An investigation on effect of variation of mass flow rate and number of collectors on yearly efficiency of single slope solar still by incorporating N similar photovoltaic thermal flat plate collectors Open Access

A_m

area covered by PV module (m²)

A_c

area covered by glass (m²)

area of glass cover (m²)

area of basin (m²)

L

latent heat(J/kg)

L_g

thickness of glass cover (m)

K_g

thermal conductivity of glass (W/m-K)

I(t)

global radiation falling on collector (W/m²)

T_a

ambient temperature (°C)

L_i

thickness of insulation (m)

K_i

thermal conductivity of insulation (W/m-K)

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)

length of collector covered by glass (m)

length of collector covered by PV module (m)

solar cell efficiency

PV module efficiency

temperature dependent electrical efficiency of solar cells of a NPVTFPCs

breadth of collector (m)

product of effective absorptivity and transmittivity

collector efficiency factor

solar cell temperature (°C)

absorber plate temperature (°C)

thickness of absorber plate (m)

thermal conductivity of absorber 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 PVTFPC 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/m²-K)

overall heat transfer coefficient from cell to ambient (W/m²-K)

overall heat transfer coefficient from cell to plate(W/m²-K)

heat transfer coefficient from blackened plate to fluid (W/m²-K)

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 glazing to ambient (W/m²-K)

annual power generated from photovoltaic module (kWh)

PVT

photovoltaic thermal

annual power utilized by pump (kWh)

є

emissivity

absorptivity

hourly exergy (W)

(t)

solar intensity on glass cover of solar still of single slope type (W/m²)

glass temperature at inner surface of 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)

evaporative heat transfer coefficient (W/m²-K)

mass of water in basin (kg)

mass of distillate from of double slope solar still (kg)

a

clear days (blue sky)

b

hazy days (fully)

c

hazy and cloudy days (partially)

d

cloudy days (fully)

the rate of useful thermal output from N identical partially (25%) covered PVTFPC water collectors connected in series (kWh)

annual exergy gain (kWh)

natural logarithm

SS

single slope

t

time, h

R

reflectivity

SEBWP

solar energy based water purifier

T_w

temperature of water in basin, °C

ambient temperature, °C

T_wo

water temperature at t = 0, °C

overall annual energy available from PVT-CPC solar distillation system (kWh)

N

number of PVTFPC water collector

E_in

embodied energy (kWh)

FPC

flat plate collector

PVT

photovoltaic thermal

number of sunshine hours

daily diffuse to daily global irradiation ratio

glass

water

incoming

outgoing

effective

The various efficiencies analyses of an active solar still are the demand of time to lessen the existing issue of paucity of freshwater in different regions of the globe. An active solar still is generally self-sustainable and one can install it in the remote locations also to supply freshwater as well as electricity. Its working principle is based on the greenhouse effect, and it has the potential to meet the scarcity of freshwater partly/fully. Moreover, the solar still takes solar energy as input which is freely available and will continue to persist during the existence of life on the planet Earth. It does not emit pollutants and hence is environmentally friendly. The solar still can broadly be categorized as passive or active. The output of a passive solar still ranges from 1 kg to 3 kg for unit basin area in most cases. This issue of the passive type solar still having low output can be taken care of by adding some kind of arrangement that can supply heat to the basin of solar still and the resulting system is commonly known as an active solar still. The rise in temperature of water kept in basin is improved due to the addition of heat which compels water in the basin to evaporate faster and improved freshwater yielding is obtained. The active solar still was first of all introduced by Rai and Tiwari in 1983 and a lot of improvements in that system have been addressed by researchers around the globe. Their findings have been summarized in the paragraphs that follow.

The active solar still reported by Rai & Tiwari (1983) presented a single slope solar still included with one flat plate collector (FPC). It was concluded that the freshwater output of active solar still was higher than the corresponding passive solar still containing same basin area. The main drawback was that the system was not self-sustainable. It was felt that the active system could be made self-sustainable by including solar panels. Keeping this aspect in mind and inspired by the work of Kern & Russell (1978) who reported an improvement in efficacy of solar panels when integrated with FPC due to heat removal, Kumar & Tiwari (2008) reported a self-sustainable active solar still which contained one FPC integrated with a PVT. In conclusion, it was said that the output of the active solar still was 3.5 times more than the corresponding passive solar still due to heat addition to the basin in the case of the active system. An extension of this work was reported by Singh et al. (2011) for a double slope (DS) solar still. A further extension of the work of Kumar & Tiwari (2008) was done by Singh et al. (2016) and Tiwari et al. (2015) by integrating two FPCs with PVT identically. An improved electrical energy was obtained due to the enhanced area of PVT. A study of basin type solar stills included with collectors under optimized conditions was done by Singh & Tiwari (2017e), Singh (2017), Singh (2018), Singh et al. (2018) and Singh et al. (2019). It was concluded that the active solar still performed better than the corresponding passive solar still due to supply of heat by collectors to the basin. Sahota & Tiwari (2017) studied an active solar still loaded with nanofluid to get an enhanced value of yield because of enhanced thermophysical characteristics. Another study of an active solar still loaded with nanofluid was done experimentally by Carranza et al. (2021) and Kouadri et al. (2021). They reported an improved value of yield because of improved thermophysical characteristics of fluid used.

The performance of the active solar still could further be improved by attaching a parabolic surface to PVTFPC which could provide higher amounts of heat to the basin due to concentration of solar energy on receiver surface. Having this idea in mind, Atheaya et al. (2015) reported thermal modeling of compound parabolic concentrators, which was further carried forward by Tripathi et al. (2016) for N number of collectors. Singh & Tiwari (2016), Singh & Tiwari (2017a, 2017b), Gupta et al. (2018, 2020); Singh et al. (2020a, 2020b) and Sharma et al. (2020b, 2020c) investigated active solar stills by focusing on the development of equations and it was reported that the DS active solar still performed better than the corresponding single slope type at 280 kg of water mass in the basin due to better distribution of solar energy in the case of the DS type. Prasad et al. (2019), Bharti et al. (2021) and Singh (2021) studied a DS active solar still from the sensitivity viewpoint and it was reported that designer and installer benefitted because they had information in advance on which input parameter was having more influence on the output.

The performance of the active solar still could further be improved by preventing convective heat loss which could be done by making arrangements for a vacuum as a convective heat loss need medium. Sampathkumar et al. (2013) studied a solar still included with evacuated tubular collectors (ETCs) and an improvement of 129% was reported compared to passive solar stills of same basin area due to heat supplied by ETCs to basin. An investigation of an active solar still in circulation of fluid due to density difference was carried out by Singh et al. (2013) and they obtained exergy efficacy lying in the range of 0.15% to 8%. An extension of this work was carried out by inserting a pump between the basin and 1st ETC. They obtained an improved value of yield in comparison with the active solar still working on circulation of fluid due to density difference because of more effective circulation of fluid in the forced mode. (Kumar et al. (2014)). The equation development for ETCs was reported by Mishra et al. (2015) which was further carried forward by Singh et al. (2017e) and Singh & Tiwari (2017c, 2017d). The development of equations based on heat balance for a solar still with ETCs was reported by them. A comparative investigation between SS and DS active solar stills was also carried out at a water mass of 280 kg in the basin and it was concluded that DS performed better than SS due to a more uniform distribution of solar energy in the case of DS. An extension of work by Singh et al. (2017e) was carried out by Issa & Chang (2017) in which ETCs were arranged in a mixed mode and they concluded an improved output in comparison with a passive solar still of same geometrical dimensions. Furthermore, the investigation of a solar still included with ETCs and concentrator integrated ETC was carried out by Singh & Al-Helal (2018), Singh et al. (2021b) and Sharma et al. (2020a, 2020b, 2020c) separately. An improved performance of a solar still with a concentrator integrated ETC as compared to a solar still with ETC was reported due to a higher amount of heat supplied to the basin by a concentrator integrated ETC.

A review of solar stills included with various kinds of collectors was reported by Patel et al. (2021a, 2021b, 2021c) and it was concluded that the shape of the basin liners and types of collectors affected the yield marginally. Further, a short review of an active solar still loaded with nanofluid was reported by Singh et al. (2021a) and they concluded that the application of nanofluid resulted in an improved output because of the improved thermophysical properties of the fluid. One can get nanofluid by mixing a controlled amount of nanoparticles to the base fluid. Bansal et al. (2020) reviewed a solar still from an absorbing material viewpoint. Shankar et al. (2021) investigated a solar still included with ETCs working in both natural and forced modes. They concluded that the forced mode was better for the environment because of increased carbon credit in the forced mode as higher amounts of heat were supplied to the basin in the forced mode. Abdallah et al. (2021) studied solar stills containing spherical-shaped and pyramid-shaped basins and reported an improved yield of 57.1% in the case of the spherical-shaped basin due to better deployment of solar flux by the spherical basin. Sharma et al. (2021) carried out experimental validation of an SS solar still and it was reported that the correlation coefficient for yield was 0.9951. Attia et al. (2021a) investigated hemispherical and SS solar stills, experimentally. Upon comparison of results, they concluded that yield of a hemispherical solar still was 47.96% higher than the SS because of having enhanced area of condensing surfaces in the case of the hemispherical solar still. Chandrika et al. (2021) investigated a passive solar still containing an aluminum foil sheet and mirror as a reflecting surface and it was concluded that the solar still containing mirror as a condensing surface gave a 62.46% higher yield than a conventional solar still. Further, Attia et al. (2021b) suggested the application of a phosphate bag as an energy storage material for enhancing yield of a solar still.

From the current research study, it is seen that the effect of mass flow rate and N on various yearly efficiencies for a single slope solar still by incorporating series connected N similar photovoltaic thermal flat plate collectors (NPVTFPCSS) has not been reported by any researcher throughout the globe. Hence, an effort has been made in this research paper to investigate the effect of variation of and N on various yearly efficiencies of NPVTFPCSS. All four kinds of weather situations have been considered, while estimating values of energy, exergy and different kinds of efficiencies using computer code in MATLAB-2015a to calculate the effect of dissimilarity in values of and N on yearly efficiencies of NPVTFPCSS. The difference between the earlier reported work and the proposed work lies in the fact that the effect of dissimilarities of and N on yearly efficiency has been estimated for NPVTFPCSS, whereas, in the earlier reported works, hourly and daily efficiencies for the active system have been estimated at particular selected values of and N. The main objectives of the proposed work can be stated as follows:

• i.

  To examine the effect of variation of and N on annual thermal and annual overall thermal efficiencies and suggest the optimal value of N at selected values of from an annual overall thermal efficiency viewpoint.

• ii.

  To study the effect of variation of and N on annual exergy, annual electrical exergy and annual overall exergy efficiencies and suggest the optimal value of N at selected values of from an annual overall exergy efficiency viewpoint.

The specification of NPVTFPCSS is shown in Table 1. Figure 1 represents the set-up of NPVTFPCSS. It consists of a series of connected PVT flat plate collectors, a pumping system and a solar still of the single slope type. In the set-up revealed in Figure 1, the series connected N number of PVTFPCs have been connected to a solar still of the SS type. A pump has been inserted between solar still and inlet of first photovoltaic-thermal flat plate collector (PVTFPC) for overcoming the head loss. Pump runs on the power generated by PVT. N similar PVTFPCs have been put in a series connection as the solar still needs fluid at higher temperatures for higher freshwater production. The material for the solar still is fiber reinforced plastic. The inner surface of the solar still has been painted black for better absorption and outside surfaces have been covered with insulator to prevent heat loss.

The condensing cover surface made of glass has been inclined by 15° from horizontal as most of the season in New Delhi is summer. When the short wavelength solar flux impinges on the surface of the glass condensing cover surface, some part is reflected and absorbed by the glass and remaining part comes to the surface of water in the basin. The water surface again reflects some part of the received solar flux, some part is absorbed by water mass and the remaining is transmitted to the basin liner kept at the bottom. Due to the absorption of solar flux, the basin liner is heated and transfers heat to the water mass. Some part of the energy from basin liner is lost to the environment. Water mass receives heat from N similar collectors, from sunlight directly and from the basin liner indirectly. In this way, the temperature of water is enhanced, and evaporation occurs due to the temperature difference between the water surface and the glass condensing cover. The vapor further is condensed on the inner surface of glass condensing cover surface and trickles down to the tray and then the distilled water is siphoned off to the beaker/jar.

The thermal modeling for NPVTFPCSS can be carried out by writing equations based on equating input and output heats for various components which can further be simplified using simple mathematics for expressing unknown parameters in terms of some known parameters. While doing thermal modeling, one makes some assumptions for simplifying the practical situation. Considering assumptions reported in Singh et al. (2016), thermal modeling can be carried out as follows:

Here, is the efficiency for a given standard test condition, while is the average temperature of the solar cell for the Nth PVTFPC. is calculated using the results of Shyam et al. (2015) in which since a number (N) of series connected PVTFPC are in a closed loop including the basin of NPVTFPCSS.

Here, L is latent heat which can be taken as 2,400 kJ/kg-K.

The thermal model of NPVTFPCSS has been taken from Singh et al. (2016). They validated water temperature, glass temperature and yield of NPVTFPCSS for November 2013 and February 2014 taking N = 2. A fair agreement was found between theoretical and experimental values of water temperature, glass temperature and yield with correlation coefficients of 0.964, 0.98 and 0.988 for February 2014 respectively. The same thermal model has been used for computation of various parameters with the help of MATLAB in this work.

For the analysis of the influence of differentiation of and N on various efficiencies of NPVTFPCSS, all the four climatical conditions of New Delhi have been considered during the evaluation of various relevant parameters. The climatical condition can be categorized in terms of number of sunshine hours and ratio of daily diffuse to daily global irradiation as given below Singh & Tiwari (2005):

• (a)

  Clear day (blue sky) ≤ 0.25 and ≥ 9 h

• (b)

  Hazy day (fully) 0.25 ≤ ≤ 0.50 and 7 h ≤ ≤ 9 h

• (c)

  Hazy and cloudy (partially) 0.50 ≤ ≤ 0.75 and 5 h ≤ ≤ 7 h

• (d)

  Cloudy day (fully) ≥ 0.75 and ≤ 5 h

The value of daily electrical energy can be computed for type (a) climatic condition by totaling hourly electrical energy for 10 h due to the existence of solar flux for 10 h in a day. Values of daily electrical energy for other types of climatical conditions can be computed in the similar fashion. The monthly values of electrical exergy for various types of climatic situations can be computed by multiplying daily values with the corresponding number of clear days. By totaling daily monthly electrical exergies for all four types of climatic situation, net monthly electrical exergy/energy can be computed. Further, annual electrical energy can be computed by totaling monthly electrical energy for 12 months. The value of annual yield can be computed in the similar fashion with the help of Equation (7).

The value of daily thermal exergy can be computed for type (a) climatic condition by totaling hourly thermal exergy for 10 h due to the existence of the solar flux for 10 h in a day. Values of daily thermal exergy for other types of climatical conditions can be computed in a similar fashion. The monthly values of electrical exergy for various types of climatic situations can be computed by multiplying daily values with the corresponding number of clear days. By totaling daily monthly thermal exergies for all four types of climatic situations, net monthly electrical exergy/energy can be computed. Further, annual thermal exergy can be computed by totaling monthly thermal exergy for 12 months.

Various efficiencies of NPVTFPCSS for different values of and N have been estimated as follows:

Here, one can note that hourly freshwater yield has been integrated for 24 h to get daily fresh water yield; whereas input intensity has been integrated for 10 h only to get its daily value. The reason lies in the fact that the value of solar intensity exists for sunshine hours only; however, fresh water yield continues to be produced at night also due to the heat content of the water mass.

One should note here that the factor 0.933 which has been used for converting solar energy into the corresponding exergy has been obtained using the expression proposed by Petela (2003).

The solution procedure regarding the computation of efficiency for different values of mass-flow-rate and number of PVTFPCs (N) can be stated as:

Step-I: All required data have been accessed from IMD, Pune, India. The expression given by Liu and Jordan has been employed for the estimation of solar intensity on the inclined surface using computing code in MATLAB.

Step-II: Value of evaporative HTC has been computed using Equation (11). Values of different temperatures namely and have been computed using Equations (4)–(6) respectively.

Step-III: Values of hourly yield has been evaluated for different values of and N using Equation (7) followed by the evaluation of yearly yield for different values of and N.

Step-IV: Value of hourly exergy has been evaluated for different values of and N using Equation (10) followed by the evaluation of yearly exergy for different values of and N. Value of hourly gross exergy has been evaluated for different values of and N using Equation (15) followed by the evaluation of yearly exergy for different values of and N.

Step-V: Value of hourly gross energy has been evaluated for different values of and N using Equation (8) followed by the evaluation of yearly gross energy for different values of and N.

Step-VI: The various efficacies have been computed using Equations (16)–(30).

For a better understanding of the solution procedure followed to estimate different parameters of NPVTFPCSS, the flow chart has been depicted in Figure 2.

All input parameters of NPVTFPCSS have been made input to computing code developed in MATLAB for computation of various efficacies of NPVTFPCSS. All input data have been accessed from IMD, Pune, India. The detailed data have been provided as Appendix – B. The solution procedure is presented in Figure 2 for better understanding. Outputs from the computing code have been presented as Figures 3–12 and Tables 2–4.

The evaluation of annual yield for NPVTFPCSS at ⁠, water mass = 280 kg and N = 6 is presented in Table 2. The computation of annual yield at other values of and N has been carried out in the similar fashion and they is depicted as Figure 3. One can observe from Figure 3 that the value of annual yield decreases with the increase in the value of at given value of N. The decrease in yield is due to less heat absorption by water flowing through the tubes of PVTFPC as the time available for heat absorption is less at an increased value of ⁠. One can also observe that the value of annual yield becomes almost constant after the initial decrease in its value. The reason being that the system behaves in a passive mode at very high values of because the speed of the water flow is so high that water does not find time to absorb heat while passing through the tubes of PVTFPC. It is also clear from Figure 3 that the value of annual yield increases with the increase in value of N at selected values of because increase in N results in the addition of more heat at enhanced values of N, which further enhances the evaporation rate and hence yield is enhanced with increase in N at a given ⁠.

The evaluation of annual thermal exergy for NPVTFPCSS at ⁠, water mass = 280 kg and N = 6 has been presented in Table 3. The computation of annual thermal exergy at other values of and N has been carried out in the similar fashion and they is been depicted as Figure 4. One can observe from Figure 4 that the value of annual thermal exergy decreases with the increase in values of at given value of N. The decrease in thermal exergy is due to less heat absorption by water flowing through the tubes of PVTFPC as the time available for heat absorption is less at an increased values of ⁠. Due to less heat supplied to basin, rise in temperature is comparatively less. One can also observe that the value of annual thermal exergy becomes almost constant after the initial decrease in its value. The reason being that the system behaves as a passive mode at very high values of because the speed is so high that water does not find time to absorb heat while passing through tubes of PVTFPC. It is also clear from Figure 4 that the value of annual thermal exergy increases with the increase in value of N at selected values of because increase in N results in the addition of more heat at enhanced value of N which further enhances the evaporation rate and hence thermal exergy is enhanced with increase in N at a given ⁠.

The evaluation of annual electrical exergy for NPVTFPCSS at ⁠, water mass = 280 kg and N = 6 is also presented in Table 3. The computation of annual electrical exergy at other values of and N has been carried out in the similar fashion and they are depicted in Figure 5. One can observe from Figure 5 that the value of annual electrical exergy increases with the increase in value at a given value of N. The increase in electrical exergy can be attributed to increased speed of flowing water through tubes of PVTFPC which carries away higher amounts of heat and the temperature of cell remains within limits. Due to the diminished temperature rise of the solar cell, enhanced solar cell efficiency is obtained. This enhanced efficiency of the solar cell contributes to increase in electrical exergy. It is also seen that the value of annual electrical exergy becomes almost constant after the initial rise in its value. The reason being that the enhanced speed of flowing fluid through PVTFPC does not have time to absorb heat below the solar cell and hence fluid is not able to carry heat below the solar cell. Further, the value of electrical exergy increases as the value of N is enhanced at given value of because increase in N results in the addition of heat collection area as well as the photovoltaic (PV) area as depicted in Figure 5.

The differentiation of annual overall energy and annual overall exergy for NPVTFPCSS at ⁠, water mass = 280 kg and N = 6 has also been depicted as Figures 6 and 7 respectively. The value of annual gross energy diminishes with the increase in value of as depicted in Figure 6. The reason may be attributed to the similar variation in annual yield. One can note here that the differentiation in annual yield and annual electrical energy is opposite and the variation in annual yield overcomes the variation in electrical energy. A similar differentiation is seen in the value of annual overall exergy. Table 4 reveals the estimation of solar energy falling on the surface of NPVTFPCSS. The solar energy incident on each collector of 1 m² is estimated in Table 4. Using these data, solar energy falling on N number of collectors has been estimated. The solar energy falling on the surface of a solar still of basin area 2 m² has also been estimated.

The dissimilarity of annual thermal efficiency with at different values of N for NPVTFPCSS is revealed in Figure 8. It is clear from Figure 8 that the value of annual thermal efficiency diminishes as the value of is increased. The reason may be attributed to the similar variation in annual fresh water yielding as well as annual thermal energy output. The value of annual thermal efficiency becomes almost constant beyond = 0.10 kg/s. It occurs due to the fact that the fresh water yield and hence energy output becomes almost constant as the water coming from collectors does not add much heat to basin water and further increase in temperature of basin water does not take place. It is also seen that the value of annual thermal efficiency first increases up to N = 4 and then starts diminishing beyond N = 4. Hence, the optimum value of N from annual thermal efficiency viewpoint is 4 for all values of ⁠.

Figure 9 reveals the differentiation of annual exergy efficiency at various values of N for NPVTFPCSS. One can observe from Figure 9 that the value of annual exergy efficiency decreases with the increase in value of at selected values of N. The decrease in annual exergy efficiency is due to decrease in annual exergy which in turn happens due to less heat absorption by water flowing through tubes of PVTFPC, as the time available for heat absorption is less at increased values of ⁠. Due to less heat supplied to the basin, the rise in temperature is comparatively less. One can also observe that the value of annual exergy efficiency becomes almost constant beyond kg/s. The reason may be attributed to the behavior of the system as a passive mode at very high values of because the speed is so high that water does not find time to absorb heat while passing through tubes of PVTFPC. It is also clear from Figure 9 that the value of annual exergy efficiency first increases with the enhancement in the value of N at given value of up to N = 8 and then the annual exergy efficiency either diminishes or remains constant. Hence, the optimum value of N from annual exergy efficiency viewpoint is 8 for all values of⁠.

The dissimilarity of annual electrical efficiency with at different values of N for NPVTFPCSS is revealed in Figure 10. It is clear from Figure 10 that the value of annual electrical exergy increases marginally with the enhancement in the value of and becomes almost constant beyond 0.1 kg/s. The reason being that the heat removal rate from PVT increases at enhanced values of a which results in keeping the temperature lower when intensity is high. Also, at very high values of ⁠, the heat will not be removed because of the lower temperature difference between the fluid and surroundings and the time available is also less. It is further seen that the value of annual electrical exergy diminishes with the enhancement in value of N for all values of due to the fact that the heat removal rate from PVT diminishes because of diminished temperature difference between solar cell and fluid flowing through the tubes beneath the solar cells.

The dissimilarity of annual overall exergy efficiency with at different values of N for NPVTFPCSS has been depicted as Figure 11. One can observe from Figure 11 that the value of annual overall exergy efficiency decreases with the increase in value at given value of N up to = 0.10 kg/s and then becomes constant. The reason for this behavior may be attributed to the same type of variation occurring in annual thermal exergy efficiency. The annual overall exergy is the function of thermal exergy and electrical exergy. Thermal exergy and electrical exergy have an inverse relationship; however, decrease in annual thermal exergy is at a faster rate than the increase in annual electrical exergy. So, the enhancement in value of annual thermal exergy overcomes the decrease in value of annual electrical exergy and finally annual overall exergy decreases with increase in the value of ⁠. It is further seen that the value of overall annual exergy efficiency increases with the enhancement in the value of N. Again, annual overall exergy depends on both annual overall thermal exergy and annual overall electrical exergy. The annual overall thermal exergy has an inverse relationship with annual electrical exergy as the value of N increases; however, increase in annual thermal exergy overcomes the decrease in annual electrical exergy as the value of N increases. Hence, the value of annual overall exergy efficiency enhances with increase in the value of N for all values of ⁠. One can also observe from Figure 11 that the value of annual overall exergy efficiency becomes either constant or diminishes beyond N = 10 for all values of ⁠. Hence, the optimal value of N from the overall annual exergy efficiency viewpoint has been found as 10.

The dissimilarity of annual overall thermal efficiency with at different values of N for NPVTFPCSS is revealed in Figure 12. It is clear from Figure 12 that the value of annual overall thermal efficiency decreases with the enhancement in the value of and it becomes almost constant beyond = 0.10 kg/s due to the similar variation in annual thermal efficiency. Annual overall thermal efficiency is the function of annual thermal efficiency and annual electrical efficiency. Also, the decrease in annual thermal efficiency overcomes the increase in annual electrical efficiency. Hence, annual overall thermal efficiency first decreases with the enhancement in the value of and then it becomes almost constant beyond = 0.10 kg/s. It is further seen that the value of annual overall thermal efficiency increases up to N = 6 for all values of and then it diminishes for all values of with the enhancement in the value of N due to the similar variation in the value of annual thermal efficiency. So, the optimal value of N from an overall thermal efficiency viewpoint is 4. The comparison of different systems on the basis of efficiency is presented in Table 5.

An investigation on dissimilarity of and N on different annual efficiencies for NPVTFPCSS has been done considering all four kinds of atmospheric situations to determine the effect of dissimilarities of and N on different efficiencies of NPVTFPCSS. Based on the current research study the following conclusions have been drawn:

• i.

  Values of annual thermal efficiency, exergy efficiency, overall exergy efficiency and overall thermal efficiency have been found to diminish first with the enhancement in the value of and then become almost constant beyond = 0.10 kg/s.

• ii.

  The value of annual electrical exergy efficiency first increases with the enhancement in the value of and then it becomes almost constant beyond = 0.10 kg/s.

• iii.

  The optimal value of N from annual thermal efficiency and annual overall thermal efficiency viewpoints has been found to be 4. Optimal values of N from annual exergy efficiency and annual overall exergy efficiency viewpoints have been found to be 8 and 10, respectively.

The authors declare that there is no competing interest

All data are given in the manuscript

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There is no funding received for the research work carried out

All relevant data are included in the paper or its Supplementary Information.