no. of collectors DC motor rating Radius of inner copper tube Thickness of copper tube

ETC, N 12 V, 24 W 0.0125 m 0.0005 m

ap

0.8 0.968 0.95 1.09

Outer radius of outer glass tube of evacuated coaxial glass tube Inner radius of inner glass tube of evacuated coaxial glass tube Thickness of outer/inner glass tube of evacuated coaxial glass tube

F0

sg K g ðW m1 K1 Þ Angle of ETC with horizontal Length of each Copper tube

0.024 m 0.0165 m

30° 2.0 m

0.002 m

side walls of solar still are painted black so that maximum portion of solar flux is absorbed. The solar flux at the outer surface of transparent glass is transmitted to water after reflection and absorption. Water mass reflects and absorbs some portion of transmitted solar flux and transmits the remaining part to basin liner. Basin liner absorbs almost total radiation falling on its surface. Hence, temperature of basin liner increases which transmits heat to water and temperature of water rises. Water gets evaporated due to temperature difference between the surface of water and glass cover. This evaporated water gets condensed at the inner surface of glass cover through film type condensation. The condensed water trickles down to the channel fixed to the front side of solar still and it is collected in an external container (jar) through pipe. Saline/brackish water flows to the basin with the help of pipe through an opening provided at the rear wall of solar still. An opening is also given at the bottom to facilitate the washing of basin after some use. The entire unit is fixed on iron stand. The proposed N-ETC-DS is oriented along East-West direction to get the maximum annual solar intensity. The working principle is same as N-ETC-SS. Here, N identical collectors have also been connected in series to get higher temperature of water in the basin. 3. Thermal modeling

ðAF R ðasÞÞ1 ¼ PF 1 as2 AR F R ;

where

hpf F 0 hpf þU tpa

PF 1 ¼
 R F R UL 1  Am _ c

h

U

; U L ¼ F 0 ht;paþUpft;pa ; pf

_ f cf ; ðAF R U L Þ1 ¼ ð1  K k Þm h
i 0 0 _ C m F R ¼ ULf ARf 1  exp  2pm_r Lc UL ; K K ¼ f f

f f

hpf ¼ 100 Wm2 K1 and U t;pa

 2 31 2 2 Ro2 ln Ri Ro2 ln Ro Ri1 Ro1 R 1 1 o2 ¼4 þ þ þ þ 5 Kg Kg C ev ho Ro1 hi In the set-up reported by Mishra et al. (2015), a number (N) of series connected ETC do not form loop. However, they form a loop with basin of single slope solar still in the proposed system as hot water available at the outlet of Nth ETC is discharged to basin and 1st ETC is fed with water from basin with the help of pump. Hence, the value of T fi is same as the value of T w . The expression of temperature at the exit of Nth ETC (T foN ) can written as

T foN ¼

ðAF R ðasÞÞ1 ð1  K Nk Þ ðAF R U L Þ1 ð1  K Nk Þ IðtÞ þ T þ K Nk T fi _ f Cf _ f C f ð1  K k Þ a ð1  K k Þ m m

ð2Þ

where the value of T fi is equal to T w . The hot water obtained at the exit of Nth ETC is discharged to the basin. Hence, the value of T wo is equal to the value of T foN . 3.2. Energy balance equations for single slope solar still

Following assumptions reported by Singh and Tiwari (2016, 2017a, 2017b), characteristic equations of the proposed N-ETC-SS and N-ETC-DS have been developed by writing energy balance equations for various components which are as follows. 3.1. Useful energy gain for N identical ETC connected in series

Following Singh and Tiwari (2016, 2017a, 2017b), various equations on the basis of balancing of energy for various components of active single slope solar still can be inscribed and they can be solved with the help of Eqs. (1) and (2) to get water temperature and glass temperatures which are as follows.

Following Mishra et al. (2015), the rate of useful thermal output from N identical ETC connected in series can be written as,

Tw ¼

ð1  K Nk Þ ð1  K Nk Þ ðAF R ðasÞÞ1 IðtÞ þ ðAF R U L Þ1 ðT fi  T a Þ Q_ uN ¼ ð1  K k Þ ð1  K k Þ

T gi ¼

ð1Þ

f1 ðtÞ ð1  ea1 t Þ þ T w0 ea1 t a1

a0g Is ðtÞAg þ h1w T w Ab þ U c;ga T a Ag U c;ga Ag þ h1w Ab

ð3Þ

ð4Þ

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846 Kg Lg

T go ¼

T gi þ h1g T a Kg Lg

ð5Þ

þ h1g

where T w0 is the temperature of water at t ¼ 0 and f1 ðtÞ is the average value of f 1 ðtÞ during the time interval 0 to t. After computing the value of water temperature (T w ) and glass temperature, the _ ew Þ can be computed as hourly production of potable water ðm follows.

hewg Ab ðT w  T gi Þ  3600 L

_ ew ¼ m

ð6Þ

where L stands for the amount of thermal energy required to evaporate unit mass of water (latent heat) and can be computed with the help of the expression for the same reported by Fernandez and Chargoy (1990) and Toyama and Kagakuv (1972). 3.3. Energy balance equations for double slope solar still

f2 ðtÞ ð1  ea2 t Þ þ T w0 ea2 t a2

T giE ¼

T goE ¼

ð7Þ

A1 þ A2 T w P

ð8Þ

B1 þ B2 T w P

ð9Þ

T giW ¼

Kg Lg

T goW ¼

T giE þ h1gE T a Kg Lg

Kg Lg

ð10Þ

þ h1gE

T giW þ h1gW T a Kg Lg

ð11Þ

þ h1gW

After computing the value of water temperature (T w ) and glass temperature ðT giE and T giW Þ; the hourly production of potable water _ ew Þ can be computed as follows. ðm

_ ew ¼ m

hewgE A2b ðT w  T giE Þ þ hewgW A2b ðT w  T giW Þ  3600 L

(c) Hazy and cloudy (partially) (d) Cloudy day (fully)

ð12Þ

where L stands for the amount of thermal energy required to evaporate unit mass of water (latent heat).

r  0.25 and N 0  9 h 0.25  r  0.50 and 7 h  N0  9 h 0.50  r  0.75 and 5 h  N0  7 h r  0.75 and N 0  5 h

where N 0 represents number of sunshine hours and r represents the ratio of daily diffuse to daily global irradiation. 4.1. Energy analysis Annual thermal energy ðEout Þ of ETC active solar distillation systems can be written as

Eout ¼

Following Singh and Tiwari (2016, 2017a, 2017b), various equations on the basis of balancing of energy for various components of active double slope solar still can be inscribed and they can be solved with the help of Eqs. (1) and (2) to get water temperature and glass temperatures which are as follows.

Tw ¼

(a) Clear day (blue sky) (b) Hazy day (fully)

ðMew  LÞ 3600

ð13Þ

Here, Mew is annual yield obtained from ETC active solar distillation system. The value of latent heat has been taken as 2400 kJ/kg-K. The daily yield of N-ETC-SS for clear days (type (a)) can be computed by adding hourly yield obtained from Eq. (6) for 24 h and the same process has been implemented to compute the daily yield for other climatic conditions namely (b), (c) and (d). The monthly yield of N-ETC-SS for clear days (type (a)) can be evaluated by multiplying daily yield with the corresponding number of clear days and the same process has been implemented to compute the monthly yield for other climatic conditions namely (b), (c) and (d). The sum of yield for climatic conditions (a), (b), (c) and (d) gives the net yield for each month. The annual yield of N-ETC-SS used in Eq. (13) can be computed by adding monthly yield for 12 month. Similarly, annual yield for N-ETC-DS can be computed with the help of Eq. (12). Tables 3 and 4 show the calculation of yield for N-ETC-SS and N-ETC-DS. 4.2. Exergy analysis It has been done on the basis of first law of thermodynamics (energy) and second law of thermodynamics (entropy). Following Nag (2004), the hourly exergy gain ðG_ ex Þ for N-ETC-SS can be expressed as

   ðT w þ 273Þ G_ ex;ss ¼ hewg Ab ðT w  T giE Þ  ðT a þ 273Þ ln ðT gi E þ 273Þ

ð14Þ

Similarly, hourly exergy gain ðG_ ex Þ for N-ETC-DS can be expressed as

4. Analysis The theoretical analysis of proposed N-ETC-SS and N-ETC-DS has been done for a year on the basis of data for solar flux and ambient air temperature taken from Indian Meteorological Department (IMD) Pune, India. The following four weather conditions for each month of year have been considered for the analysis of the proposed systems.

   Ab ðT w þ 273Þ ðT w  T giE Þ  ðT a þ 273Þ ln G_ ex;DS ¼ hewgE ðT gi E þ 273Þ 2 þ hewgW    Ab ðT w þ 273Þ  ðT w  T giW Þ  ðT a þ 273Þ ln ðT giW þ 273Þ 2

ð15Þ

Table 2 Average wind velocity for each month of year for N-ETC-SS and N-ETC-DS. 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 / Solar Energy 155 (2017) 829–846 Table 3 Daily, monthly and annual production of potable water (yield) at 0.14 m water depth, optimum number of collectors and mass flow rate for N-ETC-SS. Month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Ya

n0a

ma

Yb

n0b

mb

Yc

n0c

mc

Yd

n0d

md

17.75 18.22 21.34 25.87 26.72 25.92 23.64 23.21 26.61 21.22 18.85 17.53

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

53.24 54.65 106.68 103.47 106.89 77.76 47.28 46.42 186.30 106.12 113.07 52.59

16.87 18.95 24.01 27.33 26.74 27.19 24.03 23.59 25.79 18.20 13.74 14.43

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

134.93 75.79 144.04 191.32 240.68 108.77 72.08 70.78 77.37 182.04 137.43 100.99

6.68 7.21 12.29 16.90 24.19 22.47 19.15 17.19 20.68 12.80 5.74 8.06

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

73.49 86.52 147.53 236.67 290.31 314.54 191.51 120.30 206.80 166.38 68.91 104.83

2.56 2.89 9.82 17.47 19.07 14.56 12.80 11.73 12.52 7.30 5.35 3.04

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

23.08 25.97 78.55 87.37 114.41 131.00 217.62 222.90 125.19 21.90 10.70 24.30

Annual yield (kg)

Monthly yield

284.73 242.93 476.79 618.83 752.29 632.07 528.50 460.39 595.67 476.43 330.12 282.72 5681.48

Table 4 Daily, monthly and annual production of potable water (yield) at 0.14 m water depth, optimum number of collectors and mass flow rate for N-ETC-DS. Month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Ya

n0a

ma

Yb

n0b

mb

Yc

n0c

mc

Yd

n0d

md

19.30 19.67 22.21 25.83 26.58 25.91 28.47 22.15 26.60 21.03 19.15 18.87

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

57.89 59.02 111.07 103.31 106.31 77.74 56.95 44.31 186.17 105.14 114.88 56.60

18.40 20.17 24.66 27.37 26.17 27.07 23.93 23.45 25.63 18.35 13.10 16.59

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

147.20 80.66 147.98 191.57 235.53 108.26 71.79 70.34 76.90 183.47 131.02 116.10

8.61 9.81 15.23 18.23 23.92 22.69 19.71 17.88 20.55 14.24 6.22 10.42

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

94.70 117.67 182.74 255.24 287.04 317.63 197.08 125.13 205.54 185.16 74.68 135.40

3.76 4.31 12.56 18.40 19.27 16.02 15.32 14.01 13.98 9.53 5.92 6.21

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

33.88 38.82 100.51 91.98 115.65 144.18 260.47 266.24 139.85 28.59 11.84 49.65

Annual yield (kg)

Monthly yield

333.67 296.18 542.30 642.10 744.52 647.81 586.29 506.02 608.45 502.35 332.41 357.75 6099.85

Table 5 Daily, monthly and annual exergy at 0.14 m water depth, optimum number of collectors and mass flow rate for N-ETC-SS. Month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Exa

n0a

Exma

Exb

n0b

Exmb

Exc

n0c

Exmc

Exd

n0d

Exmd

1.70 1.48 1.71 2.02 1.96 1.94 1.81 1.91 2.31 1.79 1.61 1.50

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

5.11 4.43 8.55 8.08 7.83 5.83 3.63 3.82 16.18 8.94 9.66 4.51

1.43 1.57 2.07 2.22 1.95 2.12 1.86 1.99 2.19 1.37 0.96 1.11

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

11.42 6.28 12.42 15.53 17.55 8.46 5.59 5.97 6.56 13.73 9.64 7.74

0.35 0.36 0.71 0.98 1.64 1.52 1.27 1.17 1.49 0.77 0.25 0.45

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

3.84 4.32 8.55 13.78 19.67 21.29 12.68 8.17 14.91 10.05 3.04 5.91

0.08 0.09 0.50 1.04 1.08 0.74 0.65 0.63 0.65 0.32 0.23 0.10

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

0.75 0.81 4.02 5.21 6.50 6.67 10.99 11.97 6.47 0.96 0.46 0.83

Annual exergy (kWh)

The daily exergy of N-ETC-SS for clear days (condition (a)) can be computed by adding hourly exergy obtained from Eq. (14) for 24 h and the same process has been implemented to calculate the daily exergy for other climatic conditions (b), (c) and (d). The

Monthly exergy

21.12 15.85 33.55 42.60 51.55 42.26 32.90 29.92 44.12 33.68 22.78 18.98 389.30

monthly exergy for clear days (condition (a)) can be evaluated by multiplying daily 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

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

sum of the exergy in the climatic conditions (a), (b), (c) and (d) gives the total exergy for each month. The annual exergy can be calculated by adding monthly exergy for 12 month. Table 5 represents the computation of exergy for N-ETC-SS. Similarly, annual exergy for N-ETC-DS has been computed and presented in Table 6.

includes the cost of piping and labor. The life of pump is ten years and it has been assumed that the increase in cost of pump due to inflation is overcome by salvage value of pump.

4.3. Production cost of water

The following methodology has been employed for computation of annual yield, energy and exergy for N-ETC-SS and N-ETC-DS.

5. Methodology

The production cost of water for the proposed system can be written as

C wp ¼

UAC Mw

Step I The solar radiation on a horizontal surface, ambient air temperature and number of days for the weather conditions (a), (b), (c) and (d) have been made input to computational program in MATLAB. These data have been taken from IMD, Pune, India. Liu and Jordon formula has been employed to calculate the solar radiation for inclined surface at 30° north latitude.

ð16Þ

Here, UAC and Mw represent uniform end-of-year annual cost and annual production of potable water from N-ETC-SS/N-ETC-DS respectively. Following Tiwari (2013), the value of UAC for N-ETCSS/N-ETC-DS can be expressed as

UAC ¼ Ps  F CR;i;n þ M  F CR;i;n  Ss  F SR;i;n

Step II

ð17Þ

The value of T foN has been computed with the help of Eq. (2) followed by the evaluation of T w ; T gi and T go for N-ETC-SS using Eqs. (3)–(5). Then, yield for the system has been evaluated with the help of Eq. (6). Similarly, values of various temperatures for NETC-DS have been computed using Eqs. (7)–(11). Then, values of yield for N-ETC-DS have been computed using Eq. (12).

The maintenance cost (M) is the product of the net present cost (Ps) and maintenance cost factor which is generally taken as 0.1. Here, it should be noted that the maintenance cost also includes the cost of electrical power required to run the pump. The capital recovery factor (F CR;i;n ) and sinking fund factor (F SR;i;n ) can be written as n

F CR;i;n ¼

i  ð1 þ iÞ n ð1 þ iÞ  1

ð18Þ

Step III

and

F SR;i;n ¼

i n ð1 þ iÞ  1

The thermal energy for N-ETC-SS and N-ETC-DS has been computed using Eq. (13). Then, exergy for N-ETC-SS and N-ETC-SDS has been computed using Eqs. (14) and (15) respectively.

ð19Þ

Step IV

where i and n are the rate of interest and life of the system respectively. The capital recovery factor and sinking fund factor have been used to convert the present cost and future cost into uniform endof-year annual cost respectively. Net present cost (Ps) for the 50 years life span of N-ETC-SS/N-ETC-DS can be expressed as

Ps ¼ P þ Pp þ

Pp ð1 þ iÞ

10

þ

Pp ð1 þ iÞ

20

þ

Pp ð1 þ iÞ

30

þ

Pp ð1 þ iÞ

The production cost of potable water for the proposed systems has been calculated with the help of Eq. (16). Step V N-ETC-SS and N-ETC-DS have been compared for same basin area under similar climatic condition on the basis of annual energy, annual exergy and cost of potable water. The calculation flow chart for better understanding the methodology is as follows.

ð20Þ

40

where P = C solar still + C ETC + C fab . Here, C solar still represents the cost of solar still, C ETC represents the cost of ETC and C fab represents the fabrication cost which

Table 6 Daily, monthly and annual exergy at 0.14 m water depth, optimum number of collectors and mass flow rate for N-ETC-DS. Month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Monthly exergy

Exa

n0a

Exma

Exb

n0b

Exmb

Exc

n0c

Exmc

Exd

n0d

Exmd

1.75 1.66 1.92 2.30 2.256 2.23 2.63 2.04 2.63 1.97 1.75 1.66

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

5.26 4.98 9.61 9.21 9.03 6.70 5.25 4.08 18.44 9.86 10.51 4.98

1.57 1.76 2.32 2.54 2.24 2.44 2.12 2.24 2.48 1.52 0.76 1.25

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

12.56 7.05 13.93 17.75 20.18 9.76 6.37 6.72 7.45 15.15 7.57 8.73

0.44 0.48 0.86 1.14 1.88 1.75 1.45 1.33 1.67 0.89 0.23 0.57

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

4.80 5.72 10.28 15.99 22.54 24.49 14.53 9.30 16.67 11.59 2.75 7.35

0.12 0.13 0.63 1.21 1.25 0.88 0.76 0.74 0.75 0.41 0.21 0.25

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

1.07 1.17 5.03 6.04 7.48 7.89 12.98 14.03 7.45 1.22 0.42 1.99

Annual exergy (kWh)

23.69 18.93 38.86 48.98 59.22 48.85 39.13 34.13 50.01 37.82 21.25 23.05 443.92

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

6. Results and discussion All relevant equations and climatic data namely solar radiation, ambient air temperature and average wind velocity have been fed to MATLAB. Total radiation on horizontal surface and ambient air temperature are represented by Tables B1–B5. Average wind velocity is shown in Table 2. The output obtained is shown in Figs. 4–13 and Tables 3–6.

837

Fig. 4 represents the variation of maximum temperature of water at the outlet of Nth ETC ðT foN;max Þ with number of collectors _ f Þ for N-ETC-SS for a typical day in (N) at given mass flow rate ðm the month of June. The addition of heat per unit time ðQ_ Þ in the

_ f C f ðT f Þ; where T f ¼ T foN  T fi . basin of N-ETC-SS is given by Q_ ¼ m _ f , higher will be the amount of heat It means higher the value of m added per unit time to the basin. However, the value of T foN _ f due to lesser time decreases with the increase in the value of m

838

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

350

= 0.002 kg/s = 0.004 kg/s = 0.006 kg/s = 0.008 kg/s = 0.010 kg/s = 0.012 kg/s = 0.014 kg/s = 0.016 kg/s = 0.018 kg/s = 0.020 kg/s = 0.022 kg/s

300 TfoN, max (oC)

250 200 150 100 50 19

17

15

13

11

9

7

5

3

1

0 No. of ETC (N) _ f for N-ETC-SS for a typical day in the month of June. Fig. 4. Variation of T foN;max with N at given m

= 0.002 kg/s = 0.004 kg/s = 0.006 kg/s = 0.008 kg/s = 0.010 kg/s = 0.012 kg/s = 0.014 kg/s = 0.016 kg/s = 0.018 kg/s = 0.020 kg/s = 0.022 kg/s

350 300 TfoN, max (oC)

250 200 150 100 50 19

17

15

13

11

9

7

5

3

1

0 No. of ETC (N) _ f . for N-ETC-DS for a typical day in the month of June. Fig. 5. Variation of T foN;max with N at given m

45

Daily yield (kg)

40 35 30

= 0.016 kg/s Jun-ETC-SS

25 20

Jun-ETC-DS

15

Jan-ETC-SS

10 Jan-ETC-DS

5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0 No. of ETC (N) Fig. 6. Variation of daily yield with N for N-ETC-SS and N-ETC-DS for a typical day in the month of June and January.

available for liquid in the collector for absorbing heat. Also, the amount of heat loss from absorber increases with the increase in _ f . Hence, one will have to compromise between the value of m _ f and T foN . the value of m It is observed from Fig. 4 that the gap between curves decreases _ f increases and the gap becomes insignificant as the value of m

_ f ¼ 0:016 kg/s. Also, slope of curves decreases as the beyond m _ f is increased and it becomes insignificant beyond value of m _ f ¼ 0:016 kg/s. It means that the change in value of T foN for a m given mass flow rate becomes insignificant if N is increased for _ f is 0.016 kg/s. Fur_ f P 0:016 kg/s. Hence, optimum value of m m ther, the value of daily yield increases with the increase in the

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

120 Temperature (oC)

= 0.016 kg/s, N= 12 100 80 60 40 20 06:00

04:00

02:00

00:00

22:00

20:00

18:00

16:00

14:00

12:00

10:00

08:00

0

Time of day (h) Fig. 7. Hourly variation of temperature of N-ETC-SS for a typical day in the month of June.

120

= 0.016 kg/s, N= 12

Temperature (oC)

100 80 60 40 20 Ta 06:00

04:00

02:00

00:00

22:00

20:00

18:00

16:00

14:00

12:00

10:00

08:00

0

Time of day (h)

Yield (kg)

06:00

04:00

02:00

00:00

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 22:00

20:00

18:00

16:00

12:00

10:00

14:00

= 0.016 kg/s, N=12

100 90 80 70 60 50 40 30 20 10 0 08:00

Heat transfer coeff. (W/m2-K)

Fig. 8. Hourly variation of Temperature of N-ETC-DS for a typical day in the month of June.

Time of day (h) Fig. 9. Hourly variation of heat transfer coefficient and yield of N-ETC-SS for a typical day in the month of June.

_ f ¼ 0:016 kg/s as observed from Fig. 6; however, one value of N at m cannot go beyond N = 12 as the value of T foN becomes more than _ f ¼ 0:016 kg/s as observed from Fig. 4. 100 °C beyond N = 12 at m So, the optimum value of N is 12 for N-ETC-SS as boiling point of water is 100 °C. Similarly, one can observe from Fig. 5 that the _ f for N-ETC-DS is also 0.016 m/s as the gap optimum value of m

_ f ¼ 0:016 kg/s between curves becomes insignificant beyond m and curves are getting overlapped on further increasing the _ f . Further, value of T foN becomes higher than 100 °C value of m _ f ¼ 0:016 kg/s if N is greater than 12. Also, the value of at m daily yield increases with the increase in the value of N at _ f ¼ 0:016 kg/s as observed from Fig. 6; however, one cannot go m

160 140 120 100 80 60 40 20 0

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

06:00

04:00

02:00

00:00

20:00

22:00

18:00

16:00

14:00

12:00

10:00

08:00

= 0.016 kg/s, N=12

Yield (kg)

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

Heat transfer coeff. (W/m2-K)

840

Time of day (h) Fig. 10. Hourly variation of heat transfer coefficient and yield of N-ETC-DS for a typical day in the month of June.

30

DS-Jun

1.45

1.35

0.08

1.25

0.064

1.15

0.048

1.05

0.032

0.95

0.016

= 0.016 kg/s, N=12

0.05

0

DS-Average

0.85

5

DS-jan

0.75

SS-jan

0.65

10

0.55

DS-Jun

0.45

15

0.35

SS-Jun

0.25

20

40 35 30 25 20 15 10 5 0 0.15

N=12 Yield (kg)

Yield (kg)

25

DS-Jan

Depth of water (m) Fig. 11. Hourly variation of yield of N-ETC-SS and N-ETC-DS for a typical day in the month of June and January.

35 30 25 20 15 10 5 0

SS-jan

SS-average

1.45

1.35

1.25

1.15

1.05

0.95

0.85

0.75

0.65

0.55

0.45

0.35

0.25

0.05

= 0.016 kg/s, N=12

0.15

Yield (kg)

SS-Jun

Depth of water (m) Fig. 12. Variation of daily yield with water depth of N-ETC-SS for a typical day in the month of June and January.

beyond N = 12 as the value of T foN becomes more than 100 °C _ f ¼ 0:016 kg/s. Hence, optimum value of N for beyond N = 12 at m N-ETC-DS is 12. Figs. 7 and 8 represent the hourly variation of various temperatures of N-ETC-SS and N-ETC-DS respectively for a typical day in the month of June. It is observed that values of T foN is less than that of T w for both systems because water at higher temperature from the outlet of Nth collector is mixed with lower temperature of water (T wo ) in the basin. Also, value of glass temperature is lower than T w because glass is in direct contact with ambient air and this

Fig. 13. Variation of daily yield with water depth of N-ETC-DS for a typical day in the month of June and January.

difference in water temperature in basin and glass temperature (DT) need to be maintained if distillation has to occur continuously. Higher the value of DT higher will be the rate of distillation. It is also observed from Figs. 6 and 7 that highest value of DT occurs at 13:00; however, maximum value of solar intensity occurs at 12:00 noon. It happens because of the existence of time gap between solar intensity and actual increase in temperature of water in the basin. Figs. 9 and 10 represent hourly variation of heat transfer coefficient (HTC) and production of potable water of N-ETC-SS and NETC-DS for a typical day in the month of June. It is observed that values of convective and radiative HTCs are very low in comparison to evaporative HTC which is as per expectation because convective and radiative HTCs are responsible for losses and evaporative HTC contributes to output. Radiative HTC is low because the operating temperature is low (<100 °C) as radiative HTC is effective for higher temperature of the order of 1000 °C. It has also been observed that evaporative HTC is maximum at 17 h whereas hourly production of potable water is maximum at 15 h. It happens because hourly production of potable water is a function of both evaporative HTC and DT. Fig. 11 represents the hourly variation of production of potable water with mass flow rate at N = 12 for the proposed systems for a typical day in the month of June and January. It is observed that the daily yield decreases with the increase in mass flow rate because temperature of fluid at the outlet of Nth collector becomes lower due to increase in heat loss from absorber plate. If T foN is lower, rise in the value of T w will be lower resulting in

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

lowering the value of DT and hence daily yield becomes lower. Also, daily yield in the month of June is higher than the daily yield in the month of January because solar intensity is higher in the month of June. Figs. 12 and 13 represent the variation of daily yield with _ f ¼ 0:016 kg/s and N = 12 of N-ETC-SS and water depth at m N-ETC-DS respectively for a typical day in the month of June and January. It is observed that the value of daily yield is higher in the month of June than the daily yield in the month of January for both systems because solar intensity in the month of June is higher than the solar intensity in the month of January. It is also observed that the daily yield first increases and then it becomes almost constant. The initial rise in the value of daily yield is obtained because increase in yield at night is higher than the decrease in yield in day time. The increase in yield at night is higher due to higher heat content of water mass at night which in turn occurs due to higher water depth in the basin. The daily yield becomes almost constant after an initial rise because water temperature does not increases after certain water depth due to higher mass of water and increase in yield due to heat content of water mass at night gets balanced by the decrease in yield in day time at higher water depth. Tables 3 and 4 show the calculation of daily, monthly and annual production of potable water for N-ETC-SS and N-ETC-DS respectively at 0.14 m water depth, optimum number of collectors and mass flow rate. It is observed that the monthly yield of both systems is highest in May and lowest in February. They happen because the monthly production of potable water depends on daily production of potable water and number of clear days. Further, daily production of potable water depends on hourly yield which depends on HTC and DT. The evaporative HTC and DT are governed by solar intensity. Tables 5 and 6 show the calculation of daily, monthly and annual exergy for N-ETC-SS and N-ETC-DS respectively at _ f ¼ 0:016 kg/s. It is observed 0.14 m water depth, N = 12 and m that monthly exergy is highest for both systems in the month of May and lowest for both systems in the month of February.

Table 7 Capital investment for N-ETC-SS and N-ETC-DS. S. No.

Parameter

Cost of N-ETC-SS

Cost of N-ETC-DS

1 2 3 4 5

Cost of solar still Cost of ETC @ 10,500 each Cost of motor and pump Fabrication cost Salvage value of the system after 50 years, if inflation remains @ 4% in India, [using present value of scrap material sold in Indian market]

23,143 22,590 1000 6000 32,501

19,183 22,590 1000 6000 29,687

It happens because of similar variation in the value of solar intensity for both systems. Further, annual exergy for N-ETC-DS is higher by 12.30% for N-ETC-DS than N-ETC-SS because solar intensity in the case of N-ETC-DS is more uniformly distributed than N-ETC-SS. Also, loss is lower in the case of double slope active solar still. Table 7 represents the capital investment for N-ETC-SS and NETC-DS. Table 8 represents the calculation of UAC and production cost of potable water at 0.14 m water depth, optimum number of collectors and mass flow rate for both the proposed systems. It is observed that value of UAC is lower by 7.30% for N-ETC-DS than N-ETC-SS at 2% rate of interest and 50 year life span because of lesser material requirement due to the geometrical shape of double slope solar still. Further, production of potable water is higher by 6.85% for N-ETC-DS than N-ETC-SS due to lesser loss and more uniform variation in solar intensity in the case of double slope solar still. Hence, production cost of potable water is lower by 15.19% for N-ETC-DS than N-ETC-SS at 2% rate of interest and 50 year life span as production cost is the ratio of UAC and annual production of potable water. 7. Conclusions and recommendations 7.1. Conclusions The theoretical analysis of N-ETC-SS and N-ETC-DS has been done at 0.14 m water depth and optimum number of collectors and mass flow rate considering four weather conditions for each month of year for New Delhi, India. On the basis of current research study, the following conclusions have been drawn. (i) The optimum number of collectors and mass flow rate for both systems has been found as 12 and 0.016 kg/s respectively. (ii) The annual production of potable water, energy and exergy are higher by 6.85%, 6.85% and 12.30% respectively at 0.14 m water depth for N-ETC-SS than N-ETC-DS for same basin area under similar climatic condition. (iii) The production cost of potable water is lower by 15.19% at 0.14 m water depth, 2% rate of interest and 50 year life span for N-ETC-DS than N-ETC-SS. 7.2. Recommendations The proposed system should be studied for local climatic condition before its installation. The theoretical results of proposed N-ETC-DS using thermal model developed can be validated by experimental results under optimized condition. The effect of salt concentration/salinity/particulates/nanofluids should be studied.

Table 8 Value of UAC and production cost of water for N-ETC-SS and N-ETC-DS. n Yr.

i %

Ps

M @ 10%

Ss

F CR;i;n Fraction

F SR;i;n Fraction

UAC

Mw kg

C wp =kg

N-ETC-SS 50 50 50

2 5 10

55231.28 54381.56 53346.59

5523.128 5438.156 5334.659

32,501 32,501 32,501

0.031823 0.054777 0.100859

0.01182 0.00478 0.00086

1549.226 3121.39 5890.581

5681.48 5681.48 5681.48

0.273 0.550 1.037

N-ETC-DS 50 50 50

2 5 10

51271.28 50421.56 49386.59

5127.128 5042.156 4938.659

29,687 29,687 29,687

0.031823 0.054777 0.100859

0.01182 0.00478 0.00086

1443.87 2896.23 5453.66

6099.85 6099.85 6099.85

0.237 0.475 0.894

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D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

Appendix A

U1 ¼

h1wE A2b þ hEW AgE þ U cgaE AgE AgW

U2 ¼

h1wW A2b þ hEW AgW þ U cgaW AgW AgE

B1 ¼

ðR2 P þ A1 hEW ÞAgW U 2 AgE

B2 ¼

Ph1wW A2b þ hEW AgW A2 U 2 AgE

Expressions for various terms used in Eqs. (3)–(6) are as follows.

a1 ¼

i 1 h _ f C f ð1  K Nk Þ þ U s Ab ; m Mw C w

f 1 ðtÞ ¼

" ! # 1 ð1  K Nk Þ ð1  K Nk Þ ðAF R ðasÞÞ1Ib ðtÞ þ ðAF R U L Þ1 þ U s Ab T a ; a0eff AbIs ðtÞ þ Mw C w ð1  K k Þ ð1  K k Þ

a0eff ¼ a0w þ h1 a0b þ h01 a0g ; h1 ¼

hbw ; hbw þ hba

0

h1 ¼

h1w Ag ; U c;ga Ag þ h1w Ab

hewg ¼ 16:273  103 hcwg



h1w ¼ hrwg þ hcwg þ hewg ;

R1 ¼ a0g ISE ðtÞ þ U cgaE T a

 Pw  Pgi ; T w  T gi

R2 ¼ a0g ISW ðtÞ þ U cgaW T a

 1 ðPw  Pgi ÞðT w þ 273Þ 3 hcwg ¼ 0:884 ðT w  T gi Þ þ ; 3 268:9  10  Pw 

hEW ¼ 0:034  5:67  108 ½ðT giE þ 273Þ2 þ ðT giW þ 273Þ2 ½T giE þ T giW þ 546



Pw ¼ exp 25:317 

5144 ; T w þ 273

 Pgi ¼ exp 25:317 

 5144 ; T gi þ 273 8

K

g h1gE l ; U cgaE ¼ K g g þ h1gE lg

h

2

2

i

hrwg ¼ ð0:82  5:67  10 Þ ðT w þ 273Þ þ ðT gi þ 273Þ ½T w þ T gi

K

g h1gW l U cgaW ¼ K g g ; þ h1gW lg

h1gE ¼ 5:7 þ 3:8 V; h1gW ¼ 5:7 þ 3:8 V; h1wE ¼ hrwgE þ hcwgE þ hewgE

þ 546; Us ¼ Ut þ Ub ;

Ub ¼

hba hbw ; hbw þ hba 

K

g h1g l U cga ¼ K g g ; þ h1g lg

hba ¼

Ut ¼

Li 1 þ K i hcb þ hrb

h1w U cga Ag ; U cga Ag þ h1w Ab

1 ;

hcb þ hrb ¼ 5:7 W m2 K1 ; hbw ¼ 100 W m2 K1 ; Expressions for various terms used in Eqs. (7)–(12)are as follows.   1 h1wEðP  A2 ÞAb h1wWðP  B2 ÞAb _ f C f ð1  K Nk Þ þ U b Ab þ m þ ; a2 ¼ 2P 2P Mw C w

f 2 ðtÞ ¼

1 Mw C w



a0w 2



 þ h1 a0b Ab ISE ðtÞ þ ISW ðtÞ

! ð1  ð1  K Nk Þ ðAF R ðasÞÞ1Ib ðtÞ þ ðAF R U L Þ1 þ U b Ab T a ð1  K k Þ ð1  K k Þ   h1wE A1 þ h1wW B1 Ab ; þ P 2 þ

K Nk Þ

A1 ¼ R1 U 1 AgE þ R2 hEW AgW Ab Ab þ hEW h1wW 2 2 ! 2 h Ab AgW U 1 U 2  EW h1wW AgE 2

A2 ¼ h1wE U 2

P¼

h1wW ¼ hrwgW þ hcwgW þ hewgW  Pw  P giE ; hewgW T w  T giE   Pw  PgiW ; ¼ 16:273  103 hcwgW T w  T giW

hewgE ¼ 16:273  103 hcwgE



 1 ðPw  Pgi EÞðT w þ 273Þ 3 ; hcwgE ¼ 0:884 ðT w  T giE Þ þ 3 268:9  10  Pw  1 ðP w  PgiW ÞðT w þ 273Þ 3 hcwgW ¼ 0:884 ðT w  T giW Þ þ ; 268:9  103  Pw Pw ¼ exp½25:317 

5144 ; T w þ 273

 PgiE ¼ exp 25:317 

 5144 ; T gi E þ 273

 PgiW ¼ exp 25:317 

 5144 ; T giW þ 273

hrwgE ¼ ð0:82  5:67  108 Þ½ðT w þ 273Þ2 þ ðT giE þ 273Þ2   ½T w þ T giE þ 546; hrwgW ¼ ð0:82  5:67  108 Þ½ðT w þ 273Þ2 þ ðT giW þ 273Þ2   ½T w þ T giW þ 546;

843

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

Appendix B See Tables B1–B6. Table B1 Solar global irradiance data for a typical day of a-type weather conditions for New Delhi. Solar radiation

Time

Month January

February

March

April

May

June

July

August

September

October

November

December

Global

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

132.99 355.56 554.69 680.73 726.74 733.85 656.08 500.00 311.46 106.42

180.29 403.58 594.44 729.39 786.02 792.03 728.58 584.23 391.22 178.23

266.77 488.94 671.21 804.33 866.93 869.28 803.15 665.33 483.01 264.10

368.14 588.48 767.81 888.32 941.01 944.12 878.68 746.90 568.30 348.61

406.31 608.84 776.26 897.98 956.82 950.51 886.62 761.37 580.81 372.48

436.67 637.22 802.22 915.00 951.67 946.11 882.78 765.56 611.67 420.00

367.36 587.04 737.27 831.71 881.48 896.53 820.60 753.24 569.68 373.15

333.59 528.54 674.49 820.20 868.18 807.83 766.67 658.08 477.78 305.81

277.96 501.30 682.04 809.07 869.07 855.19 779.81 656.48 483.89 270.19

168.75 364.58 565.28 694.45 761.80 756.25 686.11 543.75 362.50 152.08

121.46 316.04 485.35 609.97 664.01 657.45 587.37 454.17 274.62 84.09

93.12 275.27 443.25 565.87 621.83 618.39 553.31 426.19 253.97 68.78

Diffuse

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

52.60 86.28 107.29 121.53 126.39 136.63 128.30 110.94 90.28 41.84

73.30 105.82 126.08 137.36 141.31 145.07 138.35 123.84 101.52 63.98

94.23 123.02 142.20 154.11 153.21 153.21 151.12 136.54 116.35 85.74

122.47 139.54 159.40 174.84 180.39 181.78 177.45 163.24 146.08 115.36

117.68 137.12 153.28 166.67 174.24 177.02 175.76 165.66 154.29 133.08

123.89 149.44 157.22 158.89 167.78 185.00 180.56 176.11 142.78 116.11

109.03 141.44 171.07 205.09 218.75 219.68 204.86 179.63 149.54 110.42

86.62 100.00 155.30 176.26 189.65 201.26 197.48 172.72 128.28 93.69

100.00 124.81 140.93 151.67 152.41 160.00 164.26 150.74 123.15 91.30

44.44 68.75 119.45 137.50 147.92 154.17 142.36 121.53 93.06 59.72

42.80 61.36 77.15 109.60 141.67 136.36 131.82 114.77 88.01 43.05

36.37 53.31 60.19 81.61 142.46 141.27 119.18 105.03 78.84 37.43

Beam

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

80.38 269.27 447.40 559.20 600.35 597.22 527.78 389.06 221.18 64.58

106.99 297.76 468.37 592.03 644.71 646.95 590.23 460.39 289.69 114.25

172.54 365.92 529.01 650.21 713.73 716.08 652.03 528.79 366.67 178.37

245.67 448.94 608.41 713.48 760.62 762.34 701.23 583.66 422.22 233.25

288.64 471.72 622.98 731.31 782.58 773.48 710.86 595.71 426.51 239.40

312.78 487.78 645.00 756.11 783.89 761.11 702.22 589.45 468.89 303.89

258.33 445.60 566.20 626.62 662.73 676.85 615.74 573.61 420.14 262.73

246.97 428.54 519.19 643.94 678.53 606.57 569.19 485.36 349.50 212.12

177.96 376.48 541.11 657.41 716.67 695.19 615.56 505.74 360.74 178.89

124.31 295.83 445.83 556.95 613.89 602.08 543.75 422.23 269.44 92.36

78.66 254.67 408.21 500.38 522.35 521.09 455.56 339.39 186.62 41.04

56.75 221.96 383.07 484.26 479.37 477.12 434.13 321.16 175.13 31.35

Table B2 Solar global irradiance data for a typical day of b-type weather conditions for New Delhi. Solar radiation

Time

Month January

February

March

April

May

June

July

August

September

October

November

December

Global

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

119.58 332.50 516.25 650.41 708.75 723.33 650.41 498.75 315.00 110.84

186.67 425.84 609.59 752.50 813.75 822.50 758.33 603.75 408.33 183.75

300.45 540.22 733.78 872.45 933.11 938.89 869.55 713.55 522.89 288.89

413.11 635.55 808.89 936.00 999.55 982.22 901.34 751.11 557.55 332.22

439.11 641.34 794.45 898.45 947.55 936.00 852.22 722.22 540.22 340.89

433.34 641.34 794.45 912.89 999.55 996.66 912.89 808.89 635.55 416.00

398.66 592.22 751.11 840.66 936.00 907.11 837.78 707.78 554.66 352.45

366.89 551.78 713.55 832.00 881.11 881.11 808.89 687.55 505.55 317.78

277.34 499.78 687.55 788.66 837.78 860.89 800.22 667.34 462.22 265.78

260.00 442.00 598.00 693.34 728.00 702.00 615.34 465.11 283.11 98.22

153.11 332.22 470.89 574.89 606.66 563.34 491.11 352.45 193.55 86.66

86.66 280.22 456.45 580.66 629.78 635.55 566.22 424.66 228.22 63.55

Diffuse

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

52.75 102.57 123.09 149.46 155.32 161.18 155.32 128.94 96.71 46.88

84.99 143.60 167.04 181.69 190.49 190.49 181.69 158.25 123.09 70.34

119.58 160.42 180.83 201.25 204.16 207.08 198.33 177.91 154.58 110.84

134.17 166.25 186.67 201.25 215.84 215.84 210.00 201.25 175.00 125.41

204.16 247.92 274.17 297.50 300.42 300.42 297.50 271.25 239.17 189.59

198.33 250.83 277.08 297.50 300.42 335.41 315.00 291.67 274.17 207.08

192.67 229.50 283.34 320.17 340.00 328.66 311.67 291.83 243.67 198.33

170.00 218.17 252.16 260.67 277.66 280.50 252.16 232.34 218.17 178.50

104.84 144.50 204.00 226.66 240.83 232.34 223.83 204.00 170.00 133.17

133.17 187.00 212.50 232.34 238.00 232.34 218.17 184.17 141.67 70.83

107.67 158.67 192.67 212.50 218.17 206.84 201.16 170.00 121.83 48.16

28.34 99.16 133.17 155.84 170.00 172.83 161.50 136.00 99.16 51.00

Beam

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

66.83 229.94 393.17 500.95 553.43 562.15 495.09 369.81 218.29 63.95

101.68 282.24 442.55 570.81 623.26 632.01 576.64 445.50 285.25 113.41

180.86 379.80 552.95 671.19 728.95 731.81 671.22 535.64 368.31 178.05

278.94 469.31 622.22 734.75 783.72 766.38 691.34 549.86 382.55 206.81

234.95 393.42 520.28 600.95 647.14 635.58 554.72 450.97 301.05 151.30

235.00 390.50 517.36 615.39 699.14 661.25 597.89 517.22 361.39 208.92

206.00 362.72 467.77 520.50 596.00 578.44 526.11 415.95 311.00 154.12

196.89 333.61 461.39 571.33 603.44 600.61 556.73 455.22 287.39 139.28

172.5 355.28 483.55 562.00 596.95 628.56 576.39 463.34 292.21 132.61

126.83 255.00 385.50 461.00 490.00 469.66 397.17 280.94 141.44 27.39

45.44 173.55 278.22 362.39 388.50 356.50 289.94 182.44 71.73 38.50

58.33 181.05 323.27 424.83 459.78 462.73 404.72 288.67 129.05 12.55

844

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846

Table B3 Solar global irradiance data for a typical day of c-type weather conditions for New Delhi. Solar radiation

Time

Month January

February

March

April

May

June

July

August

September

October

November

December

Global

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

71.11 235.55 360.00 457.78 515.55 515.55 462.22 353.34 217.78 71.11

117.78 284.45 420.00 522.22 562.22 562.22 506.66 384.45 266.66 111.11

197.78 366.66 513.34 613.34 664.45 662.22 602.22 497.78 353.34 188.89

288.89 453.34 582.22 677.78 724.45 720.00 664.45 564.45 420.00 233.34

361.11 566.67 708.33 841.67 894.44 872.22 805.56 666.67 513.89 322.22

358.33 555.56 727.78 816.67 833.33 861.11 763.89 688.89 538.89 333.33

333.33 530.67 642.66 744.00 778.67 762.66 722.67 602.67 469.33 280.00

297.50 490.00 597.50 700.00 702.50 702.50 630.00 540.00 430.00 282.50

261.25 456.53 617.50 691.39 730.97 752.09 712.50 575.28 414.30 255.97

195.83 365.56 496.11 587.50 624.06 608.39 514.39 383.83 229.77 73.11

66.66 206.66 333.34 415.55 444.45 453.34 406.66 313.34 177.78 62.22

66.66 216.00 365.34 482.67 544.00 522.66 448.00 341.34 200.00 58.67

Diffuse

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

64.16 146.66 195.56 220.00 226.12 226.12 210.84 180.28 122.22 51.94

91.66 161.94 201.66 232.22 244.44 241.38 247.50 213.88 168.06 85.56

134.44 192.50 229.16 241.38 253.62 268.88 259.72 232.22 189.44 128.34

187.50 236.11 277.77 305.55 319.45 326.39 322.91 284.73 246.53 177.09

215.28 291.66 336.80 392.36 440.97 440.97 378.47 333.34 319.45 253.47

277.77 350.70 378.47 416.66 434.03 423.61 402.78 385.41 347.22 246.53

205.84 263.89 295.55 345.70 387.91 366.80 340.41 321.95 263.89 184.72

239.58 290.70 348.20 370.55 376.95 367.36 351.39 316.25 277.92 207.64

169.30 239.58 300.28 313.05 367.36 364.17 345.00 303.47 255.55 198.05

130.56 172.22 205.56 230.56 241.67 236.11 213.89 188.89 141.67 63.89

63.89 137.36 185.28 223.61 245.97 258.75 230.00 191.67 140.55 61.89

45.84 122.22 171.12 226.12 250.56 247.50 235.28 189.44 125.28 61.16

Beam

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

6.95 88.89 164.44 237.78 289.44 289.44 251.39 173.06 95.56 19.17

26.11 122.51 218.34 290.00 317.78 320.84 259.16 170.56 98.61 25.55

63.33 174.16 284.17 371.95 410.83 393.34 342.50 265.56 163.89 60.55

101.39 217.22 304.45 372.23 405.00 393.61 341.54 279.72 173.47 56.25

145.84 275.01 371.53 449.31 453.47 431.25 427.08 333.33 194.44 68.75

80.56 204.86 349.31 400.01 399.31 437.50 361.11 303.48 191.67 86.80

127.49 266.78 347.11 398.30 390.75 395.86 382.26 280.72 205.44 95.29

57.92 199.30 249.30 329.45 325.56 335.15 278.61 223.75 152.08 74.86

91.95 216.95 317.22 378.34 363.61 387.92 367.50 271.81 158.75 57.91

65.27 193.34 290.55 356.94 382.39 372.28 300.50 194.94 88.10 9.22

2.77 69.31 148.06 191.95 198.47 194.59 176.66 121.67 37.22 1.67

23.60 102.78 209.44 276.66 316.11 296.94 231.39 166.12 83.05 3.05

Table B4 Solar global irradiance data for a typical day of d-type weather conditions for New Delhi. Solar radiation

Time

Month January

February

March

April

May

June

July

August

September

October

November

December

Global

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

51.20 140.11 237.11 301.78 379.92 379.92 328.72 261.36 161.67 45.80

94.30 188.61 247.89 291.00 369.14 412.25 374.53 299.08 204.78 88.92

169.75 331.42 479.61 552.36 590.08 627.80 568.53 463.45 307.17 161.67

266.75 441.89 600.86 716.72 773.30 757.14 689.78 541.58 425.72 239.80

304.12 503.44 623.56 702.78 761.56 764.12 621.00 529.00 426.78 255.56

235.12 350.12 454.88 595.44 672.12 682.34 631.22 536.66 426.78 281.12

262.50 397.50 515.00 587.50 605.00 615.00 517.50 445.00 347.50 232.50

208.47 358.89 440.70 530.41 572.64 588.47 562.09 496.11 348.34 195.28

155.00 287.50 425.00 557.50 585.00 585.00 530.00 442.50 350.00 187.50

110.84 237.66 375.66 488.12 503.44 511.12 454.88 339.88 237.66 113.75

63.88 184.00 273.44 375.66 444.66 477.88 424.22 337.34 198.33 66.44

54.45 176.95 272.22 356.61 397.45 405.61 359.34 239.55 141.55 52.72

Diffuse

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

48.16 107.67 175.66 221.00 246.50 255.00 240.83 187.00 138.83 42.50

90.67 150.16 204.00 229.50 269.17 289.00 272.00 204.00 150.16 82.17

147.33 229.50 297.50 351.33 357.00 374.00 328.66 303.16 212.50 144.50

207.85 261.95 321.74 387.22 404.30 432.78 387.22 333.12 298.96 205.00

236.17 342.14 372.42 429.94 466.28 466.28 399.67 372.42 314.89 230.11

169.56 251.31 360.31 405.72 454.17 481.42 448.11 393.61 330.03 260.39

215.96 298.08 377.16 438.00 441.04 431.91 386.29 358.92 276.79 197.71

177.50 257.38 340.20 375.71 396.41 428.96 402.34 346.13 266.25 162.71

127.20 224.83 310.63 405.30 414.17 402.34 360.92 295.84 266.25 174.54

107.34 195.42 280.00 335.41 364.58 332.50 282.91 259.58 224.58 104.78

49.58 116.67 145.83 207.08 256.66 306.25 277.08 239.17 196.78 64.17

52.50 140.00 186.67 227.50 262.50 303.33 291.67 207.08 122.50 51.50

Beam

8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm

3.03 32.44 61.44 80.77 133.42 124.92 87.89 74.36 22.84 3.30

3.64 38.44 43.89 61.50 99.98 123.25 102.52 95.08 54.61 6.75

22.42 101.92 182.10 201.03 233.08 253.80 239.86 160.28 94.67 17.17

58.90 179.94 279.12 329.50 369.00 324.37 302.55 208.46 126.76 34.80

67.94 161.30 251.14 272.84 295.28 297.83 221.33 156.58 111.89 25.45

65.55 98.80 94.57 189.72 217.94 200.92 183.11 143.05 96.75 20.73

46.55 99.42 137.84 149.50 163.95 183.09 131.21 86.08 70.70 34.78

30.96 101.51 100.49 154.70 176.23 159.51 159.75 149.98 82.09 32.57

27.79 62.66 114.37 152.20 170.83 182.66 169.08 146.67 83.75 12.95

3.50 42.25 95.66 152.70 138.86 178.61 171.97 80.30 13.08 8.97

14.30 67.33 127.61 168.58 188.00 171.63 147.14 98.17 1.56 2.28

1.95 36.95 85.56 129.11 134.95 102.28 67.67 32.47 19.05 0.78

845

D.B. Singh, G.N. Tiwari / Solar Energy 155 (2017) 829–846 Table B5 Ambient temperature for a typical day in different months for New Delhi. Time

12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm 6pm 7pm 8pm 9pm 10pm 11pm

Month January

February

March

April

May

June

July

August

September

October

November

December

7.80 7.30 6.60 5.00 4.00 5.30 6.40 6.80 7.90 7.90 7.90 6.60 6.40 7.70 10.60 13.00 15.00 16.50 17.00 15.80 14.10 12.90 10.20 8.20

10.00 9.80 9.60 8.30 8.00 8.10 9.00 9.20 9.20 9.10 8.90 8.80 8.90 11.40 15.10 18.30 20.10 21.60 22.20 20.70 19.60 18.30 15.20 13.50

15.10 14.20 14.00 13.30 13.10 14.10 15.50 15.70 15.80 15.90 15.90 15.80 16.60 19.90 22.80 26.20 27.00 28.90 25.30 24.20 21.10 20.30 18.20 15.00

28.40 27.60 26.00 24.20 24.00 24.00 25.50 25.10 25.00 25.00 25.00 25.10 25.90 27.60 30.30 31.70 33.20 34.40 35.30 34.20 32.30 30.00 29.30 29.00

36.00 34.10 31.00 28.10 27.00 27.60 28.00 30.80 30.80 30.80 30.10 30.60 31.80 33.80 35.30 36.60 37.60 38.50 40.30 40.00 38.60 38.00 38.00 37.30

32.10 27.10 25.20 24.10 24.00 25.00 26.90 26.60 26.50 26.30 26.30 26.50 27.30 29.90 31.40 32.20 33.60 34.30 34.20 34.20 34.10 34.00 35.00 35.00

30.20 28.00 26.20 24.00 25.00 26.50 26.20 26.10 26.10 26.10 26.20 26.30 26.60 28.00 28.40 29.30 30.40 32.20 33.80 33.00 32.60 32.40 31.50 31.20

27.00 25.50 25.30 25.00 24.60 24.60 24.00 24.10 24.30 24.30 24.30 24.30 24.40 25.50 25.60 26.00 26.40 27.10 28.30 28.00 27.30 27.00 27.50 27.20

28.00 27.10 26.00 26.90 25.00 26.00 26.10 27.50 27.90 27.90 27.90 28.30 28.90 30.60 32.30 33.50 33.90 35.50 36.00 35.00 32.00 29.20 28.10 28.00

24.90 23.00 21.10 21.00 19.00 20.00 19.50 20.10 21.00 21.00 20.50 20.50 22.70 25.00 28.30 30.50 31.60 32.70 34.00 32.30 30.00 28.10 27.20 26.00

19.00 19.10 17.00 16.00 15.00 15.40 16.30 16.20 17.00 16.70 16.50 16.00 16.20 20.50 25.00 27.60 28.50 29.60 30.20 27.00 25.10 23.00 21.00 19.10

13.00 10.00 9.20 8.50 7.00 9.00 9.30 9.50 9.60 9.10 8.90 8.70 9.40 13.10 16.80 19.30 20.90 21.70 20.00 18.00 17.00 15.00 14.50 14.20

Table B6 Number of different types of days in various months for New Delhi. Type of days

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

a b c d

3 8 11 9

3 4 12 9

5 6 12 8

4 7 14 5

4 9 12 6

3 4 14 9

2 3 10 17

2 3 7 19

7 3 10 10

5 10 13 3

6 10 12 2

3 7 13 8

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