Augmentation of freshwater productivity in a single-slope solar still using ball marbles

In the current research, the energy and economic performance in single-slope solar still using ball marbles (BMSS) has been investigated and compared the results with conventional solar still (CSS) under the similar weather conditions of Karaikal (10.92° N, 79.83° E), India, during October 2020. The experiments have been conducted on both sunny and cloudy day to evaluate the performance of solar still. The BMSS has increased the evaporation rate and productivity when compared to CSS due to the sensible heat energy stored by the ball marbles in the absorber basin. The potable water yield of the BMSS is improved by 21.23% and 22.86%, respectively, during sunny and cloudy days. The maximum cumulative productivity obtained in the BMSS is 2950 mL/m2.day and 2150 mL/m2.day, respectively, on sunny and cloudy days. In economic analysis, the payback period (PBP) of the BMSS is 5.7 months, whereas the PBP of the CSS is 6.5 months, respectively. Furthermore, the cost per litre (CPL) potable water produced by BMSS is 8% lower than the CPL of CSS.


Introduction
Drinking water and energy are the two crucial needs required to survive on Earth. Owing to the exponential growth in the population around the world, the abundance of freshwater is rapidly increasing day by day. The supply of freshwater is also affected by the rapid rise in industrialization and agricultural practices across the globe. The scarcity of freshwater is also leading to various health problems which adversely affect people's economic prosperity (UNESCO 2019). The potential way of solving this freshwater crisis is through various desalination approaches by converting the available seawater into drinking water. Desalination with solar energy is proven as a viable way of desalinating seawater (Sharon and Reddy 2015). It was mainly due to the abundant solar energy and also the energy cost is less when compared to fossil fuels (Natarajan et al. 2019a(Natarajan et al. , 2019b(Natarajan et al. , 2019c(Natarajan et al. , 2019dRavi Kumar et al. 2021). In various desalination approaches, solar still is considered one of the best ways to desalinate seawater effectively and economically. Solar still is eco-friendly and economical in such a way that everyone can easily implement it for seawater desalination (Arjunan et al. 2009;Aybar and Assefi 2009;Manchanda and Kumar 2015;Sharon and Reddy 2015;Dsilva Winfred Rufuss et al. 2016). Nevertheless, the solar still efficiency is comparatively lower than other approaches and many researchers are working to boost solar efficiency through various design improvements and incorporations into the still such as fins/energy storage (Muthu Manokar et al. 2014;Durkaieswaran and Murugavel 2015;El-Sebaii and El-Bialy 2015;Yadav and Sudhakar 2015;Bait and Si-Ameur 2018;Selvaraj and Natarajan 2018;Dhivagar and Sundararaj 2018;. In this aspect, Kumar and Tiwari evaluated the internal heat transfer coefficients of solar stills by utilizing various thermal models. It was found that the Kumar and Tiwari model (KTM) validated the results better when compared with other models. The internal heat transfer coefficients of passive and active solar stills were found to be 0.78 and 2.41W/m 2 .K (Kumar and Tiwari 2009). Khalifa and Hamood evaluated the Responsible Editor: Philippe Garrigues influence of brine water depth on the freshwater yield of solar still. It was seen that the water depth of the solar still influenced productivity by 48% (Khalifa and Hamood 2009). Tanaka and Nakatake analysed the performance of tilted wick solar still theoretically with an inclined flat reflector that attached externally to the system. It was inferred that the yield of solar still was increased by 15% and 27% when the length of the reflector was half and the same of the solar still, respectively (Tanaka and Nakatake 2009). Sakthivel et al. studied the regenerative type solar still with jute cloth for better productivity. It was found that the modified solar still had an increase in the yield by 20% and efficiency was improved by 8% compared to CSS (Sakthivel et al. 2010). Dashtban and Tabrizi analysed the performance of solar still with paraffin wax for better yield. It was found from the theoretical analysis, the PCM-based solar still achieved 31% higher productivity compared to CSS (Dashtban and Tabrizi 2011).
Arunkumar et al. studied the significance of PCM on the yield of solar still. It was found that the inclusion of PCM enhanced the distillate yield by 26% when compared to CSS (Arunkumar et al. 2013). Ziabari et al. assessed the cascade type of solar stills. It was found that the cascade solar still achieved 6.7 L/m 2 which was 26% higher than the CSS (Ziabari et al. 2013). Gad et al. studied the performance of conical type solar still for enhancement of productivity. It was found that the conical solar still attained a yield of 3.38 L/m 2 whereas the CSS attained only 1.93 L/m 2 (Gad et al. 2015). Panchal et al. examined the effect of sandstones and marble pieces on the yield of solar still. It was observed that the solar still with sandstones achieved a better yield than the marble pieces and a conventional one (Panchal et al. 2017). Shalaby et al. studied the working of solar still with wax and wicks for better productivity. It was observed that the solar still with PCM achieved a 12% and 11.7% increase in productivity when compared to setup without PCM and setup with PCM using wick material respectively (Shalaby et al. 2016). Sahota and Tiwari studied the impact of Al 2 O 3 nanoparticles on the yield of solar still with 35-kg and 80-kg water depth. It was noticed that the yield of solar still with 0.12% concentration of Al 2 O 3 nanoparticles enhanced by 12.2% and 8.4% for 35-kg and 80-kg water depth, respectively, when compared to CSS (Sahota and Tiwari 2016). Singh et al. estimated the life cycle cost analysis of passive solar stills. It was observed that the kilowatt-hour per unit cost based on the analysis for a single-slope and double-slope passive solar stills was about 0.144 kW h/ and 0.137 kW h/ , respectively. It was concluded from the analysis that the single-slope passive solar still performs better than the double-slope setup (Singh et al. 2016).
Kabeel and Abdelgaied analysed solar still with parabolic concentrator and energy storage for better productivity. It was inferred from the experimental investigation, the yield of modified solar still was improved by 140.4% when compared to CSS (Kabeel and Abdelgaied 2017). Fathy et al. examined the performance of double-slope solar still with parabolic trough concentrator system for augmenting the freshwater productivity. It was observed from the results that the solar with tracking concentrator had an improvement in the yield by 28.1% when compared with fixed concentrator coupled solar still. Also, the solar still with tracking concentrator had an increase in productivity by 142.3% when compared to CSS (Fathy et al. 2018). Rufuss et al. studied the nanoparticles-enhanced PCM (NPCM) in solar still for better productivity. It was found that there was an increase of 35% yield in the solar still with NPCM compared to the solar still with PCM (Winfred Rufuss et al. 2017). Chamkha et al. investigated the influence of carbon nanotubes-doped paraffin wax on the performance of solar still. It was observed that the hybrid PCM had an enhancement in productivity by 41.4% and 26.4% compared to CSS and virgin PCM (Chamkha et al. 2020). Kabeel et al. investigated the influence of sand wrapped in a jute cloth as sensible heat energy storage on the solar still. It was observed that the modified still attained the yield of 5.9 kg/m 2 whereas the conventional still achieved only 5 kg/m 2 . Kabeel et al. studied different PCMs for augmenting the productivity of the solar still. It was inferred that the capric-palmitic and PCM A48 had better advantages compared to other PCMs considered in terms of high yield and low cost. Also, it was found that the thickness of PCM used had no significant effect on the yield (Kabeel et al. 2018a) (Kabeel et al. 2018b). Manokar et al. studied the inclined solar panel basin still in both passive and active modes for enhancement of yield. It was noticed that the active solar still had an increase in freshwater productivity by 44.63% (Manokar et al. 2018). Sathyamurthy and El-Agouz studied the effect of Fresnel lens and blue stones on the performance of solar still. The solar with Fresnel lens and with blue stones achieved 26.64% and 35.55% better yield compared to CSS (Sathyamurthy and El-Agouz 2019). Sathish Kumar et al. analysed the performance of fin-type solar still with energy storage media (ESM). It was found that the efficiency was increased by 64% and 94% in solar still with fins alone and solar still with fins cum ESM respectively when compared with the conventional setup (Sathish Kumar et al. 2019).
Dhivagar and Sundararaj studied the effect of copper tube heat exchanger in coarse aggregate on the productivity of solar still. It was found that the efficiency was improved by 17% in the modified still compared to CSS (Dhivagar and Sundararaj 2019). Dhivagar et al. investigated the gravel coarse aggregate as energy storage in the solar still for better productivity. It was found that the yield of modified solar still was about 4.21 kg/m 2 . Also, the simulation results of this work showed that the results were experimentally validated with a maximum deviation of 14% (Dhivagar et al. 2020. Sakthivel and Arjunan evaluated solar still with cotton cloth as an energy storage medium. It was noticed that the productivity of modified solar still was increased by 24.1% when compared with traditional solar still without energy storage (Sakthivel and Arjunan 2019). Vigneswaran et al. investigated the effect of multiple PCMs in the solar still for better productivity. It was observed that the solar still with multiple PCMs attained a yield of 4.400 L/m 2 /day, whereas the solar still with single PCM and CSS yielded about 4.020 L/m 2 /day and 3.680 L/m 2 /day (Vigneswaran et al. 2019). Dumka et al. investigated the effect of sand-filled cotton bags on the productivity of solar still. It was seen that the yield of modified solar still was increased by 28.56% and 30.99% when compared with traditional still at 30-kg and 40-kg basin water (Dumka et al. 2019). Raj et al. evaluated the influence of metal chips, sandstones and calcium oxide as heat energy storage on the solar desalination system. It was noticed that the solar still with calcium oxide had a 26.98% improvement in the yield when compared to CSS (Raj et al. 2020). Patel et al. investigated the double solar still with reflectors for producing the drinking water from the feed water of Gomti River, India. It was found that there was an increase in the yield by 10.4% and 10.0% during summer and winter, respectively, with a reflector at an angle of 60° (Patel et al. 2020). Suraparaju and Natarajan studied the impact of the ridge gourd natural fibres on the performance of the single-slope solar still. It was depicted that more natural fibres in the absorber reduced the performance of solar still (Suraparaju and Natarajan 2020). Dumka et al. studied the influence of jute covered plastic balls on the productivity of solar still. It was found that there was an increase in the yield by 64% when compared to conventional still (Dumka et al. 2020). Khechekhouche et al. investigated the effect of thickness of glass cover on the productivity of solar still. It was noticed that the solar still with a 3-mm thick glass cover attained more productivity relative to the solar stills with 4mm and 5-mm thick glass covers (Khechekhouche et al. 2021). Mohammed et al. investigated the impact of phase change energy storage material (RT42PCM) with various quantities on the solar still. It was observed that the 4-kg PCM in the solar still increased the productivity by about 18.6 and 27.7%, compared to 2-kg and 6-kg PCM (Mohammed et al. 2021). Attia et al. studied the performance of hemispherical solar still with phosphate pellets as an energy storage medium. It was found that the solar still with phosphate layer of 5 mm thickness and phosphate pellets in saltwater with 1% and 2% had enhanced the yield compared to conventional one (Attia et al. 2021b). Attia et al. investigated the performance of solar still with 25 phosphate bags on the freshwater yield. It was observed that the solar still with phosphate bags had a yield of 5.27 and 4.87 kg at 1-cm and 2-cm basin water depth, whereas the CSS had a yield of 3.8 kg (Attia et al. 2021a). Dhivagar et al. studied the influence of graphite plates and block magnets on the productivity of solar still. It was observed that the hourly yield of modified solar still was increased by 19.6% and 22.8% during summer and winter days, respectively ).
Based on the above literature, it can be outlined that many researchers utilized various approaches like energy storage materials (sensible heat and latent heat), absorber coatings, nanofluids and nanopowders and surface enhancers such as fins and wicks in the basin for improving the freshwater productivity of solar still. It was found that as of the authors' knowledge, there was no particular extensive research on ball marbles as a heat energy storage material in the solar still basin. In this aspect, the current research aims to investigate the inclusion of the ball marbles into the solar still for enhancing freshwater productivity. Hence, the experiments are conducted with ball marble solar still (BMSS) and compared the productivity improvements with conventional solar still (CSS). In the end, the cost-effectiveness of both the solar stills is estimated using economic analysis.

Materials and experimentation
The experiments are carried out with BMSS and CSS at the NIT Puducherry (10.92°N, 79.83°E), Karaikal, India, during the sunny and cloudy days of October 2020.

System description
In the present investigation, two similar single-slope solar stills are designed and fabricated to examine the effect of ball marbles on the improvement of freshwater productivity in the solar still. The two solar stills that have been developed for analysis are as follows:

Materials and fabrication
The two solar stills are made of durable plywood and the internal structure of the solar still has an aluminium layer of 2 mm thickness, which restricts the direct interaction between water vapour and plywood. Also, the aluminium sheet is coated with standard black paint for absorbing more solar radiation into the system. The absorber basin is made of a 1-mm copper sheet, and the dimensions of the absorber basin are 1000 mm × 600 mm × 50mm (0.6m 2 absorber area). The solar still is covered with a transparent and the glass cover is fixed at an angle equal to the latitude of Karaikal for the efficient operation of the system (Singh and Tiwari 2004). The absorber basins of CSS and BMSS are filled with seawater at a particular depth. The black-coated marble balls of 25 mm diameter are introduced into the absorber basin of BMSS. The entire absorber area is equipped with black-coated marbles to study the impact on the productivity of solar still. The complete outer area of the solar still is insulated with 2-cm thick Thermocol sheets to reduce the heat losses from the system. The photograph of the BMSS and CSS is depicted in Fig. 1.

Preparation of black-coated ball marbles
The study is mainly focused on the use of black-coated ball marbles for augmenting the freshwater production from the solar still. The ball marbles are commercially available in the market and procured from the market for experimental investigation. The marble balls are coated with selective black paint (Thurmalox®) for better absorption of incident global solar radiation. The arrangement of ball marbles in the solar still basin is shown in Fig. 2. The ball marbles have a specific heat capacity of about 850 J/kg.°C which stores and releases the heat energy at the desired temperatures required for operating the solar still with energy storage. Hence, the black-coated ball marbles are chosen for the experimental investigation in the current research.

Experimentation
The performance investigation of single-slope solar still with and without black-coated marble balls is carried out on a sunny day and cloudy day of October 2020 to study the effect of marble balls on freshwater productivity. The feed water for this investigation is collected from the Bay of Bengal sea located adjacent to the NIT Puducherry. The seawater in the absorber basin is filled to a depth of 2 cm and maintained constant throughout the investigation by adding makeup water at regular intervals. The temperatures of the glass cover, seawater, absorber basin, marble balls and ambient temperature are measured using calibrated K type thermocouples connected to the data acquisition system (Agilent 34972A ). The global radiation of the particular testing day at the testing location is measured using the "Hukseflux pyranometer".
The experiments are conducted on 14.10.2020 (cloudy day) and 15.10.2020 (sunny day), respectively. The readings are recorded from 08:00 am to 06:00 pm (Indian Standard Time) for every half an hour.

Uncertainty analysis
The uncertainties in measuring instruments are estimated using the following relations (J. P. Holman 2007): Here, the total uncertainty is w r , the function is R, x is called the independent variable and w is also the independent variable with respect to the uncertainty. The uncertainty of the thermocouple, pyranometer and measuring cylindrical jar used in the experimental investigation is tabulated in Table 1.
The uncertainty in the efficiency and hourly freshwater yield is given by the following formulae (Suraparaju and Natarajan 2021a): It was assessed that the error in total potable water yield is ±1.5%. In addition to that, the error in global radiation and temperature measurement is 0.05% and 0.1%. Hence, the total error is about ±2%.

Energy and economic analysis
The thermal efficiency of the passive solar still is evaluated by using the following formula (Kabeel and Abdelgaied 2016): where P.Y is the overall potable water yield, λ is the latent heat of evaporation of water, A b is the absorber basin area in, G is the daily overall incident global solar radiation and Δt is the duration of the cumulative readings in second.

Results and discussion
The experimentations have been carried out in both BMSS and CSS during the sunny and cloudy days of October 2020 to assess the performance. The results observed in BMSS are compared with CSS under the same climate conditions.

Experimental observation
The variations of solar irradiation and ambient temperature in both days are illustrated in Fig. 3. On sunny and cloudy days, during morning hours, the solar irradiation was gradually increasing and attained a higher value of about 1052.63 W/m 2 and 983.38 W/m 2 , respectively. In between, the formation of clouds was reducing the length of sunshines considerably. Hence, during evening hours, the intensity of solar irradiation was reduced slowly and reached to lesser value of about 27 W/m 2 . It was noticed that, during afternoon hours, the maximum ambient temperatures were about 35.2°C on both testing days. During evening time, it was reduced to about 27.6°C and 25.2°C, respectively, for a sunny day and cloudy day. The phenomenon was due to the reduction in the intensity of solar irradiation. The variations of wind velocity on both days are illustrated in Fig. 4. The wind velocity played a major role during the condensation of water vapour at the bottom of the glass cover. The wind velocity was changing in the range between 1.6 and 5.1 m/s during the experimentation.
The variations of different temperatures of both BMSS and CSS on day 1 are illustrated in Fig. 5. It was noticed that the maximum glass temperature of BMSS and CSS was about 57.7°C and 56.8°C, respectively, and it was reduced to about 36.5°C and 30.8°C, respectively. The maximum absorber basin temperatures of BMSS and CSS were reported as 64. 2°C and 58.1°C, respectively. It was observed that the absorber temperature of BMSS was about 10% higher than CSS. Along with the absorber, the maximum ball marbles temperature was recorded as 69.9°C in BMSS. Furthermore, it was observed that the maximum water temperature in BMSS and CSS was 63.1°C and 56.8°C, respectively. The water temperature was Measuring cylinder 0 to 1000 mL ±10 mL 5.774 mL improved significantly in BMSS due to the impact of blackcoated ball marbles. The observed saline water temperature in BMSS was 12% higher than the saline water temperature of CSS.
The variations of different temperatures of both BMSS and CSS on day 2 are illustrated in Fig. 6. It was seen that the maximum glass temperatures of BMSS and CSS were about 55.8°C and 54.2°C, respectively, and during evening time, it was reduced to about 30.4°C and 30.1°C, respectively. The absorber basin temperatures of BMSS and CSS were augmented during the morning and attained the maximum value of about 72.5°C and 67.1°C, respectively. On day 2, the basin absorber temperature of BMSS was 9% higher than CSS. The maximum ball marble temperature was 73.5°C in BMSS. Furthermore, the maximum saline water temperatures in BMSS and CSS were observed to be about 71.1°C and 65.2°C , respectively. The observed saline water temperature in BMSS was 14% higher than CSS. Thus, the incorporation of black-coated ball marbles in the solar still effectively increased the absorber and water temperatures to a greater extent compared to CSS. The rise in the difference between water and glass temperatures (ΔT = T water − T glass ) leads to enhanced condensation and hence attained more freshwater yield in the BMSS compared to CSS.

Effect of ball marbles on the system temperatures
The inclusion of sensible energy storage into the solar still significantly improved the temperatures of the system. The ball marbles improved the water and absorber temperature enormously. The ball marbles in the absorber basin played a dominant role in heat transfer between absorber and water during diurnal hours. The ball marbles facilitated the solar still to maintain the highest temperatures of water and absorber from 12.00 pm to 02.30 pm when compared to CSS. The upsurge in the water temperatures leads to an enhancement in the evaporation rate in BMSS which caused an improvement in freshwater yield compared to CSS. However, the inclusion of ball marbles into the solar still increased the water and absorber temperatures led to an improvement in the freshwater yield of solar still.

Productivity
The hourly productivity and cumulative productivity for BMSS and CSS on both testing days are depicted in Fig. 7a and b. On day 1, during the morning to afternoon hours (11.00 to 15:00 h), the hourly productivity of BMSS was significantly improved when compared to CSS. In BMSS, the maximum hourly productivity of about 270 mL/m 2 was observed during 14:00 h due to the heat energy retained by ball marbles. Similarly, during 14:00 h, improved productivity of about 230 mL/m 2 was collected in CSS. In BMSS, the observed maximum productivity is 18% higher than CSS. On day 2, the maximum hourly productivity of about 340mL/m 2 was observed in BMSS. In CSS, it was observed to be about 300mL/m 2 , which was 14% lower than BMSS. The productivity of BMSS and CSS on both the testing days is represented as a histogram in Fig. 8. On day 1, it was noticed that the cumulative productivity of BMSS and CSS was about 2150 mL/m 2 .day and 1750mL/m 2 .day, respectively. On day 2, it was observed as 2950mL/m 2 .day and 2430mL/m 2 .day, respectively, in both BMSS and CSS. The cumulative production of the BMSS was 22.8 % and 21.3% higher than the productivity collected in CSS for day 1 and day 2, respectively. It was noticed that the average freshwater productivity from the BMSS was 2.7 L/m 2 .day, whereas the average freshwater productivity from the CSS was 1.9 L/m 2 .day.

Effect of ball marbles on the productivity of solar still
The freshwater productivity of the solar still was significantly influenced by the ball marbles as thermal energy storage. The adequate heat-storing capacity of ball marbles allowed the ball marbles to receive and store the incident solar radiation in the form of heat. The stored heat was the key factor for rising the water and absorber temperatures during the peak hours of sunshine. Also, when the sunshine was reduced, the stored heat in the ball marbles got liberated and helped in maintaining the maximum water temperatures for better performance of the solar still. From the above discussion, it was observed that the inclusion of ball marbles into the desalination system significantly enhanced the freshwater productivity of the system. Nevertheless, the incorporation of ball marbles in the absorber basin substantially improved the freshwater yield by enhancing the heat transfer between the water, absorber and ball marbles.

Energy analysis
The thermal efficiency of the single-slope solar stills was evaluated using Eq. (3). The average thermal efficiency of the BMSS on a cloudy day was 34.9%, whereas the average thermal efficiency of CSS was 25.6%. It was observed that there was an increase of 36.67% in the average thermal efficiency of BMSS on a cloudy day. Besides, the average thermal efficiency of the BMSS on a sunny day was 47.5% whereas the average thermal efficiency of CSS was 34.4%. It was observed that there was an increase of 38.11% in the average thermal efficiency of BMSS on a sunny day. From the above inferences, it was noted that the addition of black-coated ball marbles in the absorber basin as a sensible energy heat storage material significantly increased the performance of singleslope solar still by increasing the system temperatures, productivity and energy efficiency. The outcomes of the energy analysis on both testing days are pictorially illustrated in Figs. 9 and 10, respectively.

Economic analysis
The capital investment was considered by taking the prices of each part of the desalination system assembly, according to the Indian costs. The capital cost was calculated by considering all the fabrication, maintenance and operation costs. The cost-effectiveness of both the solar stills was estimated using economic analysis and listed in Table 2. From Table 2, it was observed that the cost per litre (CPL) of BMSS and CSS was $0.025 and $0.027, respectively. Besides, the CPL of BMSS is 8% lower than the CPL estimated in CSS. Furthermore, the PBP of BMSS and CSS was 5.8 months and 6.5 months, respectively. The outcomes of the economic analysis were represented graphically in Figure 11. From the outcomes of the economic analysis, it was observed that the inclusion of ball marbles in the absorber basin is economically viable and sustainable. The outcomes of the economic analysis were compared with existing literature and tabulated in Table 3 which infers that this research paves a way for the most economical approach to enhance productivity as the payback period and cost per litre is the lowest in this research. As a whole, the inclusion of ball marbles in the solar still is economically viable.

Conclusion
The experimentations have been conducted in both the BMSS and CSS to assess the effect of ball marbles on the performance of solar still. The experimental investigation was carried out for 2 days under the same meteorological conditions of Karaikal city in India during October 2020. The observed major results are given below: a) The solar still with ball marbles had a better performance compared to CSS.  b) The water temperature was significantly improved using ball marbles in a solar still basin absorber. On day 1, the BMSS has a 12% improved water temperature when compared to CSS. Similarly, on day 2, it was improved to about 14% than CSS. The maximum observed ball marbles temperatures in BMSS were 69.9°C and 73.5°C, respectively, during sunny and cloudy days. c) The productivity improvement observed on an hourly basis of BMSS was 18% and 14%, respectively, higher than the CSS on both day 1 and day 2. Besides, the cumulative productivity in BMSS was 22.8% (day 1) and 21.3% (day 2), respectively, higher than the cumulative productivity observed in CSS. The outcomes proved that the usage of ball marbles has enhanced daily productivity considerably. d) The average energy efficiency of BMSS and CSS was about 34.9% and 25.6% on day 1, respectively. It was observed that there was an increase of 36.7% in the energy efficiency of BMSS compared to CSS. Besides, the average energy efficiency of BMSS and CSS was about 47.5% and 38.1% on day 2, respectively. It was observed that there was an increase of 38.1% in the energy efficiency of BMSS compared to CSS. e) The economic analysis reported that the PBP of the BMSS and CSS was observed as 5.7 months and 6.5 months, respectively. Similarly, the CPL of BMSS and CSS was about $ 0.025 and $ 0.027, respectively.
It has been concluded from the above results that ball marbles had a better heat transfer rate and raised the system temperatures effectively. Also, the productivity from the BMSS was comparatively better than CSS. The economic analysis also proved that the BMSS was sustainable compared to CSS.  Abbreviations AC, annual cost; AMC, annual maintenance cost; ASV, annual salvage value; BMSS, ball marbles solar still; CC, capital cost; CPL, cost per litre; CRF, capital recovery factor; CSS, conventional solar still; FAC, fixed annual cost; PBP, payback period; S, salvage value; SFF, sinking fund factor Units mL millilitre mm millimetre cmcentimetre m metre L litre°C degree Celsius Other abbreviations p.y potable water yield λ latent heat of vaporization of water A b area of the absorber basin G.R global solar radiation Δt duration of the cumulative readings in sec u η uncertainty of the efficiency u dw uncertainty in instantaneous productivity I(t) radiation at a particular time W r total uncertainty R function w,x independent variables Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11356-021-15117-5.

Data Availability
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations
Conflict of interest The authors declare no competing interests.