Evaluation of Efficiency of a Finned Corrugation Basin in Inclined Basin-Type Solar Stills in Regulating the Water Supply of the CaspiCement Plant

Abstract

The need for fresh water production is especially high in hot dry climates without any sources of drinking water but with an abundance of sea and underground water. The solution is water desalination with efficient solar-powered water treatment plants. This article proposes a new modification of a basin made of thin-finned corrugation with 43°-angle-inclined sides, equal to the region’s latitude, which provide strong heating. The experiments were carried out in the hot climate of Aktau city (43°49′ N, 51°1′ E). The study’s outcomes can be useful for regions with drinking water scarcity. To define the level of the corrugated basin’s efficiency, two versions (SS-1, SS-2) of experiments were carried out on a two-slope distiller, complete with two basins. In SS-1, basin-2 was heated by air. By 15:00, basin-2 had heated up to 98.5 °C, and the acrylic cover above had heated up to 101.6 °C, which led to its “deformation”. By 12.00 p.m., the temperature differentials between the glass (40.7 °C), the air–water mixture (57.3 °C), and basin-1 (61.1 °C) were 16.6 °C and 20.4 °C. This resulted from the wind speed increasing up to 5.9 m/s. The large temperature differential contributed to the condensate yield increasing from 0.128 kg at 11 o’clock to 0.293 kg at 12 o’clock. The throughput capability of basin-1 per day was equal to 2.094 kg. Basin-2’s input to the performance in SS-1 was only the thermal effect. In SS-2, basin-2 was used as a regular basin. The plexiglass temperature was lower than the temperatures of the water and basin-2. The temperature differential between the glass and air–water mixture at 10:00 a.m. was 20 °C; at 12:00 p.m. it was 30.6 °C; and a value of 30.6 °C was recorded at 3:00 p.m. The thermal differential between the glass and the air-water mixture provided the highest condensate yield of 1.114 kg at 3.00 p.m. The condensate yield from the basins in SS-2 was 8.72 kg, including 3.5 kg from basin-1, which is 1.7 times more than from basin-1 in SS-1. The experimental results are consistent with the equations coming from the models of Clark J.A. and Dunkle R.V. T_condensation ≠ T_evaporation is an irreversible process. When the basins are heated, the heat is consumed; when the glass cools down, the heat is given off. Heat losses are minimized due to the “gap” and positive energy is provided. The still’s throughput capability can be made larger by increasing the basin’s area, reducing the water layer thickness, and regulating the flowrate of the desalinated water.

1. Introduction

An acute shortage of fresh water is experienced by more than 40 countries located in arid territories with hot climates, including the Mangistau region of the Republic of Kazakhstan, located on the eastern coast of the Caspian Sea, which has no fresh water sources [1].

Water desalination is carried out by the Mangyshlak Nuclear Power Plant, MAEK-Kazatomprom, which provides the regional center, enterprises, and adjacent settlements with all types of water. In remote areas, water deficiency is solved by imported water and underground sources. At remote enterprises, technical purposes are satisfied by seawater. The CaspiCement plant, built by HeidelbergCement Group (Germany), in order to keep chalk dust low, waters roads with sea and underground water, which leads to even greater salinity of the saline soils [2]. Because of this, the groundwater and seawater need demineralization via solar energy-driven desalination, with a great deal required due to the hot dry climate.

Refs. [3,4] propose methods of waste and sea water desalination for arid regions lacking fresh water. Sangeetha A et al. [5] report that in coastal marine areas, water is abundant but not suitable for drinking. It is economically feasible to distill and purify these waters in simple solar-powered stills. However, their widespread use is constrained by their low throughput capability. In remote coastal regions, where advanced desalination technology is not available, sustainable fresh water production methods are absolutely crucial. Stiubiener notes that the development of economically and technically efficient stills has attracted extensive attention from researchers [6].

Dev, R. and Tiwari, G. N. [7] determined that the optimal number of still basins is no more than seven. To enhance heating and boost the still’s throughput capability, much attention has been paid to the use of thin corrugated sheets (Selvakumar P. [8]). In order to determine the optimal inclination angle in an efficient solar still, it was determined that 23° is the best angle of inclination for the transparent cover for the latitude of Muscat in Oman. This made it possible to increase the condensate yield to 13% more than in a conventional solar still [9]. Y.P. Yadav., in their research [10], compared the performance of a three-basin solar still with that of a single-basin still. It was found that the three-basin still’s high efficiency was due to minimization of heat losses from the lower basins’ surfaces by the upper (heat-insulating) basin. Mohd Zaheen Khan., in his work [11], analyzed the effect of wind on the performance of passive and active solar plants. Also, Mit Patel., in his work [12], showed the results of the temperature regime of a three-basin still. This demonstrated an increase in the output of a three-basin solar still by 12.6 l/m² per day compared to a conventional solar still. Prachi K. Ithape [13] investigated multislope solar stills’ throughput capability in relation to climatic factors, slope angle, and insulation thickness. Rahul et al. formulated the characteristic equation for a two-slope solar still [14] in the conditions of Delhi. The work concluded that linear graphs determining the dependence of the basin’s heating on the slope angle were less accurate than the curves of graphs based on nonlinear dependence. Hanane et al. [15] studied the efficiency of a two-slope solar distiller, accounting for changes in the temperatures of water and glass depending on the radiation intensity. It was established that a higher distillate yield is achieved at a higher temperature differential between the glass and heated water. The still output totaled 4 l/m² per day [15], which is consistent with Kalidas’s [16] results. In experiments, Rajamanickam et al. [17] studied the effect of the water level of a double-basin solar still on the processes of mass exchange in its capacity. It was assumed that a basin water depth of 0.1 m would increase the distiller’s throughput capability. Hence, according to the experiments’ outcomes, the condensate yield was 3.074 l/m² day. This value turned out to be less than the throughput capability value obtained in Hanane’s work [15]. Trad et al. conducted comparison studies of the efficiency of single- and double-slope solar stills. They came to the following conclusion: for a one-slope plant, with its one slope oriented in the north–south direction, the maximum throughput capability temperature was achieved, in comparison with the two-slope plant [18].

Halimeh et al. [19], in their studies, compared the energy efficiency and exergy efficiency of a solar still equipped with a staged absorber-basin. Thus, the efficiency of solar energy use equaled 83.3% while the exergy (energy efficiency) equaled 10.5%. Low exergy efficiency factor is conditioned by the biggest absorber surface heat loss to the environment. Sadineni et al., in their work [20], carried out experiments on a solar still where its throughput capability was 20% higher than that of the conventional ones. Therewith, they also avoided scale formation on the plates of a staged absorber. Nidal, in his [21] experiments, used a condenser to remove vapor from the glass surface. Thus, water vapor was captured by the condenser and did not reach the glass surface.

In Rahim’s work [22], a staged aluminum liner was covered with black paint. Shallow water allowed maximum basin heating, which ensured night production of distillate. Velmurugan et al., in their study [23], carried out an analysis of the thermal characteristics of a stage-type desalination still with heat-accumulating materials (sand, pebbles, etc.). Productivity increased by 98% compared to the stage-type asphalt-cover unit [24].

The purpose of this work is the evaluation of efficiency of a modified corrugated basin with air heater and a conventional basin in a 2-slope distiller.

To achieve this goal, we conducted experiments with two variants of pool-2: in the first case, the pool was used as an air heater without water (SS-1), and in the second—as a regular pool with water (SS-2).

This study is important because it can lead to improvements in the design of solar distillers and increase their productivity, which in turn can contribute to ensuring the availability of fresh water in regions with limited water resources. In addition, the results of the study can be used to optimize other solar technologies related to heating water and air.

Our study confirms the hypothesis that using pool-2 as a conventional pool with water (SS-2) will lead to higher distiller performance compared to the option when the pool is used as an air heater without water (SS-1). We also investigate the effect of various environmental parameters, such as air temperature, solar radiation intensity, and wind speed, on distiller performance.

2. Materials and Methods

Figure 1a,b show a 2-slope still equipped with two basins (for the sake of discussion, solar still—SS) in two versions. This is used to establish how much the corrugated basin contributes to the solar still throughput capability as a whole. We set up the experimental facilities in the workshop of the Engineering Faculty of Yessenov University.

In the first version (SS-1), plexiglass 3 was over the upper basin 4, the curved edges paralleled two slopes of the glass 3 and covered the basin 5. In the second version (SS-2), the plexiglass 3 covered the two basins. It should be noted that in the first version, water was not supplied to the upper basin, since we, in this case, considered the “dry” basin in the form of an air heater [25].

The body housing was 1.040 m high, made of chipboard (also known as DSP), with a thickness of 0.02 m. The housing dimensions were 0.7 × 0.9 m. Further, the description of the plant continues from its top downwards.

The 2-slope cover (2), of plexiglass 0.003 m thick, was sealed around the unit body, using Plexiglas Acrima 82 (Röhm GmbH, Moscow, Russia), with a light transmission coefficient of 92% (tensile strength (23 °C)—70 MPa). Vicat softening temperature was 114 °C, and the fact that glass is an environmentally friendly material is of utmost importance.

For efficient use of the solar energy, the angle of both slope inclination and the sides of the finned corrugation basin-2 to the horizon was 43°, which corresponds to the angle of region latitude corresponding to 43°49′ N. The presence of a 2-slope glass cover (3) above the upper basin-2 (position 4) and above the lower basin-1 (position 5) prevents the inner surface of the cover 2 from condensing, and facilitates partial incoming solar radiation of the basin-1. A “thermal insulation”, e.g., air gap, is formed by the virtue of the second cover (3).

On the inner basin-2 side facing the basin-1, there are the condensate collectors (6). They are fixed on the body (1) walls, with condensate runoff side channels of the basin-1. The basin-1 water level is below the level of the basin shelves, which provides heating of 25% of the entire surface. For the purpose of condensate drainage, the glass (3) lower edges are curved towards the same channels of the basin-1 (position 7). Silicone pipes are inserted in holes (8) to feed and drain colder sea water. Holes (9) with silicone connecting pipes feed the basin-1 channels with water. The distillate resulting from the outer channels flows through the connecting pipes (10) into a container (not shown). The plant DSP bottom has on its surface foam plastic and basin-1 hermetically fixed with mounting foam. The temperature of glass covers (2 and 3), basin 1 and 2, water, and the ambient air temperature per the unit volume as a whole, were thermocouple-measured every 30 min, using an SMD resistance temperature detector Pt 100. Therewith, the thermocouples maximum measurement range is 150 °C, with a probe length of 1.0 m and a cable of 2.0 m.

To measure the temperature in the absorber water and the silicone connecting pipes, we used testo 905-T contact thermometer with an immersion/penetration probe of 30 cm long.

The regulation of the amount (flow rate) of water supplied to the solar still was carried out using Acetal tubing clamps of durable plastic with serrated jaws. The water levels in basin 1 and 2 and their capacity pressures were measured with a transparent U-shaped pressure gauge.

The bottom surface of a solar still plays a crucial role in the distillation process, serving as a heat-absorbing interface between the solar radiation and the water to be distilled. The choice of material for the bottom surface significantly impacts heat transfer efficiency, water evaporation rates, and overall freshwater production.

Dark (black) materials, characterized by their high absorption of solar radiation across a broad spectrum, offer several advantages for solar still applications. Common materials used for black bottom surfaces include black-painted metal, black plastic, or black concrete. These materials exhibit high absorptivity for solar radiation, effectively converting incoming sunlight into thermal energy to heat the water within the solar still.

The black bottom surface of the solar still absorbs a greater amount of solar radiation compared to lighter or reflective surfaces. This increased absorption leads to higher bottom surface temperatures, promoting more efficient heating of the water and faster evaporation rates. Additionally, the black surface facilitates the retention of heat during periods of low solar radiation, such as cloudy days or nighttime operation, ensuring continuous freshwater production.

Emissivity, a critical factor in heat transfer within the solar still, is also influenced by the bottom surface material. Black materials typically exhibit higher emissivity, facilitating efficient thermal radiation exchange between the water and the surroundings. This enhanced radiative heat transfer reduces heat losses and improves distillation efficiency, ultimately increasing freshwater yield.

A silicon pyranometer SP-Lite (manufactured by Kipp & Zonen, Delft, The Netherlands) measured the solar radiation flux density [26].

The site for the experiments was selected as the trials site of the Ecology Faculty, 21 km from the city of Aktau, in the coastal zone of the Caspian Sea (43°49′ N 51°1′ E). The distance from the site to the sea shore is 487.5 m, shown in the upper part of Figure 2. On 1 and 2 August 2023, from a depth of 5–6 m, seawater was sampled from a rubber boat, in the more seaward part of the sea, at a distance of 166 m from the seashore.

The elements of the solar still, their dimensions, the angle of inclination of the translucent covers, and the thermal characteristics are presented in

Table 1. Thermotechnical properties of the still elements and water.

Parameters	Glass Cover SS	Glass Cover of Basins	Basin-2	Basin-1	Water
					Basin-2	Basin-1
$\alpha$	${\alpha }_{g.cover}$—0.03	${\alpha }_{g.c.b2+g.c.b1 }$—0.03	${\alpha }_{b2}$—0.93	${\alpha }_{b1}$—0.93	0.05	0.05
$A$ (m2)	0.72	0.73	0.38	0.62	0.21	0.48
$\tau$	0.92	0.92	-	-	0.93	0.93
$\epsilon$	0.88	0.88	-	-	0.94	0.94
$C_{\rho }$ (J/kg K)	500	500	630	630	4190	4190
$\rho$ (kg/m3)	2500	2500	7850	7850	1010	1010
Thickness, mm	3.00	3.00	0.7	0.7	20-40-50	20-30
Slope of glass, (°)	38	38	38	-	-	-

.

3. Mathematical Model of a Solar Still Thermal Process

The complexity of using the solar energy lies in of the radiation power intensity change during a day, a month, and a year. This creates inconvenience in maintaining the temperature regime in solar-powered units. The air gap between the upper 2-slope cover and the lower cover above the basins complicates the system with radiation–conduction heat exchange. Mass-transfer processes in the system occur during condensation of moisture on the basin-2 inner surfaces and the glass over the two basins in their entirety [27].

The following assumptions are made in the modeling:

(a) Heat losses through the sides and the bottom are insignificant, the heat capacity of the cover glass is minimal, and no water stratification in the basins are observed;

(b) The heat transfer radiated into the environment from the transparent cover of the still is considered to be negligible due to the “interlayer” and is not taken into account;

(c) The temperature of the inner surface of the transparent glass covers differs from its outer surface temperature: T_gi ≠ T_go.

Heat Balance Equations for the Capacity of a Basin-Type Still

In the solar-powered still, the upper transparent cover is made of Acrima 82 plexiglass. The inner transparent cover above both the upper basin-2 and the lower basin-1 is also Acrima 82 (Figure 1,b). The figure shows that the solar radiation coming on the surface of the basin-2 is 89%, and on the surface of the basin-1 is by 27% for 2 sides.

1. The heat balance for transparent covers above the still, basin-2 and basin-1, can be estimated with the equation formulated by Velmurugan et al. in their studies [28]:

$$\begin{gathered} {\alpha }_{g\left(ss\right)}^{\prime }{I}_{s}A+{\alpha }_{g\left(b.2\right)}^{\prime }{I}_{s}A+{\alpha }_{g\left(b.1\right)}^{\prime }{I}_s+{(q}_{e.w(b.2)-g}+q_{c.w(b.2)-g}+q_{r.w(b.2)-g})A+{(q}_{e.w(b.1)-g}++q_{c.w(b.1)-g}+ \\ {q}_{r.w(b.1)-g})A=m_{g(b.2)}{C}_{\rho g}\frac{d{T}_{g(b,2)}}{dt}+m_{g(b.1)}{C}_{\rho g}\frac{d{T}_{g(b,1)}}{dt}+q_{c.g\left(ss\right)-a} \end{gathered}$$

(1)

where $q_{g\left(ss\right) }, q_{g\left(b.2\right) }, q_{g\left(b.1\right) }$ is the heat flow absorbed by the glass, (W/^m2); A—surface area of the transparent coatings, (m²); I_s—intensity of the radiation transmitted through the glass, (W/m²); ${\alpha }_{g\left(ss\right)}^{\prime }$, ${\alpha }_{g\left(b.2\right)}^{\prime }$, ${\alpha }_{g\left(b.1\right)}^{\prime }$—the radiation fraction absorbed by the glass; $q_{c.w(b\dots )-g}$, $q_{c.w(b\dots )-g}$, $q_{c.w(b\dots )-g}$—heat flow from water in the basin-2 and basin-1 to the inner surface of the cover, (W/m²); $q_{g\left(ss\right).c-a }$—the cover originated heat flow into the environment via convection, (W/m²); $m_{g(b.2)}$, $m_{g(b.1)}$—the mass of the glass cover over the basins, (kg); $C_{\rho .g}$—specific heat of glass, (J/kg × K); $T_{g(b,2)}$, $T_{g(b,1)}$—glass temperature of the cover over the basin-2 and basin-1; $q_{c.g\left(ss\right)-a}$—heat flow transferred via convection from the top cover to the environment.

It should be noted that the glass surface temperature measurement difficulties lead to unforeseen errors in predicting the performance of the stills, as shown in studies [29]. Also, Equation (1) does not take into account the radiated heat flow due to the air gap between transparent covers.

Heat transfer to the environment via convective heat exchange in the interlayer between the covers will be carried out through the upper translucent cover of the still:

$$q_{c.g\left(ss\right)-a}=h_{c,g\left(ss\right)}A(T_{g\left(ss\right)}-T_{g\left(ss\right)a})$$

(2)

where $h_{c,g\left(ss\right)-a}$—the coefficient of convective heat transfer from the glass to the environment, (W/m² °C); $T_{g\left(ss\right)}$—temperature of the inner surface of the plexiglass; $T_{g\left(ss\right)a}$—temperature of the outer surface of the solar powered still cover glass, (°C).

As for the convection coefficient, then, as shown in [30], Juan Cristóbal in [31] gives Jurges’ data obtained for a 0.5 m² plate where the coefficient $h_{c,g}$ depends on the wind speed V, is no more than 5 m/s, and is assigned by the dimensional equation:

$$h_{c,g \left(ss\right)}=5.7+3.8 V$$

(3)

The area of the upper basin-2 is 0.38 m², and of the lower basin-1—0.62 m², that is, for our case, Equation (3) is usable.

Convective heat flow $q_{cg\left(ss\right)-a }$ can be estimated with the following expression:

$$q_{cg\left(ss\right)-a}={\epsilon }_{g\left(ss\right)}\sigma \left[T_{g\left(ss\right)}^4-T_{g\left(ss\right)a}^4\right]$$

(4)

where ${\epsilon }_{g\left(ss\right)}$—the emissive ability of the glass inner surface, 0.9; σ—Stefan Boltzmann’s constant = 5.669 × 10⁻⁸ W/m²K.

Heat flow is transferred from basin-2 and basin-1 water to the inner surface of the glass during evaporation due to convection and radiation. It can be written using the instance of basin-2:

$$q_{e.w\left(b.2\right)-g.inner}=h_{e,w\left(b.2\right)-g}{·A}_{w(b.2)}(T_{w\left(b.2\right)}-T_{g.inner})$$

(5)

$$q_{c.w\left(b.2\right)-g.inner}=h_{c,w\left(b.2\right)-g}·A_{w(b.2)}(T_{w\left(b.2\right)}-T_{g.inner})$$

(6)

$$q_{r.w\left(b.2\right)-g.inner}=h_{r,w\left(b.2\right)-g}{·A}_{w(b.2)}(T_{w\left(b.2\right)}-T_{g.inner})$$

(7)

where $h_{e,w\left(b.2\right)-g}$—coefficient of evaporation heat transfer, which can be determined utilizing an equation for the model obtained in the heat transfer development [32]:

$$h_{e.w\left(b.2\right)-g_{inner}}=16.273·{10}^{-3}{h}_{c.w\left(b.2\right)-g_{inner}}·\frac{(P_{w\left(b.2\right)}-P_{g_{inner}})}{(T_{w\left(b.2\right)}-T_{g_{inner}})}$$

(8)

At the same time, we define $h_{c,w\left(b.1\right)-g}$ and ${ h}_{r,w\left(b.1\right)-g }$ employing the equations from the Dunkle’s model:

$$h_{cw\left(b.2\right)-g}= 0.884·{\left[(T_{w(b.2)}-T_{g_{inner}})+\frac{(P_{w\left(b.2\right)}-P_{g_{inner}})T_{w(b.2)}+273.15}{268.9·{10}^3-P_{w(b.2)}}\right]}^{\frac{1}{3}}$$

(9)

$$h_{r.w\left(b.2\right)-g_{inner}}={\epsilon }_{w\left(b.2\right)}\sigma (T_{w\left(b.2\right)}^2+T_{g_{inner}}^2)·(T_{w\left(b.2\right)}-T_{g_{inner}})$$

(10)

$${\epsilon }_{w\left(b.2\right)}={\left[\frac{1}{{\epsilon }_{w\left(b.2\right)}}+\frac{1}{{\epsilon }_{g_{inner}}}-1\right]}^{-1}$$

where $P_{w(b.2)}$—the partial pressure of water vapor at a certain temperature (N/m²);

$P_{g.inner}$—air–water mixture partial pressure on the inner surface of the glass.

2. The heat balance equation for the water of still basin-2 and basin-1 is formulated as the equation in [26]:

$$\begin{gathered} {\tau }_{g(b.2)}{\alpha }_{w(b.2)}{I}_s{A}_{w(b.2)}+{\tau }_{g(b.1)}{\alpha }_{w(b.1)}{I}_s{A}_{w(b.1)}+q_{c.\left(b.2-w\right)}+q_{c.(b.1-w)}=m_{w(b.2)}{C}_{\rho w}\frac{d{T}_{w(b,2)}}{dt}+m_{w(b.1)}{C}_{\rho w}\frac{d{T}_{w(b,1)}}{dt} \\ +q_{c.w\left(b.2\right)-g\left(ss\right)}+q_{c.w\left(b.1\right)-g\left(ss\right)} \end{gathered}$$

(11)

3. The heat balance equation for the basin-2 and basin-1:

$$\begin{gathered} {\tau }_{g(b.2)}{{\tau }_{w(b.2)}\alpha }_{(b.2)}{I}_s{A}_{(b.2)}+{\tau }_{g(b.1)}{\tau }_{w(b.1)}{\alpha }_{w(b.1)}{I}_s{A}_{w(b.1)}=m_{(b.2)}{C}_{\rho (b.2)}\frac{d{T}_{w(b,2)}}{dt}+m_{(b.1)}{C}_{\rho (b.1)}\frac{d{T}_{w(b,1)}}{dt}+ \\ {q}_{c.w\left(b.2\right)-g\left(ss\right)}+q_{c.w\left(b.1\right)-g\left(ss\right)}{q}_{c.g\left(ss\right)-a} \end{gathered}$$

(12)

A double-slope solar still is a type of solar still design that utilizes two sloping surfaces to maximize solar energy absorption and distillation efficiency. In this analysis, we will focus on the radiative and optical aspects of heat transfer within the double-slope solar still.

The two sloping surfaces of the solar still are typically made of a transparent material such as glass or plastic. These surfaces allow solar radiation to penetrate into the still, where it is absorbed by the water to be distilled. The transparent nature of the material ensures efficient transmission of solar radiation while minimizing reflection losses.

The material properties of the sloping surfaces play a crucial role in solar radiation absorption and heat transfer. Ideally, the surfaces should have high absorptivity for solar radiation to maximize energy absorption. Additionally, high emissivity is desirable to facilitate efficient thermal radiation exchange within the still, promoting heat transfer from the water to the surrounding environment.

Radiative heat transfer occurs between the water surface and the inner surfaces of the sloping panels. The water surface emits infrared radiation due to its temperature, and some of this radiation is absorbed by the inner surfaces of the panels. Likewise, the inner surfaces of the panels emit infrared radiation, some of which is absorbed by the water. This exchange of radiation contributes to the overall heat transfer within the solar still.

Optical efficiency refers to the ability of the double-slope solar still to effectively capture and utilize solar radiation for distillation. Factors such as the angle of inclination of the sloping surfaces, the transmittance of the material, and the cleanliness of the surfaces influence optical efficiency. Proper design and maintenance are essential to ensure optimal optical efficiency and maximize distillation performance.

Figure 3 shows the thermal flux of both systems.

The hourly condensate output for basin-2 and basin-1 is detected with formulations (13) based on the formula from the studies [33]:

$$m_{ew(b.2)}=\frac{h_{ew(b.2)-}{g}_{inner}\times (T_{w(b.2)}-T_{g_{inner}})}{L}·3600·A_{b.2}$$

(13)

$$m_{ew(b.1)}=\frac{h_{ew(b.1)-}{g}_{inner}\times (T_{w(b.1)}-T_{g_{inner}})}{L}·3600·A_{b.1}$$

(14)

$$m_{ew(b.1)}=\frac{h_{ew(b.1)-}{b.2}_{inner}\times (T_{w(b.1)}-T_{{b.2}_{inner}})}{L}·3600·A_{b.1}$$

(15)

where L is the latent heat of evaporation. For seawater heated above 70 °C:

$L$ = 31,615$·{10}^6\left[1-\mathrm{76,160}·{10}^{-4}{T}_w\right]$ and less 70 °C $L$ = 24,935$·{10}^6\left[1-\mathrm{94,779}·{10}^{-4}{T}_w+\mathrm{13,132}·{10}^{-7}{T}_w^2-\mathrm{47,974}·{10}^{-9}{T}_w^3\right].A_{b.2}$, $A_{b.1}$—area of the basin-2 and basin-1, (m²).

The daily throughput capability of the solar-powered system is calculated with the following formula:

$$M_{ew}={\sum }_{i=1}^{24}{m}_{ew}$$

(16)

The efficiency of a 2-slope double-basin solar still with seawater heating, where the seawater heats in the upper basin-2 and runs to the lower basin-1 for desalination, is established with the following formulation:

$${\eta }_{eff}=\frac{\sum _{i=1}^{24}{m}_{ew}}{\sum ({I\left(t\right)}_{b2}·A_{b2}·3600)+\sum ({I\left(t\right)}_{b1}·A_{b1}·3600)}$$

(17)

4. Results and Discussion

This daily influx of shortwave solar energy reaching the ground across a broad area comprehensively considers seasonal fluctuations in daylight duration, the Sun’s elevation, and absorption by clouds and other atmospheric components. Shortwave radiation encompasses visible light and ultraviolet rays. The average daily intake of shortwave solar energy undergoes significant seasonal shifts throughout the year. The sunnier stretch extends for 3.5 months, spanning from 4 May to 20 August, with an average daily receipt of over 6.3 kWh per square meter. June stands out as the brightest month in Aktau, boasting an average of 7.4 kWh. Conversely, the darker phase covers 3.5 months, from 30 October to 13 February, registering an average daily intake of short wave energy below 2.6 kWh per square meter. December marks the darkest month in Aktau, recording an average of 1.4 kWh. Annual average solar energy is shown in Figure 4.

Efficiency of the Basin-2 in a Double-Basin Distiller on 1 August 2023. SS-1: The Upper Basin-2 as an Air Heater (Water Free)

The corrugated basin is employed as an air heater with no water fed.

The plexiglass cover is horizontal, with a gap of 0.01 m from the top of the basin-2 (Figure 1a).

The ambient conditions as of 1 and 2 August 2023 are tabulated in

Table 2. Ambient conditions as of 1 and 2 August 2023.

(Ambient Conditions)	1 August 2023		2 August 2023
	Morning	Afternoon	Morning	Afternoon
Sunrise time (hour)	6:22	-	6:26	-
Outdoor air temperature (°C)	20.3 (7:00)	32.0 (12:00)	21.7 (7:00)	31 (12:00)
Solar radiation intensity (W/m2)	96.1 (7:00)	795 (12:00)	101 (7:00)	840 (12:00)
Atmospheric pressure (mm Hg)	759	758	756	756
Wind speed, (m/s)	3.4 (B)	5.9 (Ю)	2.1 (3)	3.0 (C3)
Relative air humidity (%)	75	39	51	41
Precipitation amount (mm)	-	-	-	-
Cloudiness	Clear	Low	Clear	Clear

.

SS-1. 1 August 2023. Sunrise time—6:22 a.m. It is clear. Outdoor air temperature: in the morning—20.3 °C, temperature maximum at 12:00 p.m.—32 °C. Relative air humidity: 75% in the morning, 39% in the afternoon. Wind speed: in the morning—3.4 m/s (east) in the afternoon—5.9 m/s (south). The maximum value of solar radiation intensity at 12:00 p.m. was 795 W/m².

The dynamics of temperature variability of glass, water, and basin-2 and basin-1 depend on the outdoor air temperature and radiation intensity; for version SS-1, these are given in

Table 3. Dynamics of a change in temperature for the glass, water, and basins in the SS-1 version. 1 August 2023.

Time (hour)	${\mathit{I}}_{\mathit{s}}$ (W/m2)	${\mathit{T}}_{\mathit{a}}$ (°C)	${\mathit{T}}_{\mathit{g}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{2}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{b}\mathbf{.}\mathbf{2}}$ (°C)	${\mathit{T}}_{\mathit{g}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{1}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{w}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{1}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{b}\mathbf{.}\mathbf{1}}$ (°C)	Distillate Output (b.1) (kg)
7:00 a.m.	96.10	21.3	18.6	21.0	18.4	18.7	19.5	0.00
8:00 a.m.	155.00	22.8	34.6	33.2	21.4	23.7	24.8	0.00
9:00 a.m.	220.17	24.1	43.3	41.0	27.0	29.5	32.3	0.014
10:00 a.m.	390.51	27.2	54.0	50.3	31.3	37.1	40.5	0.071
11:00 a.m.	590.70	29.3	64.1	61.3	42.1	44.7	49.3	0.128
12:00 a.m.	795.00	32.0	76.1	73.5	40.7	57.3	61.1	0.293
1:00 p.m.	781.33	31.4	85.0	81.2	43.0	45.8	49.4	0.173
2:00 p.m.	776.40	31.1	96.8	91.1	51.4	53.1	57.3	0.270
3:00 p.m.	713.51	30.6	101.6	98.5	53.1	58.3	61.1	0.337
4:00 p.m.	681.70	30.2	97.3	92.4	49.2	54.6	58.0	0.283
5:00 p.m.	635.50	29.0	93.6	89.3	45.0	50.1	55.3	0.219
6:00 p.m.	593.00	28.5	88.1	84.0	39.3	45.2	48.9	0.121
7:00 p.m.	475.30	28.1	81.6	77.5	31.4	39.6	44.7	0.088
8:00 p.m.	189.65	27.0	76.0	71.3	28.0	36.0	40.3	0.052
-	-	-	-	-	-	-	-	2.049

.

A. The temperature of the glass ($T_{g(b.2)}$) above basin-2 at 7:00 a.m. was 2.4 °C lower than that of the basin capacity; at 8 p.m., the temperature was 4.7 °C. The basin-2 temperature prevailed over the glass temperature ($T_{g(b.2)}$). Heating basin-2 at 3:00 p.m., up to 98.5 °C, and heating the acrylic up to 101.6 °C resulted in acrylic “deformation”. The reason is the tight adjacency (0.01 m) of the glass to the “hot” tops of the basin-2 corrugation (Figure 2a). As the studies show, application of corrugation requires a gap of at least 0.35 m between the tops, or plexiglass replacement with a regular one.

Thus, Alessandro Franco [34] came to the conclusion that for air heating it is advisable to utilize thin corrugated sheets. But at the same time, the main requirement is to ensure a gap between the absorbing surface and the cover glass. This was also noted by A. Alahmer [33].

Starting at 3.00 p.m., the glass temperature was dropping from 101.6 °C to 76 °C at 8:00 p.m. The temperature of the basin capacity also was decreasing from 98.5 °C at 3:00 p.m. to 71.3 °C. The temperature gradient totaled 3–5 °C.

The excess of the glass temperature ($T_{g(b.2)}$) over the temperature of the basin-1 glass ($T_{g(b.1)}$) totaled 0.2 °C at 7:00 a.m., 48.5 °C at 3:00 p.m., and 48.0 °C at 8:00 p.m. This shows that the heat transfer from basin-2 glass to basin-1 glass was negligible.

B. The glass temperature ($T_{g(b.1)}$) was also lower than the temperature of the water and basin-1. At 12:00 a.m., the temperature differential between the glass (40.7 °C), air–water mixture (57.3 °C), and basin-1 (61.1 °C) was 16.6 °C and 20.4 °C. This difference is the biggest one obtained in the course of the experiment, due to the wind speed increase up to 5.9 m/s starting from 11:00 a.m. with the maximum air temperature (32 °C) and intensity of 795 W/m². The temperature drop made condensate yield rise from 0.128 kg at 11.00 a.m. to 0.293 kg at 12.00 a.m. Thus, a high wind speed provokes glass cooling, air–water mixture condensing, and distiller performance increase. On the other hand, high wind speed causes heat losses to the environment [35]. In our case, the heat losses are minimized due to the “air gap” between the covers.

C. The SS-1 solar still throughput capability. The contribution of basin-2 to throughput capability is conditioned with heat transfer from the lower surface to the water surface in basin-1. The condensate output from the basin-1, from 9:00 a.m. through 8:00 p.m., was 2.094 kg.

2 August 2023. The upper basin-2 in the form of a conventional basin (with water). The basin-2 plexiglass cover, 2-slope, parallel to the still cover, with a gap of 0.06 m, is common for the two basins (the upper one and the lower one). The height from basin-2 plane to the top of the cover glass was 0.4 m (Figure 1b).

SS-2. 2 August 2023. Sunrise time—6:26 a.m. In the afternoon—slightly cloudy. Air temperature: in the morning—21.7 °C, maximum at 12:00 a.m.—31 °C. Relative humidity: 51% in the morning, 41% in the afternoon. Wind speed: in the morning—2.1 m/s (west) in the afternoon—3.0 m/s (northwest).

The peak intensity of the solar radiation at 12:00 was 840 W/m². The dynamics of changes in the temperature of glass, water, and basins 2 and 1, for version SS-2, are given in

Table 4. Dynamics of change in temperature of glass, water, and basin in SS-2. 2 August 2023.

Time (hour)	${\mathit{I}}_{\mathit{s}}$ (W/m2)	${\mathit{T}}_{\mathit{a}}$ (°C)	${\mathit{T}}_{\mathit{g}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{2}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{w}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{2}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{b}\mathbf{.}\mathbf{2}}$ (°C)	${\mathit{T}}_{\mathit{g}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{1}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{w}\mathbf{(}\mathit{b}\mathbf{.}\mathbf{1}\mathbf{)}}$ (°C)	${\mathit{T}}_{\mathit{b}\mathbf{.}\mathbf{1}}$ (°C)	Distillate Output, (kg)
									(b.2)	(b.1)	∑ (b.2 + b.1)
7:00 a.m.	101.5	21.7	19.3	19.8	22.0	19.0	19.7	20.0	0.000	0.000	0.000
8:00 a.m.	160.19	22.4	21.7	32.5	36.0	20.3	25.6	26.4	0.031	0.000	0.031
9:00 a.m.	225.07	26.0	23.6	40.8	45.1	22.5	31.8	35.0	0.114	0.026	0.14
10:00 a.m.	379.00	29.6	27.0	47.0	54.8	25.0	38.5	42.8	0.216	0.040	0.256
11:00 a.m.	580.13	30.1	32.3	61.3	67.1	28.3	46.0	50.8	0.410	0.186	0.596
12:00 a.m.	840.00	31.5	38.7	69.3	76.0	32.7	55.3	61.1	0.452	0.271	0.723
1:00 p.m.	811.36	31.2	46.4	76.2	84.5	38.0	63.1	69.0	0.475	0.421	0.896
2:00 p.m.	792.16	31.0	56.5	87.0	96.1	43.1	73.4	79.0	0.513	0.448	0.961
3:00 p.m.	731.41	30.6	64.8	95.4	101.0	48.8	81.0	88.3	0.621	0.493	1.114
4:00 p.m.	698.62	30.4	61.2	89.6	94.3	43.7	75.3	82.7	0.527	0.413	0.940
5:00 p.m.	730.09	29.8	57.9	85.4	90.7	38.0	70.0	76.1	0.493	0.436	0.929
6:00 p.m.	583.10	29.0	53.3	78.2	81.4	32.7	62.3	71.5	0.481	0.410	0.891
7:00 p.m.	481.00	28.5	49.7	69.0	76.1	28.4	56.1	65.0	0.450	0.267	0.717
8:00 p.m.	124.83	28.3	43.5	61.8	69.3	23.1	49.2	58.6	0.415	0.108	0.523
-	-	-	-	-	-	-	-	-	5.198	3.519	8.717

.

A. In contrast to the option without water (air heater) in SS-1 during the day, the temperature of the glass ($T_{g(b.2)}$) above basin-2 in the SS-2 version (for heating water) was lower.

At 7 a.m., the temperature differential between the glass and the water was 0.5 °C, at 10.00 a.m. the differential was 20 °C, at 12 noon the differential was 30.6 °C, and a value of 30.6 °C was recorded at 3:00 p.m.

The largest condensate yield was 1.114 kg at 3:00 p.m. and 0.94 kg. at 4:00 p.m. at a differential of 28.4 °C (Table 4). Large amounts of the air–water mixture condensation are justified by Equation (13) where it is clear that the value of the hourly output of condensate is directly proportional to the evaporation heat transfer coefficient ($h_{e.w\left(b.2\right)-g_{inner}}$) calculated with Equation (5). Equation (8) demonstrates that the heat transfer coefficient ($h_{e.w\left(b.2\right)-g_{inner}}$) depends on the temperature differential between the glass, the air–water mixture, and the partial pressures difference. The difference between $T_{g(b.2)} \mathrm{and} T_{w(b.2)}$ is inversely proportional.

The basin-2 throughput capability from 7:00 to 20:00, inclusive, was 5.2 kg.

B. The glass temperature ($T_{g(b.1)}$) neither exceeded the water nor the basin-1 temperature.

The maximum values of the temperature gradient between the glass above basin-1 and the water were recorded at 3:00 p.m. and 5:00 p.m. and amounted to 32.2 °C and 31.6 °C, respectively. During those hours, the highest condensate yield occurred, of 0.49 and 0.43 kg.

The distillate output of the basin-1 surface in SS-2 was 3.519 kg, which is 1.47 kg more than the distillate production (2.049 kg) obtained from the basin-1 surface in SS-1.

C. Productivity of the SS-2 solar still. In SS-2, the total daily distillate output from the surface of the upper basin-2 and the lower basin-1 was 8.717 kg.

Less condensate output from the surface of basin-1 in SS-1 is linked to the thickness of the water layer in the basin. In order to increase productivity in SS-1, the water layer in basin-1 was equal to 25 mm, which did not bring to a greater condensate output. In the SS-2 version, the water layer thickness in the basin-2 and basin-1 was 20 mm, which achieved higher productivity compared to SS-1 (Figure 5). The employment of basin-2 in SS-1 for heating the air did not contribute to the distillate output and productivity.

Thus, the SS-2 thinner (20 mm) water layer in the basin increased the productivity of the solar distiller by 1.5 times in comparison with SS-1.

This matches the results obtained in [36].

5. Conclusions

Research Conclusion:

Based on the findings from the study comparing the effectiveness of basin-2 in the distillator with 2 basins on 1 and 2 August 2023, the following conclusions can be drawn:

SS-1 Experiment (1 August 2023):

The use of a corrugated basin as an air heater without water led to the deformation of the basin due to excessive heat. It was found that a gap of at least 0.35 m between the corrugations and the glass surface is essential to prevent such issues.

The heat transfer between basin-2 and basin-1 was minimal, indicating the inefficiency of the setup.

High wind speed contributed to the cooling of the glass and condensation of the vapor–air mixture, positively impacting the distillator’s productivity.

SS-2 Experiment (2 August 2023):

The conventional basin setup with water in basin-2 showed a steady decrease in glass temperature compared to the air heater setup in SS-1.

The significant temperature difference between the glass and water surface led to increased condensate output, enhancing the distillator’s performance.

Basin-2 demonstrated higher productivity compared to basin-1, with a total condensate output of 8.717 kg for the day.

In conclusion, this study highlights the importance of proper design considerations, such as adequate spacing between layers and the configuration of the basin setup, in maximizing the distillator’s performance. The findings underscore the impact of environmental factors, such as temperature differentials and solar radiation intensity, on the efficiency of the distillation process. Further research and optimization of design parameters are recommended to enhance the overall effectiveness of the distillation system.