conservation of mass magnesium oxide experiment tes

Conservation of Mass Experiments

Start with reviewing the difference between physical and chemical changes. (Chemical changes include: gas, color change, precipitate, temperature change, or light). Get some play doh and roll it into a ball. Place it on the scale and ask students if they think the mass will change if you change the shape of the play doh. You could also use legos or anything else you have handy.

Once they’ve seen that physical changes don’t cause a mass change, move on to chemical changes. Here are some labs you can use for different grade levels to teach the law of conservation of mass.

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How does burning magnesium affect its mass? | 11-14 years

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Investigate what happens to the mass of magnesium when it burns and reacts with oxygen using this lesson plan and practical activity for 11–14 year olds

Students explore, in a practical activity, what happens to the mass of magnesium when it burns. This helps them consolidate their ideas about the increase in mass on burning due to combination with oxygen. Students also evaluate and develop their ability to draw and interpret simple graphs.

Learning objectives

Students will be able to:

• Describe and explain what happens to the mass of magnesium when it burns.
• Draw and interpret simple graphs.

Sequence of activities

Demonstration and introduction.

• Issue a blue safety glass to each student.
• Ignite a piece of magnesium ribbon over a cement mat. Ensure that students use the safety glass to observe this.
• Increase – green
• Stay the same – yellow
• Decrease – red
• A student to explain their answer.
• Other students to add to this if appropriate.
• The learning objectives.
• That they are going to investigate what happens to the mass of magnesium when it is burnt.

Practical: set-up

Describe the practical details, with students to work in pairs and follow safe procedures to:

• Weigh a crucible and lid.
• Add a prepared piece of magnesium ribbon to the crucible and weigh it again.
• Place the crucible on a pipeclay triangle supported on a tripod and heat it with a Bunsen burner flame, lifting the lid of the crucible from time to time using a pair of tongs.
• Let the crucible cool and weigh it again.
• Place the crucible on the pipeclay triangle again and re-heat for a short time, let it cool and reweigh.

Circulate and support while pairs:

• Carry out the practical.
• Add their results to a class set written on a board or projected.
• Write them down on their copy of the ’Results table’ sheet.
• Complete all parts of their ’Results table’.

A set of specimen results is provided that may be used if student data is not available (see downloads below).

Graphs exercise

Discuss with the whole class What makes a good graph? Refer to the criteria on their ‘Results table’ sheet.

Support individuals as they:

• Draw the graph of mass of magnesium against mass of magnesium oxide formed.
• Check that their graph meets the expected standard, and modify it if necessary.
• Work with the other member of the pair to discuss whether they think that the graph meets the required standard.
• Offer help to their partner only in the form of questions.
• Confirm with you that the graph is up to standard.
• Answer a question that you pose, if it is not to standard.
• Use their graphs to predict how much magnesium oxide would be produced from a specified mass of magnesium.
• Write in words on their ’Results table’ sheet how they can use their graph to predict the mass of magnesium oxide which will be formed from a particular mass of magnesium when it is burnt.

Take in the graphs and written sheets and comment on any features that the student still needs to develop.

Sharing objectives and criteria gives purpose to the activity and a framework for self criticism. Through the discussion about their own and their partner’s graphs, students will see how to improve. When interpreting their graph, students will see why certain standards need to be met.

Teacher feedback is used to affirm standards or to prompt improvement.

Practical notes

• Blue safety glass
• Set of traffic light cards
• Graph paper

For the practical (see note 4 in ‘Health, safety and technical notes’ below):

• Crucible and lid
• Pipeclay triangle
• Bunsen burner
• 10–20 cm lengths of magnesium ribbon (FLAMMABLE) ranging from 0.1 g to 0.5 g
• Access to a balance measuring to 0.01 g

Health, safety and technical notes

• Read our standard health and safety guidance .
• Wear eye protection.
• It is the responsibility of the teacher to carry out an appropriate risk assessment.
• The ‘Set of specimen results’ handout can be used in place of carrying out the practical, or if student data is not available (see downloads below).

Principal hazards

• Crucibles remaining hot for some time (leave to cool on the tripods).
• Magnesium ribbon flammability.

Results table

Set of specimen results, specimen results with answers, specimen graph, additional information.

This lesson plan was originally part of the  Assessment for Learning  website, published in 2008.

Assessment for Learning is an effective way of actively involving students in their learning.  Each session plan comes with suggestions about how to organise activities and worksheets that may be used with students.

• 11-14 years
• Practical experiments
• Formative assessment 
• Lesson planning
• Practical skills and safety
• Quantitative chemistry and stoichiometry
• Reactions and synthesis

Specification

• 1. Investigate whether mass is unchanged when chemical and physical changes take place.
• 2. Develop and use models to describe the nature of matter; demonstrate how they provide a simple way to to account for the conservation of mass, changes of state, physical change, chemical change, mixtures, and their separation.
• Students should be able to explain any observed changes in mass in non-enclosed systems during a chemical reaction given the balanced symbol equation for the reaction and explain these changes in terms of the particle model.
• The law of conservation of mass states that no atoms are lost or made during a chemical reaction so the mass of the products equals the mass of the reactants.
• Recall and use the law of conservation of mass.
• Explain any observed changes in mass in non-enclosed systems during a chemical reaction and explain them using the particle model.
• 1.47b Explain the law of conservation of mass applied to: a non-enclosed system including a reaction in an open flask that takes in or gives out a gas
• C5.3.1 recall and use the law of conservation of mass
• C5.3.2 explain any observed changes in mass in non-enclosed systems during a chemical reaction and explain them using the particle model
• C3.1b use the names and symbols of common elements and compounds and the principle of conservation of mass to write formulae and balanced chemical equations and half equations
• C1.3j explain any observed changes in mass in non-enclosed systems during a chemical reaction and explain them using the particle model
• C5.2.1 recall and use the law of conservation of mass
• C5.2.2 explain any observed changes in mass in non-enclosed systems during a chemical reaction and explain them using the particle model
• C1.3l explain any observed changes in mass in non-enclosed systems during a chemical reaction and explain them using the particle model
• The mass of a mole of any substance, in grams (g), is equal to the gram formula mass and can be calculated using relative atomic masses.
• (p) how to calculate the formula of a compound from reacting mass data
• 2.2.1 recognise oxidation and reduction in terms of loss or gain of oxygen or hydrogen and identify in a reaction or symbol equation which species is oxidised and which is reduced (link to suitable industrial processes covered in this specification);

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Experiment 4: The Law of Conservation of Mass

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Enhancing solar still performance with hybrid nanofluid: a comprehensive assessment of energy, exergy, economics, and environmental impact using a novel fractional model

• Open access
• Published: 24 August 2024

Cite this article

You have full access to this open access article

• E. F. El-Gazar 1 ,
• Mohamed S. Yousef 2 ,
• Abdelrahman M. Elshaer 3 ,
• Mahmoud A. Khattab 1 ,
• T. A. Mouneer 3 &
• A. A. Hawwash 3  

In the present study, the thermal performance of a modified solar still (MSS) system coupled with hybrid nanofluid (HNF) of titanium oxide (TiO 2 ) and silicon oxide (SiO 2 ) has been investigated theoretically based on energetic, exergetic, economic, and enviroeconomic assessment. The model of the MSS has been introduced using a new numerical technique of the Atangana-Baleanu fractional derivative. The fractional model of the MSS system is presented under various weather circumstances (winter and summer seasons) in Egypt to show the impact of HNF on the MSS output: temperatures, freshwater productivity, exergy, and energy efficiencies. The outcomes of the fractional model are contrasted to those derived from actual experimental data collected under varying climatic conditions in Upper Egypt. Numerical findings demonstrate specific consistency between the experimental results and the proposed model of the solar still (SS), with a percentage of error of 4.65% in freshwater productivity. Moreover, using hybrid nano enhances daily productivity in the summertime by 27.2% and in the wintertime by 21.7%, increasing efficiencies. Additionally, a comparative economic and environmental assessment has been investigated for all the proposed desalination systems without and with HNF. The findings found that the cost per liter of MSS was 44% lower than that of the conventional solar still (CSS) during the summer season. Using exergy and energy approaches, MSS reduced CO 2 by 22% and 29.6% more during the winter.

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• Environmental Chemistry

Avoid common mistakes on your manuscript.

1 Introduction and literature review

In recent years, access to clean, healthy, and pure water is indeed one of the most critical issues facing humanity. Without adequate access to safe water, communities face numerous challenges related to health, sanitation, food security, and economic development.

Approximately 97% of Earth's water is saline, found in oceans and seas, while only about 3% is freshwater. This freshwater exists in various forms, including surface water such as rivers, lakes, and freshwater wetlands, as well as groundwater and frozen water in polar ice caps, glaciers, and snowfields (Abujazar et al., 2016 ; Bait & Si-Ameur, 2018 ; Rashidi et al., 2016 ).

By 2035, over a quarter of the people on our planet will be affected by water scarcity due to the growth in the world's population and the increasing query for water consumption. As a result, desalination technology is regarded as one of the most significant processes for obtaining potable freshwater depending on exploiting the sources of brackish water (seas and oceans). However, most of the desalination technologies that have been developed recently have complex structures and designs. Additionally, most of these desalination systems rely on fossil fuel sources, meaning their operating and maintenance costs will continue to rise dramatically due to the limited resources for fossil fuels. Energy storage materials could used as a source of heat inside the SS during the night (Hawwash et al., 2023 ; Hawwash et al., Sep. 2019 ). The SS is a simple and economical design for producing clean water, which depends on the incident solar radiation to convert salty impure water into filtered water (El-Gazar et al., 2020 ).

Hussen et al. ( 2023 ) investigated four distinct designs of the SSs. The tested SS systems were conventional, pyramid, double slope, and tubular SS. For mitigating the effect of shadow inside the double slope SS and pyramid SS leading to a rise inside the water basin. In addition, Phase Change Materials (PCM) were employed to enhance thermal storage performance. The design of pyramid SS with PCM showed the greatest values of 116.4%/51.3%, for productivity and thermal efficiency, respectively. Aly et al. ( 2023 ) enhanced the output of tabular SS by presenting a new design, the oval tubular SS coupled with PCM and cover plate cooling. The productivity and efficiency of the oval tubular SS were enhanced by 32.42% and 41.26%, respectively.

Alshqirate et al. ( 2023 ) improved the freshwater productivity of conventional SS with natural Palmately leaf fibers. The outcomes found that the daily total freshwater yield was 5160.8 gm/m 2 by using natural fiber, with an increasing percentage of 44.5% relative to the CSS. Manoj Kumar et al. ( 2022 ) conducted an experiment investigating the effect of thermal energy storage/ SS integration. Inorganic PCM and nano-doped PCM were integrated with a single-sloped conventional SS. The findings showed that using inorganic PCM and nano/PCM composite boosted the percentage of freshwater yield from the SS by 26.63% and 45.23%, respectively. Hameed et al. ( 2022 ) evaluated the thermal performance of single slope SS integrated with fins of a square area involved in the absorber plate. The work also studied the efficacy of SS glass cover cooling methodology. The findings reported an improvement in the water productivity of the SS/fins combination by 40%. Also, the study reported a significant improvement in productivity with cover cooling.

Ahmed et al. ( 2022 ) investigated the influence of cotton wick material integrating with tubular SS and parabolic concentrator systems. The results revealed that the cotton wick enhanced the setup efficiency and productivity by 24.45% and 29.11%, respectively. Angappan et al. ( 2023 ) studied the integration of SS and box-shaped solar cookers to boost SS water productivity. The outcomes reported that the conventional and modified SS daily productivities reached nearly 4 L/m 2 and 6 L/m 2 , respectively, with an increasing percentage of 41% compared to the conventional one. Chauhan et al. ( 2023 ) improved the SS output by surface coating of Lauric acid and phosphorus quantum dot material. Two designs of SSs were adopted, the conventional SS and prism-shaped SS. The results showed that traditional and prism-shaped SS with PCM and black coating yielded about 3050 ml/m 2 and 3600 ml/m 2 , respectively.

Abdullah et al. ( 2023 ) modified a single slope SS by integrating Nano- PCM, with an external condenser, copper water heating coil, internal, and external reflectors to enhance freshwater productivity. Combining external reflectors (top and bottom) with external condenser, and PCM improved the SS productivity by about 42%, 57%, and 41%, respectively. Kumaravel et al. ( 2022 ) investigated the performance analysis of a single slope SS integrated with thermal energy storage with blue metal stones and pebble stones. The findings showed that combining the two types of rocks and their integration with the SS increased productivity by 18% relative to conventional SS.

Much research was dedicated to enhancing SS's thermal and productivity performance by adopting numerical and mathematical models. Moustafa et al. ( 2022 ) increased the tubular SS's water productivity and energy efficiency by attaching an electric heater to the still basin powered by a solar photovoltaic (PV) panel (El-Gazar et al., 2023a ). Also, the work developed a model based on artificial intelligence (AI) for predicting the SS's water yield and thermal efficiency. The findings revealed that the modified SS had an average daily accumulated water productivity of nearly 3 L/m 2 with a 31.85% enhancement percentage. Mittal ( 2021 ) delivered a Computational Fluid Dynamics (CFD) modeling of a single slope SS using ANSY S Fluent. The CFD model approach computationally proved its effectiveness in capturing the distillate water output at various configurations, provided that the bottom and top surface temperatures are identified. Mohsenzadeh et al. ( 2022 ) established and validated a transient model experimentally to investigate a passive SS. The evaporation chamber was designed with different aspect ratios, and all the cases were investigated. The study revealed that the aspect ratio of the SS evaporation chamber increased and produced more fresh water.

Lisboa et al. ( 2022 ) performed a model analysis for the freshwater productivity enhancement techniques of SSs. The study concluded that the dominant factors that enhance water productivity were structure design, water depth, basin-glass temperature difference, insulation, and solar irradiation. Keshtkar et al. ( 2020 ) introduced a CFD mathematical model to study the impact of different design factors of passive basin SS. The findings show that the SS freshwater yield increased by about 14% when the wind velocity was raised by 5 m/s. The SS productivity also increased by 3.5% when the glass width decreased to 2 mm. Hassan et al. ( 2022 ) provided a novel simulation model for estimating SS's performance. The model results were proven experimentally, and different materials of SS walls were studied. The water productivity per unit area of the basin was about 2 and 4 kg/m 2 for glass and wooden walls, respectively. A numerical simulation was modeled by Gupta et al. ( 2022 ) to investigate the performance of a single slope SS under different climate conditions in India. The model accurately predicted the SS's performance at distinct conditions.

Nanofluids were used to increase the SS efficiency in more studies (Ajit et al., 2023 ; Chen et al., 2023 ; Mustafa et al., 2023 ; Sahu & Tiwari, 2024 ). Kabeel et al. ( 2019 ) investigated experimentally a new absorber plate of a pyramid SS covered with titanium oxide nanoparticles black coating. The findings summarized that water yield was increased by the decrease in the water depth. The coated absorber plate improved the freshwater yield by 12% at maximum water depth. Rashidi et al. ( 2018 ) examined numerically the influence of nanofluid insertion on the freshwater output of a stepped SS. The outcomes showed that raising the nanoparticle percentage by 5% increased the hourly water productivity by about 22%. Sahota et al. ( 2019 ) investigated the performance of a double slope SS with alumina and Multi-Wall Carbon Nano Tubes (MWCNTs) water-based nanofluid. The results found a remarkable improvement in SS's evaporative heat transfer coefficient and freshwater output by adopting water-based nanofluids.

Sharshir et al. ( 2022 ) conducted an experimental study investigating the performance of pyramid SS integrated with evacuated tubes, nanofluid, external condensers, and ultrasonic foggers. The results showed that modified SS with six evacuated tubes, nanofluid, and an external condenser had increased the freshwater yield, exergy efficiency, and energy efficiency by about 132%, 75%, and 28%, respectively. Alsehli et al. ( 2022 ) implemented a new design for SS and improved freshwater productivity by incorporating graphene nanoplatelet/platinum hybrid nanofluid. The study found that mixing the nanoparticle with the base fluid led to a remarkable growth in freshwater productivity.

Mustafa et al. ( 2023 ) performed a two-phase analysis on integrating aluminium-based nanofluid in SS. AAluminumnanoparticles were utilized in the SS's basin. The results concluded that solar irradiation dominated the PCM maximum temperature, air temperature, and PCM volume fraction. Maatki et al. ( 2022 ) enhanced the heat transfer within a triangular SS using Carbon Nano Tube (CNTs)—based nanofluid. The results showed that the MSS design with nanofluid significantly improved the mass and heat transfer rates. Modi et al. ( 2022 ) examined the effect of thermal energy storage materials and nanoparticles on the freshwater productivity of pyramid SS with square shape. The outcome revealed that the SS's total water productivity and efficiency with energy storage were greater by 5% and 5.5%, respectively than nanofluid.

The research adopted hybrid nano-based water for enhancing SS productivity is outlined in the following paragraphs. A fractional modeling technique was adopted by El-Gazar et al. ( 2021b ) to examine the impact of HNF on the performance of a conventional SS. The HNFs adopted were alumina and copper oxide. The results revealed that adopting hybrid nanofluids increased the freshwater's daily productivity by nearly 27% in hot weather conditions and 21% in cold conditions. Shoeibi et al. ( 2022 ) numerically evaluated the cover glass cooling of a double-slope SS integrated with HNF (TiO 2- Al 2 O 3 ). The results revealed that the productivity of freshwater improved by 11.09%, compared to the model without a hybrid nanofluid. Rabbi et al. ( 2021 ) improved the SS's performance using two-hybrid nanofluids. The freshwater productivity, and efficiency, were 4.99 kg m −2 / day, 37.76%, respectively when water was mixed with Al 2 O 3 –SiO 2 hybrid nanofluid. El-Gazar et al. ( 2021b ) conducted a novel nonlocal model for SS performance investigation integrated with a PV panel, HNF, and saline water preheating. The findings show that the daily SS's productivity was 7.1 kg/m 2 per day when the HNF was employed, leading to an improvement percentage of 10% relative to the SS system without a hybrid nanofluid. Kaviti et al. ( 2023 ) studied the water desalination system of a SS using HNF of cerium oxide (CeO 2 ) nanoparticles and MWCNTs. The modified SS accomplished a high productivity of 1430 mL relative to the CSS, with a peak productivity of 920 mL.

The study of the SS systems did not stop with enhancing the yield and efficiency of the still. Still, it also included work on exergetic analysis, which mainly depends on thermodynamics's second law. Compared to energetic analysis, which relies on the 1st law of thermodynamics, exergy assessment appears to be an effective observation tool for investigating the optimization, performance, thermal design, and evaluation of various energy techniques (Asbik et al., 2016 ; Gad et al., 2022 ; Hakim et al., 2018 ; Ibrahim et al., 2017 ; Jafarkazemi & Ahmadifard, 2013 ; Kianifar et al., 2012 ; Kumar et al., 2020 ; Ranjan et al., 2016 ). Indeed, exergy analysis offers valuable insights into the performance of solar still (SS) systems by identifying locations, magnitudes, and types of irreversibilities and losses within the system. Unlike energy analysis, which focuses solely on quantity, exergy analysis considers the quality of energy and provides a more comprehensive understanding of system efficiency. Pal et al. ( 2018 ) presented a thermal model for the double slope SS, then studied the exergy and energy assessment for the still system after adding black cotton wicks in the still basin to enhance its efficiency. Another new fractional model for the SS system, which studied the energy and exergy assessment, was presented by El-Gazar et al. ( 2021a ). The fractional model was presented to show the effect of mixing hybrid nanoparticles with salty water on the exergy and energy efficiencies of a SS system coupled with a PV panel. Moreover, Sharshir et al. ( 2018 ) compared the conventional SS and the modified still with nanoparticles of copper oxide (CuO) and graphite. The comparison was presented based on evaluating the energetic, energetic, and economic parameters for both the SS with and without using the nanofluid.

Although it is widely acknowledged that the exergy technique may be utilized to represent the performance of SS systems effectively, there are still certain limitations and weaknesses in environmental and economic analyses (Abo-Elfadl et al., 2021 ; Deniz & Çınar, 2016 ; Gaur & Tiwari, 2014 ; Hassan et al., 2020 ; Joshi & Tiwari, 2018 ; Singh, 2018 ; Singh & Tiwari, 2017 ; Yousef et al., 2022 ). So, the work on the energy systems has been expanded to include how the desalination system affects the environment and how much -effectiveness it costs. Environmental and economic approaches afford in-depth insight into the cost analysis of the engineering processes and the environmental impact by recognizing the necessary tools in the work conditions. Considering the abovementioned, exergy-economic and environmental approaches are being rapidly applied to evaluate different solar distillations. Among these works, which have been developed recently, was conducted by El-bar et al. ( 2019 ), where they studied the (4E) exergy-economic, enviro-economic energy, and exergy, analysis for SS systems integrated with the photovoltaic panel. Based on the environmental approach, the results showed that the conventional still mitigated about 18.99 tons of CO 2 per year, whereas the still coupled PV mitigated 20.89 tons of CO 2 .

Yousef and Hassan ( 2018 ) studied the performance of a solar distilled system incorporated with energy storage material (PCM) from exergy-environmental and exergy-economic points of view. According to the findings of this study, it was found that the SS system with the PCM material was found to be greener than the conventional still (without PCM). Recently, Fathy et al. ( 2020 ) assessed the performance of several configurations of single slope SS with condenser and with forced air cooling based on environmental and economic approaches. Moreover, Lovedeep et al. ( 2017 ) analyzed the eco-economic and enviro-economic effects of a solar distillation machine with two basins and several types of nanofluids. The findings showed that there was an increase in annual freshwater yield by 5.2%, 10.4%, and 12% by using CuO, TiO 2 , and Al 2 O 3 nanofluids, respectively. Additionally, the nanofluid of Al 2 O 3 was reported to have a greater enviro-economic parameter than the other varieties of nanoparticles.

More studies enhanced the effectiveness of SS using nanofluids Ravinder et.al ( 2023 ) investigated the effect of TiO 2 /Jackfruit peel nanofluid with silver balls on the performance of a double-effect solar still. The results presented that the highest efficiency was 20% reached when the energy and exergy were equal 40% and 5.6% respectively, while the depth in water was 0.8 Cm. In another study, a simple stepped solar still was modified three times and investigated experimentally to boost the production rate (Adibi Toosi et al., 2023 ). The PCM, hybrid nano, and magnetic field were added separately to CSS and examined. It is concluded that the production was increased by 98%, 75%, and 37% by the magnetic field, hybrid nano, and PCM respectively, compared with CSS.

Based on the literature and regarding the author's greatest survey, it has been found that although the main importance of the theoretical works is to improve the performance of solar stills and optimize their working condition, very few mathematical models of solar stills have been presented in comparison to the vast number of experimental works. Moreover, it is discovered that the majority of the given numerical models of desalination systems have been calculated based on classical derivatives, which leads to a large error when compared to the actual experimental results. Furthermore, hybrid nanofluids have demonstrated their ability to improve various solar energy systems. The traditional numerical methods may sometimes struggle to accurately model solar still systems, leading to discrepancies between numerical predictions and actual results. So, the high motivation behind the applied method is to introduce a new nonlocal numerical method based on fractional differential equations to accurately describe the thermal performance of the SS systems and show precise outcomes about its output from water productivity and efficiencies with and without a hybrid nanofluid.

2 The problem statement and the objective of the study

The problem statement of the present study is divided into two significant points: Firstly, the limited availability of mathematical models for solar stills compared to experimental works presents a challenge in optimizing their performance. To overcome this limitation, this research introduces a novel nonlocal (fractional) model based on the Atangana Baleanu fractional derivative. Secondly, due to the lower productivity of the solar still system, hybrid nanoparticles of (Silicon oxide SiO 2 / Titanium Oxide TiO 2 ) are used with the saline water inside the still basin to enhance its thermal conductivity, and hence increase its output from the fresh water.

The objective of the current research is summarized in three main points as follows:

Addressing the Gap in Theoretical Modeling: The limited availability of mathematical models for solar stills compared to experimental works presents a challenge in optimizing their performance. To overcome this limitation, this research introduces a novel nonlocal (fractional) model based on the Atangana Baleanu fractional derivative. By embracing fractional calculus principles, this model is expected to provide more precise predictions and bridge the gap between theoretical simulations and actual experimental outcomes. With an accurate representation of the solar still system's thermal behavior, researchers and practitioners can gain deeper insights into system performance and optimize its design and operation more effectively.

Harnessing Hybrid Nanofluids for Enhanced Efficiency: Hybrid nanofluids have shown great promise in enhancing various solar energy systems, making them an attractive avenue for improving solar still performance. By incorporating Silicon Oxide (SiO2) and Titanium Oxide (TiO2) nanoparticles into the briny water, the overall efficiency and productivity of the solar still system can be significantly enhanced. These nanoparticles possess unique heat transfer and energy-absorbing properties, contributing to improved performance metrics. The study meticulously explores the influence of hybrid nanofluids on critical parameters, such as temperatures, freshwater yield, energy efficiency, and exergy efficiency. By thoroughly analyzing the impact of these novel nanofluid-based systems, this research aims to unlock their full potential in real-world applications.

In-Depth Comparative Analysis: The research goes beyond conventional evaluations by conducting a comprehensive comparative analysis encompassing energetic, exergetic, economic, and enviroeconomic parameters. This holistic approach allows for a thorough evaluation of the suggested distilled systems both with and without the implementation of hybrid nanofluids. By considering a wide range of performance metrics, the paper provides a comprehensive assessment of the system's effectiveness, efficiency, economic viability, and environmental impact. This multi-dimensional analysis empowers decision-makers with valuable insights to select the most optimized and sustainable approach for solar desalination.

In the present study, the following points summarized the novelty and contributions of the current work: (i) The suggested fractional (nonlocal) model provides more accurate outcomes and a perfect agreement with the actual data compared to the standard model. (ii) The proportion of inaccuracy between the experimental and theoretical data is reduced by the new non-local model. (iii) hybrid nanoparticles of (Silicon oxide SiO 2 /Titanium Oxide TiO 2 ) have been added to the briny water to enhance the thermophysical characteristics of the conventional fluid and hence raise the solar still's water productivity. (iv) Additionally, the hybrid nanofluid contributes to increasing the traditional SS's exergy and energy efficiencies. (iiv) A comparative study is carried out for all the proposed distillation systems with and without hybrid nanofluid, taking into account energy, exergetic, economic, and enviroeconomic factors.

3 Basic definitions

In this section, various and essential definitions of the fractional operators have been presented as follows (Obembe et al., 2016 ; Sales Teodoro et al., 2019 ; Sun et al., 2019 ; Žecová & Terpák, 2015 ):

Definition 3.1.

The Riemann- Liouville (RL) fractional operator of \(T\left(t\right)\) is (El-Gazar et al., Oct. 2023b ):

where \(\Gamma ( \cdot )\) is the common Gamma function.

Definition 3.2.

The Caputo fractional operator of \(T\left(t\right)\) can be described as.

Definition 3.3.

The Atangana-Baleanu (AB) Caputo type is.

Where \(M\left( \alpha \right)\) considers a function satisfied the relation \(M\left(0\right)=M\left(1\right)=1\) .

4 Fractional model

The energy equilibrium formulas for each of the typical SS's three components, a saline water, absorber plate and glass sheet, result in the thermal model represented in Fig.  1 . The temperature in each region of the solar still serves as the basis for the energy equilibrium equations for that component. The energy equilibrium formulas can be stated by the presumptions given in (Abujazar et al. 2016 ; Bait & Si-Ameur, 2018 ; Rashidi et al., 2016 ).

The Schematic diagram for CSS device

4.1 Glass cover equation

The energy emitted from the glass sheet equals the sum of the energy losses. Hence the glass equation can be described by:

where \({{}_{0}{}^{AB}{\mathbb{D}}}_{t}^{\alpha }\) is the Atangana Baleanu fracrional derivative. The heat transfer coefficients between the atmosphere to the glass are \({h}_{rgl-s}\) and \({h}_{cgl-a}\) , respectively, expressed in W/m 2 .K.

Additionally, the heat transfer coefficients for evaporation, radiation, and convection are \({h}_{cw-gl}\) , \({h}_{rw-gl},\) and \({h}_{ew-gl}\) in W/m 2 .K.

4.2 Salty water equation

The energy from the briny water in the desalination system is comparable to the total amount of energy that the briny water transferred to the glass by convective, radiative, and evaporative coefficients. So, the equilibrium formula for the brackish water can be expressed as:

The heat transfer coefficient between the basin and the water is specified by the following equation:

where \({G}_{r}\) , \(pr\) are Grashof and Prandtl numbers, respectively.

4.3 Solar still basin equation

The energy released from the basin can be defined as the summation of the energy transferred out by convection heat transfer between the basin and the salted water, energy loss to the air, and energy accumulation inside the SS absorber. This results in:

where \({H}_{b}\) is the total heat transfer coefficient in W/m 2 .K from the absorber plate to the air.

4.4 Output of the solar still

4.4.1 freshwater yield.

The output of the passive distilled system per hour is calculated by:

Where \(\lambda_{fg}\) and \({H}_{ew}\) are the latent heat and evaporation coefficient of heat transfer between the water and the glass, respectively, and can be assessed by:

where \({T}_{m}=\frac{{T}_{wat}+{T}_{gl}}{2}\) .

4.4.2 Energy efficiency

The conventional SS's efficiency is determined as (Abd Elbar et al., 2019 ; Elbar & Hassan, 2019 ; Hassan et al., 2019 ; Yousef et al., 2017 )

4.4.3 Exergy efficiency

The exergy analysis employs mass and energy conservation concepts (Abujazar et al., 2016 ). Exergy efficiency indeed represents the effectiveness of a system in converting input exergy into useful output exergy. It's commonly defined as the ratio of the exergy output of a process or system to the exergy input, expressed as a percentage, as shown in Sharshir et al. ( 2018 ); Abo-Elfadl et al., ( 2021 ).

4.5 Hybrid nano model

Adding nanoparticles with higher thermal conductivity to fluids, for example Titanium Oxide, Silicon oxide, Carbon Nanotubes, and Graphite, is one of the most substantial techniques for improving the heat transfer process (Hawwash et al., 2016 , 2018 , 2021 ).

4.5.1 The thermal conductivity

The most popular formula that defines the thermal conductivity for the nanofluid mainly depends on Maxwell–Garnett's model (Hassan & Harmand, 2013 ; Yang & Jiang, 2017 ) while in the case of the HNF, the property of conductivity is given by:

where \({K}_{bf}\) and \({K}_{hn}\) , are the thermal conductivities for the base fluid and hybrid nanofluid, respectively, in W/m.K, and \({\emptyset }_{hn}\) is the volume fraction for hybrid nanofluid such that \({\emptyset }_{hn}=\) \({\emptyset }_{\text{SiO}2}+{\emptyset }_{\text{TiO}2}\) .

4.5.2 The density

The density of the nanofluid can be described (Aminossadati & Ghasemi, 2009 ; Hassan, 2014 ) by:

where \({\rho }_{hn}\) describes the density of hybrid nanofluid, \({\rho }_{\text{SiO}2}\) , and \({\rho }_{\text{TiO}2}\) are densities for the Silicon oxide and the Titanium oxide, respectively, in kg/m 3 .

4.5.3 The specific heat

The specific heat of the hybrid nanoparticles (Bourantas & Loukopoulos, 2014 ) is presented by :

where \({{(C}_{p})}_{hn}\) is the specific heat of the hybrid nanofluid and \({C}_{p}\) is the specific heat of nanoparticles in J/kg.K.

4.5.4 The viscosity

The viscosity of the HNF is computed according to Batchelor's formula (Murshed et al., 2008 ) as follows:

4.6 Economic and exergoeconomic assessment

To accomplish the cost study of the distillation system without and with HNF, several parameters were considered, such as the initial cost of the solar still system (Ps), maintenance cost per year (AMC), salvage value per year (ASV), and the interest rate (i) was supposed to be equal 10%. The initial parameter in the cost analysis is the Capital recovery factor (CRF) which can be defined as (Gad et al., 2022 ):

Then, the total operational cost of the distillation system (UAC) per year is estimated by (Gad et al. 2022 ; Yousef et al., 2022 ):

where FAC is the fixed yearly cost that is calculated as the following:

and AMC is the maintenance cost per year, which is assumed to be 15% of the AMC:

The salvage value (S) of the solar still system is an important parameter and is considered by (Refat et al. 2019 ):

SFF and ASV can be assessed according to the subsequent formulations, respectively (Refat et al., 2019 ):

Finally, the price per litre for the solar still system can be computed by (Gad et al. 2022 ; Yousef et al., 2022 ):

where \({P}_{n}\) is the average annual of the produced water from the distillation system.

Due to the importance of the exergy analysis, which considers the real magnitude of thermodynamics and presents an actual measure of the system performance. So, in the current study, the exergoeconomic parameter ( \({R}_{exe}\) ) for all the suggested desalination systems can be assessed by the following relation:

4.7 Environmental and enviroeconomic evaluation

An environmental calculation had to be accomplished by computing the amount of CO 2 realized to the ambient to display the ecological and sustainability result of the MSS on the environment in addition to measuring its environmental superiority alongside the other traditional sources of energy. Therefore, the annual quantity of CO 2 mitigated in tons from the SS systems is set as (Yousef et al., 2022 ):

where \(\emptyset_{{{\text{co}}_{2} }}\) is the parameter of environmental and \({E}_{n}\) is the energy output from the solar still systems throughout the year. The enviroeconomic analysis is estimated as (Yousef et al., 2022 ):

where \({Z}_{{co}_{2}}\) is the parameter of enviro-economic and \({z}_{{co}_{2}}\) is the cost of carbon. The price was expected to be 14.5 $/ton.

5 Numerical solution

In this section, a numerical solution for computing the hourly changes in temperatures for the SS system by Atangana-Baleanu (AB) fractional operator is studied.

To rewrite the model given by Eqs. ( 4 – 8 ) in the sense of the Atangana-Baleanu fractional derivative, we need to replace the classical derivatives in the equations with Atangana-Baleanu fractional derivatives, then we have:

Now, using the following approximation (Atangana & Baleanu, 2016 ), the previous equation will be written as follows:

Use the above approximation. We get the following numerical scheme:

where \(w_{1 } \left( {n,\alpha ,\Delta t} \right) = \left[ {\frac{1 - \alpha }{{M\left( \alpha \right)}} - \frac{\alpha }{M\left( \alpha \right)\Gamma \left( \alpha \right)}\left( {\Delta t} \right)^{\alpha } \left( {\frac{{2\left( {n + 1} \right)^{\alpha } }}{\alpha } - \frac{{\left( {n + 1} \right)^{\alpha + 1} }}{\alpha + 1}} \right) - \frac{\alpha }{M\left( \alpha \right)\Gamma \left( \alpha \right)}\left( {\Delta t} \right)^{\alpha } \left( {\frac{{n^{\alpha } }}{\alpha } - \frac{{n^{\alpha + 1} }}{\alpha + 1}} \right)} \right],\)

and \(M\left(\alpha \right)\) is the Atangana-Baleanu function, where \(M\left(0\right)=M\left(1\right)=1.\) \(\Delta t\) is the time step.

6 Results and discussions

The results and discussion system are divided into two subsections: model validation and the influence of hybrid nanofluid on SS output.

6.1 Model validation

Figure  2 a–c displays a comparison between the hourly trends in glass temperature, freshwater production, and brackish water temperature in the SS basin using the experimental data from Hassan ( 2020 ) and the newly proposed fractional model. Based on the graph, the hourly variation in SS temperatures and SS freshwater production using the AB operator exhibits a remarkable consistency with the actual experimental data. The reason lies in the fact that the non-locality and non-singularity of kernel features, along with a noble memory influence, are considered by the fractional operator. The proposed fractional model simulates the SS behaviour effectively, with a percent of relative error for the greatest values of temperature of the glass, briny water temperature, and freshwater yield being 0.202%, 0.539%, and 0.757%, respectively.

Variation of the solar still temperature and water productivity for the present model and Hassan ( 2020 ) experimental results

6.2 Influence of using hybrid nanoparticles

The CSS suffers from lower productivity and inadequate thermal performance primarily due to radiative and convective heat losses. However, the utilization of nanofluids has emerged as a promising technique to address these limitations. Nanofluids, created by incorporating nanometre-sized additives into a base fluid, exhibit superior thermophysical and optical properties, enabling enhanced heat transfer and decreased heat loss, resulting in increased freshwater production. By employing nanofluids, heat transfer coefficients are elevated, leading to improved performance of solar stills. Hybrid nanofluids, in particular, offer superior heat transfer capabilities in thermal processes, showcasing enhanced thermophysical properties compared to both conventional fluids and mono nanofluids. This research suggests a mixture of SiO 2 and TiO 2 nanoparticles, each at a volume fraction percentage of 0.025%, to be added to saline water. The scientific properties of these nanoparticles are explained in Table  1 .

6.2.1 Influence on Temperatures

The evaporation of salted water and the subsequent production of freshwater in the SS system is positively influenced by boosting the temperature of the briny water. Figure  3 a, b provide a comparison of the hourly variations of the distilled system temperatures during the winter season, both with and without the utilization of hybrid nanofluids. Similarly, Fig.  4 a, b display the same temperature results but for the summer period. These figures also include the atmosphere temperature and incident solar radiation during the measurement periods. Upon examining Figs. 3 and 4 , it is evident that the behaviour of the SS temperatures remains consistent when hybrid nanofluids are employed, resembling the case of using normal saline water fluid. Notably, a comparison of the water temperatures reveals that the presence of hybrid nanofluids leads to higher water temperatures, particularly during the summer season.

Hourly change in SS temperatures in cold climate conditions

Hourly change in SS temperatures in hot climate conditions

The observed temperature increase can be attributed to the introduction of nanoparticles into the briny water, which enhances the thermophysical properties of the base fluid and consequently improves heat transfer, particularly in warm weather conditions, resulting in elevated temperature readings. For example, without the inclusion of hybrid nanoparticles, the maximum water temperatures in winter and summer peak at 47.91 °C and 64.15 °C, respectively. However, with the incorporation of hybrid nanofluids, these temperatures escalate to 50.42 °C and 69.99 °C, respectively, representing a noteworthy increase of 5.23% and 9.1% during the winter and summer seasons, respectively. Moreover, in hot climatic conditions, the peak glass temperature at midday rises from 55.73°C to 62.27°C following the introduction of the hybrid nanofluid, indicating a rise of 6.54°C in hot conditions.

6.2.2 Influence on productivity

The primary objective of the solar still (SS) system is to generate freshwater from saline water by harnessing solar radiation. Figure  5 a, b depict the hourly variations in freshwater productivity during winter and summer, both with and without the incorporation of hybrid nanofluids. It is evident from Fig.  5 that the amount of freshwater is higher in summer compared to winter, attributed to the greater solar insolation and, consequently, higher water temperature during the summer season, as previously explained. Furthermore, the use of hybrid nanoparticles leads to increased productivity in the solar still system as opposed to using only briny water. The maximum hourly values of freshwater production in winter and summer are 0.4253 kg/m 2 and 0.7317 kg/m 2 , respectively, for the system utilizing only saline water, while they reach 0.464 kg/m 2  h and 0.9772 kg/m 2  h, respectively, for the system incorporating hybrid nanoparticles.

Variations of freshwater yield with and without hybrid nano

The observed enhancement in freshwater yield can be ascribed to the improved rates of condensation and evaporation of briny water facilitated by the application of hybrid nanofluids. Detailed results are presented in Table  2 , illustrating the average daily freshwater yield for the solar still system both without and with hybrid nanoparticles. During summer, the daily productivity with hybrid nanoparticles reaches 5.2922 kg/m 2 ⋅day, reflecting a notable increase of 27.2% compared to the still without nanoparticles. In winter, there is a commendable productivity increase of 21.7%, resulting in a daily yield of 3.1295 kg/m 2 ⋅day. Importantly, the amplified freshwater production due to nanoparticle usage is more prominent in summer, aligning with the heightened solar energy availability during that season. This amplification is consistent with the augmented impact of heat transfer enhancement with saline water through nanoparticle utilization, as elucidated in earlier discussions.

6.2.3 Influence on energy efficiency

During this analysis, we analyzed the energy efficiency of SS without and with HNF, both in winter and summer. Figure  6 a, b depict the varying energy efficiency over time, with results showing an increase in energy efficiency from 8 a.m. to close 2 p.m. followed by a gradual decline, similar to the productivity curve. As expected, solar efficiency was still lower in winter than in summer. Furthermore, the use of hybrid nanofluid had a substantial effect on the SS's efficiency, as it increased still productivity, ultimately resulting in higher energy efficiency.

Variations of SS energy efficiency without and with hybrid nano

Results showed that the maximum energy efficiency with and without HNF in summer was 56.06% and 52.25%, respectively, while in winter, it was 29.45% and 26.9%, respectively. This represents an increase of 7.3% and 9.4% in summer and winter, respectively. In Table  3 , we present the average energy efficiency for the distilled system per day without and with HNF in winter and summer. The results demonstrate that in summer, the average efficiency increased by 13.1% when hybrid nano was used, achieving a maximum average efficiency of 43.95%. In comparison, the increase in efficiency in winter was 11.85%. The findings emphasize the potential of using hybrid nanofluid to enhance solar still efficiency.

6.2.4 Influence on exergy efficiency

This section delves into the influence of hybrid nanoparticles on exergy efficiency, a crucial aspect in engineering and thermodynamics for assessing and optimizing energy systems. Unlike traditional energy analysis focusing solely on energy quantity, exergy analysis studies both the quantity and property of energy, making it a powerful tool. Figure  7 a, b illustrate hourly fluctuations of exergy efficiency during summer and winter, respectively, comparing scenarios without and with hybrid nanoparticles. It's evident that exergy efficiency peaks around 1 p.m. and gradually declines. Notably, exergy efficiency tends to be lower than energy efficiency due to accounting for system irreversibilities and losses. Employing hybrid nanoparticles leads to higher exergy efficiency, with a more pronounced impact in summer due to increased solar energy availability. Peak exergy efficiency in summer rises from approximately 4.54% to nearly 5.09% with nanoparticle integration, while in winter, values increase from 3.68% to 4.11%. Table 4 presents average exergy efficiency per day, revealing a notable enhancement of approximately 20.14% in summer and 16.4% in winter with hybrid nanoparticles. This improvement stems from increased freshwater productivity facilitated by hybrid nanofluids, as previously demonstrated.

Variations of SS exergy efficiency with and without hybrid nano

6.3 Cost analysis for n = 10, i = 12%

The economic analysis, presented in Sect.  6.3 for n = 10 and i = 12%, meticulously evaluates the cost per litre (CPL) over a ten-year lifespan for the proposed SS systems during both winter and summer. Table 5 gives a detailed breakdown of the economic assessment. Notably, the incorporation of hybrid nanofluid in the modified solar still demonstrates a substantial reduction in CPL values compared to the CSS in both seasons. During summers, the CPL value for the modified SS with HNF is remarkably low at 0.0156 $/L, presenting a significant cost decrease of over 44% compared to the conventional still (0.0225 $/L). This reduction in CPL is attributed to the considerable enhancement in annual freshwater productivity resulting from the integration of hybrid nanofluid. The observed seasonal variation in CPL, with lower values during summer than winter, is primarily influenced by more favorable weather conditions and increased freshwater productivity in the former season.

6.4 Calculations of exergoeconomic parameters for n = 10, i = 12%

Exergoeconomic analysis plays a vital role in assessing the total efficiency and economic viability of energy systems. By combining the principles of thermodynamics and economics, engineers and policymakers enable to prioritize energy optimization strategies and make informed decisions regarding energy investments. The tabular representation of the calculation of R exe for both the MCC and CSS systems across various seasons, i.e., summer and winter, is depicted in Table  6 . On keenly observing the table, it becomes apparent that the MCC system, which utilizes a hybrid nanofluid, outperforms the CSS system in terms of R exe for both summer and winter. As an example, the R ex for the MCC and CSS systems in summer is calculated to be 6.605 (kWh/$) and 4.47 (kWh/$), respectively. This variance in R exe indicates that the former system outperforms the latter by approximately 47.7%. This improvement in R exe can be attributed to a minor increase in the UAC of the MCC system. However, its significant effect on the annual exergy output surpasses the decrease in UAC, resulting in a higher exergoeconomic parameter. Nonetheless, during winters, this increase of R exe with respect to the MSS system witnesses a slight reduction of 15.1%, as opposed to summers, due to a decrease in freshwater production enhancements.

6.5 Environmental and enviroeconomic analysis

Environmental and enviroeconomic analyses are of paramount importance when it comes to an understanding and mitigating CO 2 emissions, which are a major contributor to climate change. The environmental analysis focuses on assessing the mitigating CO 2 emissions. Enviroeconomic analysis, on the other hand, combines environmental factors with economic considerations to evaluate the costs and benefits associated with reducing CO 2 emissions. This analysis aids policymakers, businesses, and individuals in making informed decisions by highlighting the environmental and economic trade-offs and identifying the most effective and economically viable pathways to reduce CO 2 emissions. Table 7 provides a comparative overview of summer and winter environmental and enviro-economic evaluations conducted using energy and exergy methodologies. In terms of the environmental approach, the findings indicate that during summer, CSS and MSS mitigated 16.38 and 18.47 tons of CO 2 /year, respectively.

The exergy-environmental approach, on the other hand, found these values to be 1.68 and 2.62 tons CO 2 /year, respectively. These results reveal that MSS mitigated about 12.7% more CO 2 mitigation during summer when compared with CSS based on energy approaches. This trend is owing to the higher energy generated by MSS than the embodied energy integration of hybrid Nanofluid, resulting in increased CO 2 mitigation. Similarly, the findings based on the exergy approach suggest that MSS mitigated approximately 56.2% more CO 2 compared to CSS. Wintertime results show that compared to CSS, MSS mitigated approximately 29.6% and 22% more CO 2 based on energy and exergy approaches, respectively. Additionally, it is noteworthy that the addition of hybrid nanofluid to solar still significantly improved the enviro-economic parameter, as highlighted in Table  7 . In summer, the enviro-economic parameter for CSS and MSS was 237.6$ and 267.84$, respectively, According to the energy approach. The exergy-environmental approach produced equivalent values of 24.355$ and 38.05$, respectively.

7 Conclusion

The influence of titanium oxide (TiO 2 ) and silicon oxide (SiO 2 ) hybrid nanoparticles on the solar still performance (SS) is studied by applying a new numerical method based on the Atangana- Baleanu (AB) fractional operator. In addition, a comparison is conducted between the numerical findings of a fractional model and experimental data for the climate of Upper Egypt. The findings indicate that a fractional model corresponds to the actual experiment. It indicates that the error percentage in the extreme value of freshwater yield reaches approximately 0.757%. According to the fractional approach, the results demonstrate that the addition of hybrid nanoparticles to the solar still has a substantial influence on it in terms of boosting the quantity of freshwater production and enhancing both exergy and energy efficiency, with the winter impact being less pronounced than the summer impact. It has been shown that utilizing hybrid nanoparticles with the saltwater of CSS increases the production by approximately 27.2% in Summer and 21.7% in Winter. Additionally, its average daily efficiency increases to approximately 21.1% and 43.95% in winter and summer, respectively. In cold and hot climates, the average exergy efficiency of the SS per day is increased by 16.4% and 20.14%, respectively, when nanoparticles are added to saline water. An economic investigation showed that in the summer, SS with hybrid nanofluid reported a cost-per-liter reduction of over 44% compared to CSS. In terms of enviroeconomic analysis, findings indicate that SS with nanofluid mitigated approximately 12.7% more CO 2 during the summer than CSS based on energy approaches. Whereas, Wintertime results indicate that SS with nanofluid mitigated nearly 29.6% and 22% more CO 2 than CSS using energy and exergy approaches, respectively. For the future work, the effect of using HNF in active and passive SS should be investigated.

Our study has significant implications for key stakeholders. Policymakers can leverage hybrid nanofluids to improve solar still performance and promote sustainable freshwater production through supportive policies and funding. Academics can advance research in solar energy and nanofluid applications using our novel fractional model. Additionally, our findings offer valuable insights for researchers and businesses in renewable energy, highlighting the economic and environmental benefits of integrating hybrid nanofluids into solar still systems and suggesting avenues for commercialization and scale-up efforts.

Abbreviations

Atangana- Baleanu

Annual Maintenance Cost

Annual Salvage Value

Cost Per Liter

Conventional Solar Still

Capital Recovery Factor

Hybrid Nanofluid

Modified Solar Still

Sinking Fund Factor

Total Annual Cost

Area in m 2

Specific heat in J/kg.K

Solar irradiance in W/m 2

Heat transfer coefficient in W/m 2 .K

Evaporation coefficient of heat transfer

Thermal conductivity W/m.K

Capital Cost in $

Temperature in °C

Time in second

Wind velocity in m/s

Volume fractional

Density in kg/m 3

Order of fractional derivative ( \(0<\alpha \le 1)\)

The latent heat of vaporization

Absorber Plate

Evaporation

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El-Gazar, E.F., Yousef, M.S., Elshaer, A.M. et al. Enhancing solar still performance with hybrid nanofluid: a comprehensive assessment of energy, exergy, economics, and environmental impact using a novel fractional model. Environ Dev Sustain (2024). https://doi.org/10.1007/s10668-024-05304-y

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DOI : https://doi.org/10.1007/s10668-024-05304-y

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