Water is the most significant and essential matter for advancing the lives of humans. It is a valuable natural endowment and a significant renewable supply with inherent benefits for human communities. Today, access to potable, clean, and healthful water is the most essential requirement for people in many countries. In some situations, extraordinarily pure water is needed, such as in laboratories, hospitals, and the chemical and medical industries, etc. Contamination it transforms potable water into polluted water with potentially dangerous consequences for humans and our planet, as it could destroy people and other creatures. In the villages of many countries, people have begun to use underground water during droughts since freshwater resources have dwindled or ended. The groundwater supply in developing countries is being reduced at a more accelerated rate compared with developed countries. One of the human and significant reasons for contaminating underground water is applying extreme amounts of chemical fertilizers and pesticides in agriculture. To reuse contaminated and dirty water or desalinate saline and seawater, scientists and researchers are exploring innovative methods and technologies. They have developed methods and technologies to produce potable and pure water from resources that must be ecosystem-friendly with the least cost to nature and humans to not repeatedly pollute the environment. Recent technologies for desalination processes generally utilize high energy to provide potable water from seawater by separating impurity and solid particles from seawater. These technologies operate based on state change or filtering with membrane processes such as vapor compression, multiple effect distillation, multi-stage flash distillation, reverse osmosis, and electro-dialysis to treat saline water. These technologies are often not efficient and cost-effective due to the complexity of environmental pollution, the need for highly skilled services, and maintenance.

Employing solar radiation to supply freshwater for human utilization and industry from brackish water as an ecosystem-friendly energy source is a hopeful and intelligent choice instead of fossil fuels. Compared with other desalination processes, it has the advantages of free-cost resources and low-cost maintenance and service. Numerous styles and types of designs, fabrication substances, geometries, and configurations are used in solar stills all over the world by researchers. For rural, remote, and desert regions, the most efficient and suitable solar still is a unit that is small, uncomplicated, and self-governing. These units can help rural and remote communities to provide pure and healthy water at remarkably lower costs. Compared with other solar desalination units and systems, solar is more simplistic, portable, convenient development, scalable, easy to build that can produces distilled water for human consumption. The only problem with solar still technology is the daily productivity requirements of covering human demands, although researchers are working on it. In this regard, various solar still arrangements have been designed and constructed in recent years. Their performance, in the form of experimental and theoretical methods of improving and modifying them have been explored in a number of published articles. However, to change, modify, or redesign the experimental setup and enhance performance or study the influence parameters, experimental investigations require higher costs and time compared with theoretical studies; hence, theoretical investigations have general flexibility to examine changes. Theoretical research can analyze the significant parameters and details of solar stills, more quickly and simply to find the best performance and efficiency.

Thermal modeling is one of the most cost-effective and established theoretical methods used to assess the performance of a thermal system. In a solar still, the energy balance of the employed ingredients is utilized for thermal modeling. Thermal modeling precisely exhibits the performance of the solar still under real climatic conditions. Based on this, different thermal models have been proposed and implemented for solar still research. However, due to operational difficulties and less productivity than the prognosticated amount, the proposed models are not fit for real situations. Furthermore, during the study and design of the solar still, a distinct platform is not utilized. Hence, to recognize and propose this technology to market for use in remote regions, a basic and comprehensive study needs to consider different theories, modeling, and designs of solar stills. Usually, researchers try to investigate the meaningful topic, detail, and parameters from their point of view. There is a serious lack of reviews collecting all of points of view, bringing together effective details and information about appropriate configurations and conditions for each issue. This comparison would provide guidance and suggestions to others for improvement. Thereby, this work summarizes significant and effective theoretical papers, examining the methodologies, approaches to solving problems, and substantial improvements in theoretical studies on solar stills. It accurately analyses various thermal models and theoretical studies to present a detailed review of solar stills. The meaningful parameters and corrections on the technology of solar stills regarding thermal modeling development are analyzed precisely, and new outlines are suggested for subsequent investigations. As an introduction, the next section explores solar still systems and the basic rules used to produce potable water from a contaminated source.

The goal of this review is to provide a novel, significant, and original way to mathematically describe a solar still. This study shows genuine breakthroughs and advancements in solar stills in a theoretical form. It also offers remarkable, advanced modeling of a solar still with accurate relationships.

In this section, the simplest design of solar stills, namely the single basin single slope, is considered in comparison to other solar still systems to create thermal concepts and drive relevant equations. This work provides a thorough view of thermal modeling, as well as quick recognition of numerous theoretical solar still modeling and basic solar still relationships. The thermal model is obtained using the energy balance equation for the single basin single slope solar still components, including the basin, upper cover, and brackish water. To make working with equations easier, the energy balance for each component is written based on the average temperature of that component. To summarize, the area of each solar still component is equaled and included in the other units of that component. Furthermore, the following suitable assumptions are taken into account for the most exact modeling:

• All processes in the solar still are considered to be in a quasi-steady state.

The following is how the energy balance is applied to the main components (Tiwari et al., 2007; Sampathkumar et al., 2010; Elango et al., 2015; Sahota and Tiwari, 2017).

Ali et al. (2015) report theoretical and practical work on a solar still with a pin-fin absorber plate. The distillation of brackish water by the solar still with a regular absorber plate and a pin-fin absorber plate was examined. The energy balance was used for the main parts of the active solar still as follows (Ali et al., 2015): α u c I + Q c , b w − u c + Q e , b w − u c + Q r , b w − u c − Q c , u c − a + Q r , u c − a = ( m C p ) u c d T u c d t (50) α b w ε uc I + Q c , b − b w − Q c , b w − u c − Q e , b w − u c − Q r , b w − u c − Q f w − Q l o s s , s w − a = ( m C p ) b w d T b w d t (51) α b ε uc ( 1 − α b w − β b w ) I + Q c , b − b w − Q l o s s , b − a = ( m C p ) b d T b d t (52)

They used the convective and evaporative heat transfer coefficients proposed by Dunkle (Eqs 6, 18). However, the heat loss coefficient was calculated using the following equations (Anderson, 1983) for wind speeds (V) greater than 5 m/s (Ali et al., 2015): h c , u c − a = 6.15 V 0.8 (53)

Furthermore, the convective heat transfer coefficient between the basin liner and brackish water was considered to be 120 and 150  W / m 2 K for the regular and modified absorber plates, respectively. They also utilized Eq. 12 to estimate the temperature of the sky. There is reasonable concordance between experimental and theoretical results. Experimental and theoretical investigations demonstrate that a still with pin-fin absorber plate outperforms a regular one. However, the difference in performance between regular and modified solar still is marginal. This is owing to the little variation in their surface areas available for exchange. Compared to a regular solar still, the daily productivity of the modified example with a pin-fin absorber plate is enhanced by 12%.

Alaudeen et al. (2015) studied theoretically and experimentally a single-slope solar still with a glass basin including two compartments, the upper and lower compartments as evaporating and heating zones, respectively. The lower compartment consists of glass strips for heat storage materials to increase performance. In addition, aluminum cubes and sponges were designed to float in the upper compartment. Their results showed that the unit with the corrugated sheet has higher efficiency. They modeled the unit by using simulation software. In the theoretical modeling section, the transient form of energy balance was used for the basin as follows (Alaudeen et al., 2015): I α b − Q c , b − b w − Q l o s s = m b C p , b d T b d t (54)

The convective heat transfer coefficient between the basin and brackish water and the heat loss from the basin to the atmosphere was assumed to be 135 and 14  W / m 2 K , respectively. Equation 6 (Dunkle’s relation) was used as a convective heat transfer between brackish water and the upper cover, and Eq. 18 as an evaporative heat transfer from the basin to the upper cover. The following correlation gives the latent heat of evaporation for water at a specified basin water temperature (°C) (Alaudeen et al., 2015). h f g = 1000 ( 2503.3 − 2.398 T ) (55) In addition, at a specific temperature, the partial pressure of water vapor in the air was determined as follows (Alaudeen et al., 2015): p = 7235 − 431.43 + 10.76 T 2 (56)

The air specific heat capacity between the upper cover and the basin was estimated using the following correlation in terms of average temperature (Tav in °C) (Alaudeen et al., 2015) C p = 999.2 + 0.14339 T a v + 0.0001101 T a v 2 − 6.7581 e ( − 8 ) T a v 3 (57)

The immediate water output was offered by (Alaudeen et al., 2015), m e = h e , b w − u c ( T b w − T u c ) h f g (58)

The time interval was initially set to 5 s, and the temperature of the water, glass, and plate is considered to be the atmosphere. The parameter change for the subsequent time step is rewritten as follows (Alaudeen et al., 2015): T u c = T u c + d T u c (59) T b w = T b w + d T b w (60) T b = T b + d T b (61)

Their results showed that corrugated sheets yielded the highest distilled water at 2.64 kg/m2, which is almost 43% higher than the conventional unit. The cost of producing each liter of drinkable water, including mineral additives, was about $0.2. Furthermore, the cost of material and manufacturing for a 1 m² galvanized iron basin was about $83, but the cost of utilizing a glass basin was about $25.

Rajaseenivasan et al. (2016) investigated theoretically and experimentally a glass basin, which was divided into two sections, including preheater (lower) and evaporator (upper) sections by a glass plate. They applied energy storing materials in five rectangular hollow glasses as fins in the preheater section. The effects of preheater depth and energy storage materials on solar still performance were investigated. Their results showed that increasing water depth causes productivity to decrease and enhances nocturnal productivity. Charcoal as an energy storage material augments the total distillate output by up to 3.61 kg in a day. In the preheater and middle glass, they employed the energy balance as follows (Rajaseenivasan et al., 2016): I A w p , e f f α w p ε u c ε w e ε m g + Q c , b − w p − Q c , w p − m g − Q f , w p = m w p C w p d T w p d t (62) Where A w p , e f f = A w − A s h and A s h = n f i n [ H f i n l s h ⁡ sin ⁡ θ   + H f i n l s h ⁡ cos ⁡ θ   − l s h 2 ⁡ sin ⁡ θ   cos ⁡ θ   (Rajaseenivasan et al., 2016)]. I A m g α m g ε u c ε w e + Q c , w p − m g − Q c , w p − w e = m m g C m g d T m g d t (63) I A w e α w e ε u c + Q c , m g − w e + Q f , w e − Q c , w e − u c − Q e , w e − u c − Q r , w e − u c = m w e C w e d T w e d t (64)

They used Dunkle’s relations for convective and evaporative heat transfer coefficients. The time interval in this study was set to 10 s, and all of the parameters were evaluated on the day of the experiment. For the next step, Eqs 59–61 were employed. They observed that reducing the water depth from 8 to 2 cm increases the system’s daily production from 3.12 to 3.25 kg/day. The highest night distillate is 1.27 kg/m² for the glass basin solar still with charcoal and 0.46 kg/m² for the conventional solar still. The highest output improvement was 26.74, 29.3, and 33.7% in the glass basin solar still utilizing river sand, metal trash, and charcoal, respectively.

Karimi Estahbanati et al. (2016) conducted both experimental and theoretical studies on the issue of using an internal reflector (IR) on the productivity of a single-slope solar still. The effect of all of the solar still’s walls, including those to the north, south, west, and east of the still, on the amount of gotten solar radiation to brine is modeled in their model. They proposed the following energy balances for the main components of solar still (Karimi Estahbanati et al., 2016): Q s u n , u c + Q c , b w − u c + Q e , b w − u c + Q r , b w − u c − Q c , u c − a + Q r , u c − a = ( m C p ) u c d T u c d t (65) Q s u n , b w + Q b − b w − Q c , b w − u c + Q e , b w − u c − Q r , b w − u c = ( m C p ) b w d T b w d t (66) Q s u n , b − Q b − b w − Q b − a = ( m C p ) b d T b d t (67)

Based on the amount of shape factors between the wall-brine surface and cover-brine surface, the received diffuse solar radiation reaches brackish water and walls. As a result, the solar energy received by the solar still components can be stated as follows:

Upper cover (Karimi Estahbanati et al., 2016): Q s u n , u c = ( I B + I D ) A u c α u c + I B ( S 2 F e u c + S 1 F k u c ) ε u c β d l α u c + ( I B ( A u c − ( S 1 + S 2 ) ) + I D A u c F u c b w ) ε u c α u c F b w u c ( β w + ε u c 2 β b ) + I D A u c ε u c α u c β t l ( F u c k F k u c + 2 × F u c e F e u c + F u c f F f u c ) (68)

Basin liner (Karimi Estahbanati et al., 2016): Q s u n , b = I B ( A u c − ( S 1 + S 2 ) ) ε u c ε b w α b + I B ( S 1 ( β s l + β d l F e b w ) ε u c ε b w α b ) + S 2 ( β s l + β d l F k b w ) + I D A u c ε u c ε b w α b ( F u c b a + ρ t l ( F u c k F k b w + 2 × F u c e F e b w + F u c f F f b w ) ) (69)

East wall (Karimi Estahbanati et al., 2016): Q s u n , e = I B S 2 ε u c α e + I D A u c ε u c α e ( F u c e + β t l ( F u c t F t e + F u c k F k e + F u c f F f e ) + F u c b w F b w e ) (70)

Back wall (Karimi Estahbanati et al., 2016): Q s u n , k = I B S 1 ε u c α k + I D A u c ε u c α k ( F u c k + β t l ( 2 × F u c e F e k + F u c f F f b w ) + F u c b w F b w k ) (71)

West wall (Karimi Estahbanati et al., 2016): Q s u n , t = I B S 2 ε u c α t + I D A u c ε u c α t ( F u c t + β t l ( F u c e F e t + F u c k F k t + F u c f F f t ) + F u c b w F b w t ) (72)

Brackish water (Karimi Estahbanati et al., 2016): Q s u n , b w = α b w × Q s u n , b τ u c α b (73)

Their mathematical approach determines incident irradiance, calculates the productivity of solar stills with IRs installed on various walls, and takes into account the influence of all basin walls. Their model can accurately anticipate the trend of experimental data by comparing theoretical data with current experimental results. Their findings reveal that placing IR on the front, side, and rear walls boosts solar still efficiency by 18, 18, and 22% on all days of the year, respectively. Furthermore, installing IR on all walls increases productivity by 65, 22, and 34% during the winter, summer, and full year, respectively.

Panchal and Thakkar (2016) theoretically and experimentally studied a solar still coupled with evacuated tubes. They used fourteen double-walled hard borosilicate glass tubes inclined at an angle of 45° from the horizontal. They managed to make the outer tubes transparent and coated the inner tubes to absorb solar radiation as much as possible. They wrote the energy balance of brackish water in solar still coupled with evacuated tubes as follows (Panchal and Thakkar, 2016): α b w ( 1 − α u c ) I + h t o t a l , u c − b w ( T u c − T b w ) + Q u − h t o t a l ( T b w − T u c i ) = m b w C b w d T b w d t (74a) When the heat acquired by evacuated tubes ( Q u ) was calculated, it was found to be (Panchal and Thakkar, 2016): Q u = F R [ ( α ε ) e t I e t − U L e t A s s A e t ( T b w − T a ) ] (74b) Where ( α ε ) e t was intended to be 0.87. They discovered that actual and theoretical outcomes of an evacuated tube coupled with solar still were quite comparable in both summer and winter climate conditions. In the solar still, polyurethane foam type (5 cm) was utilized as insulation with better thermal resistance. The evacuated tubes coupled with solar still generated distilled water not only during the day but also at night.

El-Naggar et al. (2016) investigated experimentally and theoretically conventional single-basin solar still with a finned-basin liner. They used appropriate programs to optimize and predict the thermal performance of the systems under consideration. The daily distilled water of conventional and modified units was seen to be 4.235 and 4.802 kg/m²d, respectively, with daily efficiency of 42.36 and 55.37%. Their findings revealed that the convective heat transfer coefficient of the finned one was 3.6 times higher than the conventional one. The findings revealed that there is a reasonable agreement between measured and calculated daily productivity. The fee for 1 L of distilled water was determined to be 0.018 $.

When analyzing the energy balance for the basin, the fin shadow area affects the solar radiation intensity acquired by the still basin. They estimated the shadow area of the fins using the method described by Jaefarzadeh (Jaefarzadeh, 2004). The following equation was used for the shadow area caused by one fin (El-Naggar et al., 2016): A s h = H f l s h ( sin ⁡ φ + cos ⁡ φ ) − l s h 2 ⁡ sin ⁡ φ ⁡ cos ⁡ φ (75) Where (El-Naggar et al., 2016), φ = sin − 1 ⁡ cos ⁡ θ v / sin ⁡ θ i (76) For the basin with fin shadow effect, the energy balance equation is as follows (El-Naggar et al., 2016): ε u c α b w I A b w , e f f + h c b ( T p , f − T b w , f ) − h c A b w ( T b w , f − T u c i , f ) = ( m C ) b w d T b w d t (77) Where the convective heat transfer coefficient is as (El-Naggar et al., 2016): h c b = ( 0.54 K b w d s ( G r . Pr ) 0.25 ) A p , e f f + ( 0.8 K b w d b w ( G r . Pr ) 0.25 [ 1 + ( 1 + 1 p r 0.5 ) 2 ] − 0.25 ) A f η f (78)

The finned basin liner’s energy balance equation is as follows (El-Naggar et al., 2016): ε u c α b w α p I p f + h c b ( T p , f − T b w , f ) − U b A b ( T p f − T a ) = ( m C ) p f d T p f d t (79) Where the total solar radiation incident on the finned basin liner and the total mass of the basin liner and fins are as (El-Naggar et al., 2016): I p f = ( I f , b w A f 2 ) + ( I f , e A f 2 ) + ( I t A p , e f f , s h ) (80) m p = ρ p ( A p x p + n f l H f x f ) (81) Compared to a conventional unit, the unified fins with the basin produced 11.8% more distilled water and had 23.5% higher daily efficiency.

Tanaka( 2016) combined vertical multiple-effect diffusion solar still and tilted wick still to analyze solar still unit theoretically. He designed vertical multiple-effect diffusion solar still to have a series of vertical and parallel partitions and a double glass cover in contact with saline-soaked wicks with narrow air gaps between the partitions. The moisture-rich layers of air in the tilted wick still and the multiple-effect still were considered to be connected. As a result, water vaporized from the wick of the tilted wick still can gradually move to the humid air layer between the inner glass cover and the first partition of the multiple-effect still. They considered adding heat to the multiple-effect solar still by using the latent heat of condensation on the front surface of the first partition.

The energy balance for the tilted wick section’s wick and the first partition of the multiple-effect section (p1) may be stated as (Tanaka, 2016): Q d r , w + Q d f , w − Q ( c + m ) w − h a − Q r , w − g t i − Q d , w − a = Q f , w (82) Q d r , p 1 + Q d f , p 1 + Q ( c + m ) , h a − p 1 − Q r , p 1 − g m i − Q ( r + d + e ) , p 1 − p 2 = Q f , p 1 + ( m C p ) p 1 d T p 1 d t (83) Except for the first (p1) and last (pn) partitions, the energy balance for ith partition pi may be represented as (Tanaka, 2016): Q ( r + d + e ) , p ( i − 1 ) − p i − Q ( r + d + e ) , p i − p ( i + 1 ) = Q f , p i + ( m C p ) p i d T p i d t (84)

Radiation and convection mechanisms are used to release energy to the environment from the last partition (pn). This may be phrased in the following way (Tanaka, 2016): Q ( r + d + e ) , p ( n − 1 ) − p n − Q ( r + c ) , p n − a = ( m C p ) p n d T p n d t (85)

The heat transfer coefficient of forced convection from the outer plates to the ambient air in this study was determined using Eq. 20. The following relations were applied to estimate the convective heat and mass transfer between the humid air layer and the enclosing inner surfaces of both sections and the heat and mass transfer coefficients on the surfaces (Aihara, 1986): N u = 0.022 R a 2 / 5 (86) S h = 0.022 ( R a . L e ) 2 / 5 (87) R a = g l 3 Pr ν 2 ( T 1 T 2 − 1 )   (88)

The following is an expression of the heat transfer rate of mass transfer between the partitions (Bird et al., 1966): Q e , p i − p ( i + 1 ) = h l D P t o t a l R δ g p T m e a n ln ( p t o t a l − p s ( T p ( i + 1 ) ) p t o t a l − p s ( T p i )   ) (89)

The temperature differential between the humid air layer and each condensing surface determines the condensation ratio on the three internal condensing surfaces of the humid air layer. On three typical days including the spring, summer, and winter, and considering 5 mm as the diffusion gap between partitions and using 10 partitions, total daily distillate production was indicated to be approximately 19.2, 16.0, and 15.9 kg/m2d, respectively.

Sivakumar et al. (2016) developed a mathematical model that took into account the influence of the basin’s heat capacity and the glass cover on the performance and exergy destruction of typical solar still. The energy balance for the glass cover and the basin is then outlined below, taking into account their heat capacity (Sivakumar et al., 2016). I ( t ) ( 1 − β ) α uc + ( h c , b w − u c + h e , b w − u c + h r , b w − u c ) ( T b w − T u c ) − ( h c , u c − a + h r , u c − a ) ( T u c − T a ) = ( m c ) u c d T u c d t (90) I ( t ) ( 1 − β ) ( 1 − α uc ) ( 1 − α bw ) α b − h c , b − b w ( T b − T b w ) − K i n s L i n s + K w o o d L w o o d + h c , w o o d − a ( T b − T a ) = ( m c ) u c d T u c d t (91)

It was discovered that the cumulative yield when heat capacity is taken into account (2.02 kg/d) is higher than the obtained yield when heat capacity is not taken into account (1.8 kg/d). The increased cumulative production when heat capacity is taken into account may be attributed to the heat storage capacity of the basin, which raises the yield. When heat capacity is factored in, the total yield of solar energy increases by 10.38%.

Sherif et al.( 2016) used an unsaturated porous medium (sand) that was initially saturated by saline water, as well as the use of a focusing reflector to increase the productivity of solar stills. They concentrated on the porous media mathematical model and its solution through a finite volume technique. They utilized the terms absorbed/scattered solar energy and water vapor source/sink. The porous media was added to the double slope solar still (DSSS) system (sand). The porous medium, humid air region, and glass coverings are the three systems that make up the physical model. Each system has its own set of subsystems, such as scattering and absorbing models, evaporation models, capillary models, and crystallization models in the case of porous media. The gas absorption model is part of the humid air region system. As a sub-system, the glass cover system using the absorption model is used. Solar flux and ambient temperature are calculated throughout the day using solar radiation and ambient temperature models, respectively. Solar radiation on the horizontal and inclined surfaces was calculated using Ashrae clear sky model (Elsayed et al., 1994). In this study, the porous medium is thought to be a semitransparent medium for solar energy, which results in diffuse radiation. Internal reflection and scattering are also taken into account. The size of local intensity has been determined experimentally to vary with the variation in intensity at any point (Rababa’h, 2003). Absorption and scattering in sand layers are used to calculate the energy absorbed by every element inside the porous medium. The J-function (Leveret-function) (Kaviany, 2012) was employed in the capillary pressure equation. The energy balance in the porous medium mathematical model was written as follows (Sherif et al., 2016): − ∂ ∂ z ( − K e f f ∂ T ∂ z ) − ( m ˙ l ″ C p l + m ˙ v ″ C p v + m ˙ a ″ C p a ) ∂ T ∂ z − m ˙ e v p ″ h f g − m ˙ c r s ″ h c r + q s o l o 1 ″ γ e f f ⁡ exp ( − γ e f f ( L − z ) ) = ( ρ C p ) e f f ∂ T ∂ t (92)

The following is the energy balancing equation for east or west upper cover sides, taking each side orientation into account (Sherif et al., 2016): ∂ ∂ z ( − K u c ∂ T u c ∂ z ) + ∂ ∂ z ( q s o l o ″ e − γ u c L 1 − Z 1 cos ⁡ θ 2 ) − ∂ ∂ z ( q r e f l e c ″ e − γ u c Z 1 ) = ( ρ C p ) u c ∂ T u c ∂ t (93)

The second and third terms in the above equation are the solar radiation absorbed in the upper cover thickness through both sides of the upper cover, and the solar radiation absorbed in the upper cover thickness that is transferred from the humid air region, respectively. The thickness of the sand has been discovered to have a considerable impact on solar still production. When the solar flux was high, the porous medium of a large size produced more distillate, while the porous medium of a small size produced more distillate when the solar flux was low. The solar still productivity improved when a compound parabolic concentrator was added to the porous medium; the increase was 56 and 38.5% in the winter and summer, respectively.

In their evaluation, Al-Sulttani et al. (Al-Sulttani et al., 2017) compared a double-slope solar still hybrid with rubber scrapers (DSSSHS) to a conventional double-slope solar still. The suggested DSSSHS design takes advantage of employing a slight slope in the solar still’s condensing cover, which enables more solar radiation to enter the still. The rubber scrapers are used to overcome the drawbacks of utilizing a small slope. The theoretical values of convective and evaporative heat transfer coefficients, as well as theoretical values of the yields, were determined considering experimental measurements. They calculated convective heat transfer from water to glass cover using the temperature-dependent physical characteristics of humid air provided by (Jain and Tiwari, 2003) as follows: K = 0.0244 × 0.7673 × 10 − 4 T v (94) β = 1 T v (95) ρ v = 353.44 T v (96) μ = 1.718 × 10 − 5 + 4.62 × 10 − 8 T v (97) C v = 999.2 + 0.1434 T v + 1.101 × 10 − 4 T v 2 − 6.7581 × 10 − 8 T v 3 (98)

The following is the energy balance equation for brackish water that exchanges energy as heat with the basin liner, upper cover, and the atmosphere (Al-Sulttani et al., 2017). H b w ( t ) + q c , b − b w − q c b w − q e b w − q r b w = ( m C p ) b w d T b w d t (99) Where H b w ( t ) is the amount of solar energy absorbed by brackish water as a proportion of total solar radiation. The following equations [56] were used to calculate the convective heat transfer coefficient from the basin liner to brackish water: h c , b − b w = 0.54 × K b w R a b w 0.25 L b w   10 4 < R a < 10 7 (100) h c , b − b w = 0.15 × K b w R a b w 0.25 L b w   10 4 < R a < 10 7 (101) They used the following form of the energy balance equation for the basin (Al-Sulttani et al., 2017): H b ( t ) − q c , b − b w − q b − a = ( m C p ) b ∂ T b ∂ t (102) Where H b ( t ) is the amount of solar energy absorbed by the basin as a proportion of total solar radiation. Rubber scrapers improved the total internal heat transfer coefficient and productivity in the DSSSHS model. For the situation when the slope of the upper cover is relatively small (approximately 3.0°), the maximum measured value of the total internal heat transfer coefficient for the DSSSHS is 38.754 W/m2 °C, and the daily productivity is 4.24 L/m2d with a productivity improvement of 63%. Rubber scrapers also prevented re-evaporation and the condensate accumulated and left for a longer time period on the inner surface of the upper cover from falling.

Madhlopa (2017) explored different evaporative heat transfer coefficients using view factors from radiative heat exchange. The first model employed the concentration ratio, which is dependent on various thermodynamic factors within solar still (Tsilingiris, 2009). Equations 103, 104 (Madhlopa, 2017) shows convective and evaporative heat transfer coefficients, which are used to compute the concentration ratio in the first model. The concentration ratio, as shown in Eq. 105 (Madhlopa, 2017), is a ratio of the evaporative heat transfer coefficient to the convective heat transfer coefficient. In the first model, the concentration ratio is determined by the temperature-dependent specific heat capacity of air, specific latent heat of vaporization, and partial vaper pressure. h c ,   b w − u c = b K a Z 3 d − 1 ( g ρ a β a μ a α a ) [ ( T b w − T u c ) T b w ( P b w − P g ) ( M a − M v ) M a P t o − P w ( M a − M v ) ] d   (103) h e , b w − u c = 1000 H h c ,   b w − u c R a P t o C p , a R v ( P t o − P b w ) ( P t o − P u c ) (104) C r = h e , b w − u c h c ,   b w − u c (105) The study relied on the thermophysical parameters of a binary mixture. For realistic solar still applications, they discovered that d = 1/3 may be utilized in a wide range of operating temperatures, and b = 0.075 when the rate of distilled is less than 10 − 4   k g / m 2 ⁡ s , and b = 0.05 for greater distillate yields.

The concentration ratio in the second model is a function of the third-order polynomial of the solar still’s operating temperature (Rahbar and Esfahani, 2013). The following is a suggested polynomial function for the concentration ratio: C r = 0.035 + 0.058 T i + 2.5   × 10 − 4 T i + 4.23 × 10 − 5 T i   308.15 < T i < 358.15 (106)

Results revealed that in the first model, the concentration ratio has a critical value whereas, in the second model, it does not have a turning point in the temperature range under consideration. The concentration ratio of both models is the same at the stated operating temperature. In constrained situations, his results demonstrated that the quantity of evaporative heat transfer coefficient employed by the first model is higher than that of the second model. Furthermore, the root mean square error obtained with the first model was smaller than that produced with the second model.

Abu-Arabi et al. (2018) presented a model to study the solar still, which is connected to an external solar collector and consists of Sodium Thiosulfate Pentahydrate as a phase change material (PCM). They found that a high mass of PCM causes less productivity as the productivity decreases by up to 30% by increasing the PCM to water mass ratio from 10 to 100. While the basin water temperature was higher for a higher prolonged time by comprising considerable PCM mass in the system. They showed that over the outer side of solar still, decreasing the overall heat transfer coefficient from 10.4 to 2.6 W/m²·K can enhance productivity higher than 100%. They observed that as the cooling water flow rate increases from 0.01 to 0.1 kg/s over the upper cover, the productivity increases considerably. When an overall energy balance is performed in the brackish water, the following results are obtained (Abu-Arabi et al., 2018): m ˙ F H F + A p Q r + A p Q e x t + m ˙ c H c , i n − ( A p Q L t o p + m c H c , o u t + m ˙ f H f + A p Q p c m ) = m b w d H b w d t (107)

The following equation was used to determine the relationship between Q e x t and Q r , as stated by Duffie and Beckman (Panchal and Thakkar, 2016): A Q e x t = F ′ ( α p ε g Q r − U L ( T h , i n − T a ) ) (108)

They used the values of 0.83, 0.95, and 0.88 for the collector efficiency factor ( F ′ ) , the absorptivity of the solar collector plate ( α p ) and transmissivity of the solar collector glass ( ε g ) . To calculate the radiation heat transfer coefficient, Eq. 13 was used to estimate the sky’s temperature. In addition, Eq. 21 was used to compute the convection heat transfer coefficient. A Nusselt number of four was used to estimate the convection heat transfer coefficient from the upper cover to the cooling water film since the flow is laminar. The stored or released energy of PCM was calculated as follows (Abu-Arabi et al., 2018): Q P C M = ( M e q u A p d T P C M d t ) f o r     T P C M ≠ T m Q P C M = m P C M A P L Δ t     f o r   T P C M = T m (109)

The following are the energy balance equations for the system at night (discharging mode) (Abu-Arabi et al., 2018): m ˙ F H F + Q P C M − ( Q L t o p + m ˙ f H f ) = M b w d H b w d t (110)

Comparing theoretical and experimental results showed reasonable agreement for the productivity and water temperature. The chosen PCM conducted admirably in terms of providing energy during the night for steady water production and also increased total productivity.

Solar stills are an uncomplicated, economical, and vital apparatus, especially in rural and remote regions. Due to various factors such as the material, climatic conditions, water quality, and so on, serious work on using long-term processes has not yet been completed. Due to the complexity of such studies, many areas of solar still research have not yet been explored. Some researchers have investigated the intensity of water salinity, total dissolved solids, turbidity, presence of minerals, and pH value on solar still output. It is important to develop appropriate software to investigate solar stills, as simulation studies have not yet been performed, compared with other powerful simulations in thermal and fluid flow simulating. The following are suggestions for future research directions:

1) One of the important components in increasing the productivity of a solar still is the upper cover, which functions as a transmittance medium for entering solar energy and transferring the heat as the latent heat from water vapor inside the solar still to the atmosphere outside of the solar still. The second duty of the upper cover means transferring the latent heat to the atmosphere is weak due to the low thermal conductivity of the upper cover materials and high temperature of the sides because it is in front of the solar radiation and absorbs some quantity of solar energy. Therefore, absorbing a portion of solar radiation decreases the level of temperature difference required for heat transfer from the inside solar still to the outside. The solar still could be redesigned in such a way that the transmittance medium (upper cover) and condensing plate are separate from each other. According to this idea, the upper cover duty is only a medium across solar radiation, and the condensation cover is only for transferring latent heat to the atmosphere. Of course, using this idea, the solar still becomes complicated and with more details, costs, and components.

Potable water is critical for human and societal development, particularly in rural and remote regions. Solar stills were developed to produce distilled water in places with abundant solar radiation, such as the south and east. The single basin single slope solar still is the most basic form, and it is simple to design that anyone could build. Due to limited production, however, researchers have been working on a variety of alternate solar still models. This research analyzes theoretical principles and presents various thermal models of solar stills in the form of a variety of designs. All the studied thermal models have benefits and constraints due to the assumptions used to simulate the climate conditions of the region. Theoretical modeling of a solar still is a simple and quick way to study crucial factors such as efficiency, distilled water output, basin water temperature, and so on. The use of theoretical modeling aids in the selection of a suitable model as well as the evaluation of economic and technological obstacles. Accurate modeling allows for simulations that are close to real conditions, allowing for precise component selection and cost-to-productivity analysis. Before manufacturing and implementation, thermal modeling allows for an examination and comparison of alternative designs, fabrication costs, distilled water costs, climatic conditions, and numerous components. According to a review of several solar thermal models for passive and active units, further research is needed on energy loss, alternate energy use in the absence and weakness of solar radiation, and waste energy from other sources.

Due to the inexpensive cost of distilled water produced by solar stills, these devices are gaining popularity in comparison to fossil fuels. Although solar still units have poor productivity compared to current desalination systems, when fossil fuel resources grow scarcer, solar still units will become a dominant technology. On three typical days, covering the spring, summer, and winter, daily distillation production was estimated to be roughly 19.2, 16.0, and 15.9 kg/m²d, respectively, utilizing a 5 mm diffusion gap between partitions and ten partitions. Rubber scrapers enhanced the DSSSHS model’s overall internal heat transfer coefficient and productivity. The maximum observed value of the total internal heat transfer coefficient for the DSSSHS is 38.754 W/m²°C, and the daily productivity is 4.24 L/m²d, with a productivity improvement of 63% when the slope of the upper cover is relatively short (approximately 3.0°).