Introduction

The world is facing challenges like rapid population growth and expeditious industrialisation that enhanced the daily requirement of potable water. The conditions become more critical due to the rise in the level of water pollution contributed by city drainage and wastewater released by the industries in the water bodies of earth. Eventually, this makes groundwater more saline, contaminated, and toxic (Sathyamurthy et al., 2017). Thus, there is always a requirement for an efficient methodology for the purification of this brackish water so that local people and daily wage workers can get easily potable water. So far, numerous water purification techniques for unhealthy water have been developed such as electro-dialysis and reverse osmosis (Velmurugan and Srithar, 2011. & Panchal et al. 2017). However, these are bulky, have high-energy requirements, uneconomical, and infeasible for unsophisticated users.

One of the oldest and simplest proven techniques for water purification is the solar still which grabs most of the attention of the researcher all over the world owing to its renewable, eco-friendly, and economical nature. Out of passive and active solar still technology, active solar stills have been considered as effective and realistic opportunities (Panchal et al., 2017). This technology can be implemented for the daily workers at workshops, industries, and educational institutes to fulfil their daily potable water requirement with the least cost which is far from the available water resources and sustained high cost for the pure water availability.

To augment the productivity and performance of solar still, numerous design configurations (both theoretical and experimental) have been exercised by researchers in the last few decades. In one of the comparative studies, Tiwari et al. (2007) developed the thermal model of different solar collector–integrated active solar stills and evaluated their performance at New Delhi, India, July month climate condition with a water depth of 0.05 m. Based on the experimental investigation, they found the maximum total distillate output of 4.24 kg/m2 per day by the active solar still coupled with evacuated tube collectors (ETC) with a heat pipe module. Sampathkumar et al. (2012) proposed a thermal model of single basin solar still coupled with an ETC module and validated it with an experimental model. Enhanced productivity of 72% in the potable water per day was noticed and based on the economic analysis they found the payback period of 235 days for the proposed system. To investigate the performance of solar still with ETC at natural mode is being performed by Singh et al. (2013). A daily maximum of 3.8 kg/m2 of productivity was found with 10 ETC in the summer of New Delhi, India with 33% and 2.5% energy and exergy efficiency respectively. Shafii et al. (2016) in their study investigated a solar still integrated with ETC and thermoelectric modules (TEM) and reported a distilled water output of 1.11 kg/m2 per hour and 68% efficiency with forced convection air. The detailed technological advancements was studied by the researchers and found that inclined solar still can provide superior productivity compared to all best possible designs (Kumar et al. 2021a, 2021b).

Reflectors (either internal or external) are one of the promising technologies that have been used frequently in the literature so far, to enhance solar still productivity. Minasian et al. (1997) used a novel metallic cylindrical parabolic reflector which helps in directing the incident solar radiation on the tray outside surface located on the reflector focal line. The investigation found an increase in productivity of conventional still by 25–35% with proposed modification. El-Swify and Metias (2002) performed a theoretical and experimental study on double exposure solar still with the inclusion of planer reflector and found an increase in daily productivity of 82.6% in winter and 22% in summer in comparison to the ordinary system. In principle, internal and external reflectors have the potential to enhance the distillate productivity by an average of 48% of single basin single-slope solar still with integration (Tanaka and Nakatake 2006). Moreover, the average daily distillate output of the tilted wick solar still can be increased by up to 9% with the integration of a vertical flat plate external reflector (Tanaka and Nakatake 2007). Abdallah et al. (2008) modified the design of conventional solar still with the installation of an internal reflecting mirror which results in a 30% increase in thermal performance of the system because of the usage of reflected energy from all sides of the still facilitated by these mirrors. Tanaka (2009) in his theoretical investigation found an increase in distillate productivity of 21% in comparison to conventional still with the introduction of an external reflector and found optimal inclination angle of both reflector and still as per the session. Estahbanati et al. (2016) investigated the solar still with an internal reflector and performed mathematical as well as experimental analysis on the system which includes all wall effects. The outcome presents an increase in distillate productivity of 34% with an internal reflector and notices a significant decrease in the water output due to the cloud factor. Different solar thermal systems were also studied for thermal modelling (P. Mehta et al. 2018).

Flat plate collectors (FPC) are probably the oldest and effective performance improvement methodology widely used by researchers for solar stills so far. Badran and Al-Tahaineh (2005) performed an investigation effect of parameters such as depth of water, still orientation, solar radiation on the performance of solar stills coupled with flat plate collectors (FPC). The proposed unit reported being 36% efficient (with output distilled water of 3.5 kg/day) than uncoupled solar still (2.24 kg/day distilled water). In a similar study, Badran et al. (2005) noticed a rise in the distilled water production rate with 231% with augmentation of FPC while the efficiency of the system is decreased by 2.5%. In one of the studies, Samee et al. (2007) design simple single basin solar still and evaluated its performance in the arid region of Pakistan. Experiment results give the average daily production of 1.7 L of potable water and an efficiency of 30.65%. Rajaseenivasan et al. (2014) experimented on the FPC integrated single-slope basin solar still of 1m2 basin area and reported productivity of 5.82 kg/m2day which is 60% higher than conventional still for the same basin conditions with distilled water cost of 0.0276 $/kg/m2. Narayana and Ramachandra (2019) investigated in which multiple FPC is attached parallel to a single basin solar still with a 1-m2 effective area of the basin. They obtained a maximum output of 4.229 kg with three FPC at summer climate conditions in coastal areas of India. They also observed the decrease in solar still efficiency with increasing the number of collectors.

Heat-absorbing materials seem to be always beneficial to the solar thermal systems like solar stills, dryers, and many devices. Balachandran et al. (2019) investigated a single-slope solar still with heat absorbent particles due to their superior viability and affordability. These particles were added on the proportions of 10% by weight, with a model having water depth from 0.5 to 1 cm. It was observed that total output from the convention unit has been improved by 3.23 kg/m2 (for micro-absorbent particles), 4.39 kg/m2 (for nano-absorbent particles). As higher atmospheric and solar radiation at the same time domain may result in decreasing condensation rate of the simple basin type still, El-Maghlany et al. (2021) developed a hybrid system that provides continuous heat to the water as compared to the variable heat in case of natural solar heat by wind turbine power for a whole day. By implementing that technology, water output increased on average by 70%. In another study, an inclined conventional solar still was augmented with the coconut coir disk where results showed a rise in productivity around 60% (Ramalingam et al., 2021). Suraparaju et al. (2021) conducted a performance evaluation of conventional single basin solar still operated with ball marbles as heat storage material. The updated set-up was run on cloudy and sunny days and found superior to the conventional one in terms of cumulative productivity in both time slots. Graphite plate fins and magnets were employed in the conventional set-up of the still to improve performance, efficiency, and earn carbon credit. The study also concluded that CO2 emission for the conventional unit is less (8.42 tons) compared to the improved one (14.1 tons) with former materials (Dhivagar and Mohanraj, 2021). Tubular solar still units are more improved than conventional and tested with heat-storing material like a sponge with different layers and configurations. The floating sponge layer distiller gives the maximum output of 5.92 L/m2, whereas the conventional set-up provides 3.7L/m2, in the same climatic conditions (Abdelgaiedet al., 2021).

Various augmenting devices are incorporated with solar still for the performance improvement. Al-Molhem and Eltawil (2020) reported a 45% higher output than conventional solar still by using solar collectors, wick material, and orientation alteration. Water depth is one of the critical parameters, which affect the productivity of the still. A novel theoretical approach was developed which focuses on the two parametric conditions. In the first one, constant depth was maintained, and in the second it was reduced from maximum to least by a specific time interval. Analysis revealed that the former approach can augment greater productivity; however, by maintaining constant water depth, heal load penalty approach may be considered (El-Maghlany et al. 2020). To improve the condensation and evaporation rate of the conventional solar still, different economically viable and environment-friendly materials were also employed. Natarajan et al. (2021) assess the yield and the heat transfer rate of the modified solar still with the rice husk and sawdust. It was found superior over the different configurations and better than the conventional unit. Also, the still with rice husk and sawdust was reported most economically viable. A unique nano-doped black paint was used on the absorber surface for enhancing the higher productivity of a conventional solar still, outcomes demonstrate that the applied approach can attain an 8% average higher fresh water output than conventional still (Kumar et al. 2021b). Various thermal and economic aspects of conventional single-slope solar still was compared with modified solar still which was augmented with the heat storage material as crushed gravel sand and biomass evaporator for air-vapour mixture to preheat the saline water and air-vapour mixture. Significant rise in terms of productivity (34.6%), energy and exergy efficiencies (34.4% and 35%) were observed compared with the conventional set-up. Moreover, payback period was estimated to be 4.7 months which was 0.8 month higher than the single-slope solar still. However, CO2 emission was predicted to be 16.63 tons with the modified set-up. Accordingly, hourly and cumulative productivity was achieved to be 34.6% and 50.7% respectively in comparison with the conventional design (Dhivagar et al. 2021a, 2021b). Research had developed state-of-the-art regenerative solar still incorporating heat pump for water heating purpose and latent heat storage material. The investigation was carried out in terms of economic and overall productivity of the solar still. Moreover, couples of intentions have been achieved by heat pump as for preheating saline water entering into the basin and heating the water that used for the domestic application. Hence, cumulative fresh water achieved at the end of 12 h was 15 kg/day averagely. The payback period and cost per litre of potable water was estimated to be 21.46 months and 0.05471 USD respectively (Mohanraj et al., 2021). 4E analysis (Energy, Exergy, Enviro-Economic and Economic) was carried out on the single-slope solar still enhanced with the gravel coarse aggregate as a sensible heat storage material. Accordingly, highest efficiencies in terms of energy and exergy were found to be 32% and 4.2% respectively, whereas fresh water collection was found to be 4.21 kg/m2 within 12 h of data observation with water depth of 1 cm. Hence, in present literature, water depth indicates a significant role to provide better productivity and thermal sustainability of the solar still (Dhivagar et al. 2021a, b).

In the proposed study, an analysis was carried out on the solar still, which was refurbished with different arrangements to built-up its efficiency and productivity. Hence, higher distiller output with least economical aspect is the focussing point of the study. Moreover, evidences can be formed with myriad experimental data that designed still can effectively provide higher productivity through it has simple in design, easy to construct, and portable. Even though, it can be implemented on a field on large scale.

Materials and methods

Experiment set-up and procedure

To enhance system efficiency and increase the throughput of single basin solar still, flat plate collector of 2 m2 area was fabricated from locally available material as shown in Fig. 1. It is arranged in a manner that saline water first flows through the FPC, gains heat from solar radiation, and then is available to the still area. To ensure proper heat utilisation, aluminium foil is used as an insulator as shown in Fig. 1. Solar radiation has a major role to enhance any solar device’s efficiency. Here, two unique arrangements were provided in order to establish higher solar radiation along with utilising stored heat after off-sun shine hours. Moreover, the still area was 1.2 m2 which was also fabricated from the locally available material. Accordingly, image 2 shows the single basin solar still with the internal changes. The design further carried out by providing copper sheets at the bottom of the still having 0.5 mm thickness. Also, to proliferate the evaporation rate, 1 kg of stones was provided at the base of the still having average size of 1 cm, 1.5 cm and 2 cm with 200 g each of them. Moreover, different thermo-physical properties of stone are tabulated in Table 1, with Fig. 2, indicating a critical arrangement with an image of a single stone. However, it was ensured that uniform sizes of stones were kept.

Fig. 1
figure 1

Experimental set-up

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Table 1 Thermo-physical properties of heat storage material
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Fig. 2
figure 2

Conventional solar still equipped with the heat gain material at the base with clear image of stone

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They were washed properly to ensure germs-free and weighted before placing. The black-coloured stones can store the heat during the sunshine hours and able to liberate during off-sun shine hours or cloudy weather conditions. Copper sheets enable heat the water quickly with compare to simple solar still. The dimension of the basin is the same as conventional single basin solar still. The tilt angle of the still, as well as FPC, was kept at 23°, which was equal to the latitude of the location.

An experiment was conducted in non-summer months at Gujarat Power Engineering and Research Institute, Mehsana. To ensure the proper output from the system set-up, all the devices were regularly cleaned-up before starting an experiment. The charging time for the saline water was 08:30 AM. An experiment was carried out from 09:00 AM to 5:00 PM. The still was operated with two sets of experiments. In the first set of experiments, it was operated without FPC and in the second phase with FPC. As the water depth affects the output of solar still, the mass flow rate was evidenced by varying the water depth inside the still from 1 to 5 cm. As the depth of water affects the evaporation rate of water on the glass and heat gain capacity itself, all the data was measure at an hourly interval such as ambient temperature, glass temperature, water temperature, and FPC temperature. The saline water was fed inside still directly in the first phase of the experiment. The distilled water was unable to collect at two ends of the solar still. The productivity was measured at the end of an experiment of a day. After that, the same amount of water was again charged at 05:00 PM, and on the second day, the overnight productivity was also measured to get the 24-h productivity from the arranged system. The uncertainty and error range associated with the measuring instruments were provided in Table 2.

Table 2 Uncertainty and error range associated with instruments. Measuring devices specifications
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In the second phase of the experiment, water was charged inside the solar still after heating inside the FPC. It was ensured that evaporation may not initiate while heating in FPC. Water was charged initially at 08:30 AM and the second time in the evening for the overnight productivity. FPC temperature, water inlet, and outlet temperature were measured properly at an hourly interval.

Thermal model

Here, heat losses and energy utilized within an enclosed unit of solar still were considered. The thermal model considered here was briefly detailed by Tiwari, (2002).

An hourly distillate water output from the conventional still can be given by the following:

$$\dot{{m}_{\mathrm{we}}}=\frac{\dot{{q}_{w}}}{\mathrm{Latent heat of vapourization}}$$
(1)

Equation (1) is employed to determine the predicted productivity and compare it with the measured data. To determine, theoretical value of productivity, latent heat of vapourization is an important factor, which can be captured by employing Eq. (2). Here, water temperature inside still is expected to be less than 70 °C; hence, latent heat of vapourization can be formulated as follow (Tiwari, 2002):

$$\mathrm{Latent heat of vapourization}=2.43935\times {10}^{6}[1-9.4779\times {10}^{-4}\times T+1.3132\times {10}^{-7}{T}^{2}-4.7974\times {10}^{-9}{T}^{3}$$
(2)

As heat loss due to evaporation process is affected with difference in temperature of water–glass interface and convective heat transfer coefficient. By attaching different values of temperatures and heat transfer coefficient in Eq. (3), \(\dot{{q}_{w}}\) can be determined to achieve the values for Eq. (1).

$$\dot{{q}_{w}}={h}_{\mathrm{we}}\left[{T}_{\mathrm{water}}-{T}_{\mathrm{glass}}\right]$$
(3)

The water evaporation heat transfer coefficient has the major impact on the performance of solar still. Accordingly, the relation to obtain \({h}_{\mathrm{we}}\) (Cooper, 1973) can be given by following equation:

$${h}_{\mathrm{we}}=16.273*{10}^{-3}{h}_{\mathrm{wc}}\frac{\left({P}_{\mathrm{water}}-{P}_{\mathrm{glass}}\right)}{\left({T}_{\mathrm{water}}-{T}_{\mathrm{glass}}\right)}$$
(4)

Equation (4) consists of 3 main parameters difference in pressure and temperature of water–glass interface and convective heat transfer equation. So, Eqs. (5), (6) and (7) incorporate to evaluate the values of \({h}_{\mathrm{we}}\) under different climatic conditions. Subsequently, free convection plays an important role while considering heat transfer through humid air inside the distillation unit. However, it was mainly initiated by buoyancy force, density variation of water layers, and temperature gradient through water layers inside still. So, convective heat transfer between the glass cover and water surface can be given by following equation:

$$\dot{{q}_{\mathrm{wc}}= }{h}_{\mathrm{wc}}*\left({T}_{\mathrm{water}}-{T}_{\mathrm{glass}}\right)$$
(5)

The rate of heat transfer mainly depends on the convective heat transfer coefficient, which is included in the Eq. (4) of \({h}_{\mathrm{we}}\) evaporative heat transfer coefficient calculation. Moreover, considered the effect of free convection parameters that includes Prandtl number, Grashoff’s number, and average operating temperature range are considered while establishing relation of \({h}_{\mathrm{wc}}\) in Eq. (6). The empirical relation (Dunkle 1961) can be captured as follows:

$${h}_{\mathrm{wc}}=0.884{[{T}_{\mathrm{water}}-{T}_{\mathrm{glass}}+ \frac{\left({P}_{\mathrm{water}}-{P}_{\mathrm{glass}}\right)*\left({T}_{\mathrm{water}}+273.15\right)}{268.9*{10}^{8}-{P}_{\mathrm{water}}}]}^{1/3}$$
(6)

Partial pressure of water and glass again affect the evaporation of water vapour particles in the solar thermal still. Accordingly, for the standard operating temperature range (10°–90 °C) pressure can be calculated using the given equation as a function of temperature (Dunkle, 1961).

$$P=\mathrm{exp}(25.317-\frac{5144}{T+273.15})$$
(7)

Considering the above Eqs. (2–7), the hourly distillate output can be rewritten as follows:

$$\dot{{m}_{\mathrm{we}}}= \frac{{h}_{\mathrm{we}}*\left({T}_{\mathrm{water}}-{T}_{\mathrm{glass}}\right)}{\mathrm{Latentheatofvapourization}}\times 3600 \mathrm{kg}/{\mathrm{m}}^{2}\mathrm{h}$$
(8)

By utilising the Eq. 8, hourly productivity can be predicted at each time step.

Efficiency of the solar still set-up is the important parameter to establish the performance of it. In order to provide numerical evidence instantaneous efficiency of the designed set-up of solar still is modelled in the present section. Accordingly, the instantaneous efficiency for the solar still is the ratio of the rate of evaporative heat loss to the solar radiation incident of still area at an instant. The same statement can be mathematically written as equation no. (9)

$${\eta }_{\mathrm{still}}=\frac{\sum {\dot{m}}_{ev}{h}_{fg}}{\sum I\left(t\right){A}_{s} \times 3600}\times 100$$
(9)

Furthermore, the glass and water temperature can be employed to determine the overall internal heat transfer coefficient, which can be calculated employing three different possible values of heat transfer modes as shown in Eq. (10).Which can be given as follows:

$${h}_{\mathrm{overall}}= {h}_{\mathrm{we}}+{h}_{\mathrm{wc}}+ {h}_{\mathrm{wr}}$$
(10)
$${h}_{\mathrm{wr}}= \varepsilon \times \sigma \times \left[{\left({T}_{\mathrm{water}}+273\right)}^{2}+ {\left({T}_{\mathrm{glass}}+273\right)}^{2}\right]\times [{T}_{\mathrm{water}}+{T}_{\mathrm{glass}}+546]$$
(11)
$${h}_{\mathrm{glass}}=5.7+3.8*{V}_{\mathrm{wind}}$$
(12)

Radiative part of heat transfer coefficient is determine by incorporating Eq. (11), and convective heat transfer of glass cover of still considering wind velocity in ambient can be captured using Eq. (12). Hence, values of both the coefficients are obtained theoretically and applied in Eq. (10) to gain \({h}_{\mathrm{overall}}\) that further used to predict the efficiency. So, the resultant modelled equation for the efficiency can be written as follows:

$${\eta }_{\mathrm{still}}= \frac{\dot{{q}_{we}}}{I(t)}= \frac{{h}_{\mathrm{we}}*{h}_{\mathrm{glass}}\left({T}_{\mathrm{water}}-{T}_{\mathrm{ambient}}\right)}{{h}_{\mathrm{overall}}+{h}_{\mathrm{glass}}}$$
(13)

The reported thermal model incorporates to determine theoretical values of instantaneous efficiency and distillate water output. Accordingly, same environmental conditions were applied to the modelled equations to achieve the predicted results and crosschecked with the actual measure data. Moreover, all the heat transfer coefficients were calculated by attaching respective values in Microsoft Excel Office. Furthermore, emissivity, reported in Eq. 11, was considered as 0.9 for glass material. Hence, the present section of thermal model useful for data validation and provides link between theoretical and experiments results.

Results and discussion

Study of water output of CSS with and without FPC

Experiments were performed in the non-summer months of January to February 2020. The primary aim of solar distillation system is to gain higher distillate water with minimum set-up cost. The experiment has been performed in two phases. In the first phase, solar still was operated without FPC and in the second stage; it was made to operate with FPC in the environment of Mehsana. However, it was ensured that proper connection was made between the FPC and still in order to avoid leakage of water from the joints before starting an experiment on each day. The distillate water was collected through a measuring cylinder, which has an accuracy of \(\pm\) 5 mL, and can measure up to 2500 mL. Accordingly, analysis was further carried out to fetch the effect of variations in water depth inside basin for improvement in the throughput of the still. Figure 3, depicts comparison between the predicted and measure productivity at varying water depth with standard error bars. While estimating the predicted productivity and efficiency of the unit, different heat transfer coefficients in terms of evaporative heat loss vis-a-vis latent heat of vaporization are considered as they plays a significant role in the domain of thermal analysis. Furthermore, overall heat transfer coefficient covers three aspects of convection inside still area, water–glass interface and glass-ambient. Hence, incorporating equations nos.1–13 predicted productivity and instantaneous efficiency was calculated using Microsoft Excel solver software. Figure 4 represents the comparison between the measured productivity of the set-up with and without FPC at varying water depth from 1 to 5 cm with standard error bars. Accordingly, it can be clearly seen that highest productivity was 1600 mL/12 h and 1200 mL/12 h with and without FPC at a water depth of 3 cm on 07/02/2020. Also, it can be concluded that at every water depth (i.e. 1 cm to 5 cm) CSS-FPC is superior than CSS in terms of productivity. Alongside, average productivity using flat plate collector was achieved to be 1500 mL among all the water depth and in case of without FPC 1000 mL during experiment hours. However, higher output can be estimated at a water depth of 2 cm and 3 cm. Hence, 3 cm of water depth inside still layout is prominent over the rest of the studies. Furthermore, water depth affects the evaporation rate of water; hence, it can be concluded that if the water depth is kept low then there is no sufficient amount of water particles that evaporated and help to built-up the convection currents. Accordingly, for higher water depth, there are several water layers; hence, it is difficult for moist air to efficiently transfer heat as well as there is a larger temperature gradient in overall water depth, hence ultimate effect can reduce the evaporation rate and affects productivity.

Fig. 3
figure 3

A plot of predicted and measured productivity varied with water depth

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Fig. 4
figure 4

A plot of comparison between measured conventional solar still and CSS with FPC vs. water depth

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Study reported in terms of Fig. 4 can also compare with the similar studies of CSS performed in other part of the world. Designed structure can provide 3.6 L of distillate water per 24 h. While comparing former analysis with other reported work those are having 3.216 kg/m2-day output for CSS-FPC with heat storage material as wick (Negi et al., 2021). The pyramid solar still attached with FPC attempts to provide 3100 mL of daily output (Subramanian et al. 2021) 7 L/day output for 2 m2 still area enhanced with ETC (Patel et al. 2019), 60% gain in distillate output was observed in FPC augments 1 m2 CSS unit (Rajaseenivasan et al., 2014), considering climatic conditions, a superior rise (51–148%) was observed in productivity of CSS-FPC unit (Eltawil and Omara, 2014).

Study of efficiency of CSS-FPC

Plot 5 shows the variation in instantaneous efficiency of CSS-FPC over a period of five consecutive clear sky days (Fig. 5). Furthermore, it can be fetch from the plot that maximum solar radiation was measured to be 1350 W/m2 average, whereas highest efficiency was found to be 55%. Consequently, efficiency increases as the solar radiation proliferate, and in the noon time it is predicted to remain high as radiation diminish due to continuation in the evaporation of vapour particles at water–glass interface. Figure 6(A) and (B) presents experiment data for a single day of CSS-FPC. From plot (A), it can be pretend that maximum feed water temperature is 60 °C with 35% of efficiency on 16/01/2020. Correspondingly, FPC, water, and glass temperature booming with increase in solar radiation. Moreover, plot 7 depicts the results of predicted and experimental average efficiency for different water depth of CCS-FPC set-up. Hence, it can be fetch from the plot that at 3 cm of water depth, experiment and theoretical efficiency found to be maximum (i.e. 33.19.643% and 31.34222% respectively) (Fig. 7).

Fig. 5
figure 5

Variation of instantaneous efficiency for 5 consecutive days

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Fig. 6
figure 6

A Variation in efficiency with FPC temperature on a critical day. B Variation in water, glass and FPC temperature on a critical day 07/02/2020

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Fig. 7
figure 7

Plot of experimental and theorotical efficiency vs. different water depth

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Uncertainty associated with assessed experiment data

The instability of estimation is related with the result of a measurement characterising the scattering of the values that could reasonably be created to the measurement amount. Equation (14–18) represents the different parameters that utilise to predict the uncertainty in experiment data of in terms of standard deviation, mean, standard error of mean and confidence interval (Mehta et al. 2018).

$$\mathrm{average} (\stackrel{-}{\eta )}= \frac{\sum_{i=1}^{n}{\eta }_{i}}{\mathrm{Number of observations}}$$
(14)
$$\mathrm{Standard deviation} \left(SD\right)= \sqrt{\frac{\sum {({\eta }_{i}-\stackrel{-}{\eta )}}^{2}}{(\mathrm{Number of observations}-1)}}$$
(15)
$$\mathrm{Standard error of mean} \left(\epsilon \right)= \frac{\mathrm{Standard deviation}}{\mathrm{Number of observations in terms of days}}$$
(16)

Con

$$\mathrm{Confidence interval}= \overline{\eta }-1.96\left[\frac{SD}{\sqrt{N}}\right] \le E\le \overline{\eta }+1.96\left[\frac{SD}{\sqrt{N}}\right]$$
(17)
$$\mathrm{Uncertainty in} \overline{\eta } = \sqrt{\sum\nolimits_{i=1}^{n}{\left(\frac{\partial {\eta }_{i}}{\partial {X}_{i}}*{U}_{xi}\right)}^{2}}$$
(18)

Here, \({\eta }_{i}\) designates instantaneous efficiency which depends upon various parameters (\({X}_{i}\)), of the systems having uncertainties (\({U}_{xi})\). The results of reported analysis are presented in Table 3. The mean efficiency was calculated is 23.87311% with deviation of 2.865894 indicating 0.573179 standard error. Moreover, the uncertainty in the data is to be 0.551542.

Table 3 Results of performed uncertainty analysis for the efficiency
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Economic evaluation

The detailed economic study was carried out to analyze the effect of enhancing FPC on the total cost of distillate water output for CSS. The total distillate cost per litre was determined based on detailed equations provided further in the present section (Kabeel and Abdelgaied, 2017.)

Total yearly costs consist of three different costs, which can be expressed as follows:

$$\mathrm{TAC}=\mathrm{FAC}+\mathrm{AMC}-\mathrm{ASV}$$
(19)

where, in Eq. 19, FAC and AMC are fixed annual costs and yearly maintenance cost respectively, ASV is the yearly salvage cost. Furthermore, each cost can be calculated by using Eqs. 20, 22 and 23.

$$\mathrm{FAC}=F \times \left(\mathrm{CRF}\right)$$
(20)

where F is the fixed cost, CRF is the capital recovery factor that can be determined by following Eq. 21:

$$\mathrm{CRF}= \frac{\mathrm{i }\times {\left(1+\mathrm{i}\right)}^{\mathrm{n}}}{{\left(1+\mathrm{i}\right)}^{\mathrm{n}}-1}$$
(21)
$$\mathrm{AMC}=30\mathrm{ \% FAC}$$
(22)
$$\mathrm{ASV}=\mathrm{S }\times \mathrm{SFF}$$
(23)

where S is the salvage value (20% of the fixed cost) and SFF is the sinking fund factor that can be determined by following equation:

$$\mathrm{SFF}= \frac{i}{{(i+1)}^{n}-1}$$
(24)

Furthermore, interest rate (\(i)\) and total numbers of operating years \((n)\) can be taken as 12% and 10 years respectively in Eq. 24. Table 4 represents the detailed cost analysis of CSS and CSS-FPC. Accordingly, total distillate cost per litres, INR/litre for CSS and CSS-FPC is 0.577 and 0.477 respectively, which is 17% higher than that of with the FPC. The payback period is determined as 0.15 years.

Table 4 Cost analysis of CSS and CSS-FPC
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Conclusion

The FPC-augmented conventional solar still is utilized for water desalination for the favour of local communities working on site to achieve the potable water in the region where direct source of drinkable water is rare. The relevant conclusion includes:

  • Conventional solar still of 1.2 m2 area was experimentally investigated with and without FPC. From the measurement data and applied model, it can be concluded that FPC helps to improve the throughput of conventional solar still by attaching higher water temperature which could be economically viable than ETC for the same productivity output.

  • Theoretical model has been built-up for the efficiency and productivity to compare it with the experimental data. Moreover, efficiency was higher with the CSS-FPC unit compared to CSS at optimum water depth of 3 cm.

  • The overall efficiency of FPC attached solar still during the experiment was 23.87311%.

  • The economic analysis was presented to justify the least cost of the distillate water per litre. Accordingly, it was 0.577 INR/litre, which can be feasible by communities to design such type of set-up to gain drinkable water.

  • Maximum productivity reached was 3.6L/day with conventional solar still which is superior to conventional solar still.