Numerical analysis of tubular solar still with rectangular and cylindrical troughs for water production under vacuum

Abstract

This study compares and contrasts the desalination efficiency of tubular solar still using cylindrical and rectangular troughs when operating under a vacuum. For this, a two-dimensional code was created using the Comsol Multiphysics. The mass and heat transfer, inside the tubular solar still with the two different types of troughs, was simulated parametrically. The effect of the radius of the cylindrical trough, the square rib of the rectangular trough and the vertical elevation of the trough on heat and mass transfer were investigated at the same volume of seawater introduced initially. The numerical results revealed that the efficiency of the water productivity using cylindrical trough is significantly better than with rectangular trough when it is placed in the middle of the tubular shell. The opposite case of the 2 types of troughs is established when the trough advances towards the upper side of the glass cover where the condensation occurs.

KEYWORDS:

• Tubular solar still
• rectangular and cylindrical trough
• heat and mass transfer
• water productivity
• vertical elevation of the trough
• comsol multiphysics

Nomenclature

A	=	area, m2
Br	=	buoyancy ratio
c	=	concentration, kg.m −3
C	=	dimensionless concentration
D AB	=	mass diffusion coefficient, m2.s −1
di	=	diffusion volume, cm3.mol−1
g	=	acceleration of gravity, m.s−2
Lc	=	characteristic length (average distance between the evaporation and condensation surfaces), m
Le	=	Lewis number
Lw	=	width of water surface, m
M	=	molar mass, kg/mol
mhourly	=	distillation rate, kg.m−2.h−1
Nu	=	Nusselt number
P	=	dimensionless pressure
P	=	pressure, kPa
pop	=	operating pressure, kPa
Pr	=	Prandtl number
R	=	radius of the outer tube (tubular shell), m
r	=	radius of the cylindrical trough, m
RaT	=	thermal Rayleigh number
SR	=	square rib
T	=	temperature, °C
t	=	time, s
U, V	=	dimensionless velocity components
u, v	=	velocity components in x, y directions, m.s−1
x, y	=	coordinate directions, m
X, Y	=	dimensionless coordinate directions

Greek symbols

α	=	thermal diffusivity, m2.s−1
βc	=	coefficient of concentration expansion, m3.kg−1
βT	=	coefficient of thermal expansion, K−1
θ	=	Dimensionless temperature
λ	=	thermal conductivity, W.m−1.K−1
ν	=	kinematic viscosity, m2.s−1
ρ	=	density, kg.m−3
τ	=	dimensionless time

Subscripts

A	=	component A in a binary diffusion system
a	=	air
w	=	water

1. Introduction

There is no way to exaggerate the importance of supplying fresh water. Lack of access to clean drinking water has impacted many people, particularly in rural and arid locations. If these areas have a lot of solar energy, solar distillation might be a good solution for the paucity of water sources in these areas. In dry areas with plenty of renewable energy sources, sunlight has actually been considered one of the finest ways to power the desalination process. Solar stills are still the most popular solar desalination method in rural areas because of their simplicity in construction and maintenance [1–5].

The most common cover designs for solar stills are tubular [6], triangular [7], single-slope [8] and double-slope [9]. Despite numerous improvements in solar technology, their low productivity continues to be the principal obstacle to their widespread usage. As a result, more up-to-date solar stills are being developed, such as multi-stage systems [10] and outside reflectors [11], to maximize the output of freshwater.

The tubular solar still is a conventional method with a cylindrical shape that employs the same distillation process as conventional basin solar still. The use of tubular solar stills for solar distillation has attracted a lot of interest in practical and theoretical investigations [12,13].

Kumar et al. [14] found that the evacuated tubular collector is generally used to achieve higher collector efficiency. A higher rate of vapourization is achieved by integrating many series-connected evacuated tubes with solar still. The overall performance of the system depends on the heat transfer rate from the absorber tube to the working fluid. Heat transfer rate can further be improved by adding various sizes of nanoparticles to working fluid and acting as a heat-absorbing device during less sunshine or cloudy days.

Raturia et al. [15] found that the increase in the number of collectors leads to a raise in the values of freshwater yielding as well as daily exergy gain maintaining other parameters at the input of the system as constant.

Singh et al. [16] conclude that the collector’s numbers lead to an increase in the values of both the potable water (PW) and electric power output (EPO). During design and installation, one needs to maintain the water temperature below the boiling point. So, a compromise between PW output and EPO is to be made while selecting the values.

Singh et al. [17] found the proposed system has been compared with N-PVT-CPC-SS and CSSSS for the same basin area under similar climatic conditions. The yearly distillate output, thermal exergy, electrical exergy and UAC are the highest for N-FPCP-SS. However, the productivity of the proposed system is higher than that of the other two systems.

An analysis of Singh [18] has been done at 0.14 m water depth. It has been concluded that kWh per unit cost based on exergy gain is higher by 40.73 and 54.63%; environmental cost is higher by 59.70 and 92.55%; however, the output per unit input based on productivity is higher by 9.25% and lower by 25.13% for N-PVT-FPC-DS than double slope solar still integrated with N identical PVT compound parabolic concentrator collector and conventional double slope solar still, respectively.

Dhivagar et al. [19] conducted experimental and numerical studies and found the heat accumulated in crushed gravel sand and biomass evaporator has been used to preheat the inlet saline water and air vapour before entering into the solar still. This results in enhanced air vapour mixture temperature and evaporative heat transfer rate. The productivity, energy and exergy efficiencies of CGS-BSS were improved by 34.6%, 34.4%, and 35%; respectively.

The proposed still of Balachandran et al. [20] produces a maximum yield of 0.98 L during 01:00pm, while the CSS produces only 0.57 L. The distillate yield of the PSS was 3.05 L/day, whereas the CSS produced 2.47 L per day. The thermal efficiency of the still reaches its maximum in the noon time between 12-00pm and 13-00pm, and the peak value attained is 65.46%.

Sharma et al. [21] found the values of correlation coefficients for condensing glass temperature, water temperature and water yield and evaluated the energy metrics, productivity, cost of producing 1 kg of fresh water and exergoeconomic and enviroeconomic parameters.

Other results are found based on experimental theoretical work [22–26]. It has been the goal of several earlier studies to increase the efficiency of solar stills, either by enhancing the construction of solar stills [27–39] or by integrating materials for heat storage [40–46]. Running solar stills in a vacuum [47–49] is another option for enhancing their effectiveness.

Although some research has been done on the situation of tubular solar still operating with a rectangular trough under vacuum conditions [10,50,51], the effects of the trough’s position and dimensions modifying inside the tubular shell have not yet been investigated. This study specifically uses both a rectangular trough and a cylindrical trough to achieve this goal. The efficiency of water productivity between the two types of troughs is also investigated.

2. Presentation of physical problem

2.1. Presentation and description of the studied tubular solar still

The design of a tubular solar still is shown in Figure 1. It includes a cylindrical and rectangular trough that contains seawater at a temperature and concentration of Tw and Cw. The temperature of the cover, which is always lower than the temperature of the water, is Ts. The cross-section of the trough is located in the centre of the cylindrical tubular shell.

Figure 1. Schematic of the two types of tubular solar still with boundary conditions.

The enclosure is emptied. The vacuum in the chamber is maintained, while the chamber is operating, using an external vacuum pump. The trough’s liquid keeps evaporating as solar energy is absorbed. Due to buoyancy forces, water that is in a vapor condition rises to the water’s surface and condenses on the top shell’s inner surface.

Gravity causes the condensate to drip down the interior shell surface of the still and collect at the bottom, where fresh water is obtained.

2.2. Simplifying assumptions

The following assumptions [51] about the operating parameters of tubular solar still are established to study the thermal and flow properties of this two-dimensional model in an unsteady state.

• The fluid is a combination of water vapour and air that is incompressible and Newtonian.

• There is a two-dimensional, laminar flow of fluid.

• The temperatures of the water and cover are constant.

• The trough wall is adiabatic.

• Heat transfer by radiation and viscous dissipation is negligible.

2.3. Governing equations

The following are the unsteady-state controlling equations [51] for mass, momentum, concentration and energy conservation:

Equation of Continuity: (1) $\frac{\mathrm{\partial }U}{\mathrm{\partial }X}+\frac{\mathrm{\partial }V}{\mathrm{\partial }Y}=0$(1) The non-dimensional velocity components according to the X and Y axis are U and V, respectively.

The X-axis momentum equation: (2) $\frac{\mathrm{\partial }U}{\mathrm{\partial }\tau }+U\frac{\mathrm{\partial }U}{\mathrm{\partial }X}+V\frac{\mathrm{\partial }U}{\mathrm{\partial }Y}=-\frac{\mathrm{\partial }P}{\mathrm{\partial }X}+Pr\left(\frac{{\mathrm{\partial }}^{2}U}{\mathrm{\partial }{X}^2}+\frac{{\mathrm{\partial }}^{2}U}{\mathrm{\partial }{Y}^2}\right)$(2) Pr is the Prandtl number. $\tau$ and P are respectively the dimensionless time and pressure.

The Y-axis momentum equation: (3) $\begin{array}{rl}& \frac{\mathrm{\partial }V}{\mathrm{\partial }\tau }+U\frac{\mathrm{\partial }V}{\mathrm{\partial }X}+V\frac{\mathrm{\partial }V}{\mathrm{\partial }Y}\\ & =-\frac{\mathrm{\partial }P}{\mathrm{\partial }Y}+Pr\left(\frac{{\mathrm{\partial }}^{2}V}{\mathrm{\partial }{X}^2}+\frac{{\mathrm{\partial }}^{2}V}{\mathrm{\partial }{Y}^2}\right)+R{a}_{T}Pr(\theta +\mathrm{Br}C)\end{array}$(3) where Ra_T is the thermal Rayleigh number. Br is the buoyancy ratio. $\theta$ and C are the dimensionless temperature and concentration, respectively.

Energy equation: (4) $\frac{\mathrm{\partial }\theta }{\mathrm{\partial }\tau }+U\frac{\mathrm{\partial }\theta }{\mathrm{\partial }X}+V\frac{\mathrm{\partial }\theta }{\mathrm{\partial }Y}=\frac{{\mathrm{\partial }}^2\theta }{\mathrm{\partial }{X}^2}+\frac{{\mathrm{\partial }}^2\theta }{\mathrm{\partial }{Y}^2}$(4) Concentration equation: (5) $\frac{\mathrm{\partial }C}{\mathrm{\partial }\tau }+U\frac{\mathrm{\partial }C}{\mathrm{\partial }X}+V\frac{\mathrm{\partial }C}{\mathrm{\partial }Y}=\frac{1}{\mathrm{Le}}\left(\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{X}^2}+\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{Y}^2}\right)$(5) Le is the Lewis number.

The dimensionless variables are defined as follows in the previous equations: (6) $\begin{array}{rl}X& =\frac{x}{R};Y=\frac{y}{R};U=\frac{uR}{\nu };V=\frac{vR}{\nu };\tau =\frac{t\alpha }{L^2};\\ P& =\frac{p{R^2}^{}}{\rho {\nu }^2};\theta =\frac{T-T_s}{T_w-T_s};C=\frac{c-c_s}{c_w-c_s}\\ Pr& =\frac{\nu }{\alpha };R{a}_T=\frac{g{\beta }_T(T_w-T_s){L_c}^3}{\nu \alpha };\\ \mathrm{Br}& =\frac{{\beta }_c(c_w-c_s)}{{\beta }_T(T_w-T_s)}\text{ and }\mathrm{Le}=\frac{\alpha }{D_{\mathrm{AB}}}\end{array}$(6) The characteristic length L_c is the average length between the edge of the water and the shells interior surface.

The coefficient for thermal expansion ${\beta }_T$ is defined as [52] (7) ${\beta }_T=-\frac{1}{\rho }\frac{\mathrm{\partial }\rho }{\mathrm{\partial }T}$(7) The coefficient for concentration expansion is defined as [53] (8) ${\beta }_c=-\frac{1}{\rho }\frac{\mathrm{\partial }\rho }{\mathrm{\partial }c}=\frac{1}{\rho }\left(\frac{M_a}{M_v}-1\right)$(8)

The mass diffusion coefficient was determined using the following formula [54]: (9) $D_{\mathrm{AB}}=\frac{{\left(\frac{1}{M_A}+\frac{1}{M_B}\right)}^{0.5}{T}^{1.75}}{p_{\mathrm{op}}{\left[{\left({\sum }_A{d}_i\right)}^{\frac{1}{3}}+{\left({\sum }_B{d}_i\right)}^{\frac{1}{3}}\right]}^2}\times {10}^{-3}$(9) For water and air, the volume of diffusion d_i values used was 12.7 and 20.1 cm³/mol, respectively [51].

The rate at which fresh water is produced, also known as productivity ${\dot{m}}_{\mathrm{hourly}}$ was determined using the following equation [51]: (10) ${\dot{m}}_{\mathrm{hourly}}=\frac{-3600\times D_{\mathrm{AB}}}{L_W}\underset{0}{\overset{L_w}{\int }}{\frac{\mathrm{\partial }c}{\mathrm{\partial }y}|}_{y=0}\mathrm{dx}$(10) The mean Nusselt number $\stackrel{.}{\overline{N{u}_W}}$ on the water surface was determined as follows [51]: (11) $\stackrel{.}{\overline{N{u}_W}}=\frac{-L_c}{L_W(T_W-T_S)}\underset{0}{\overset{L_w}{\int }}{\frac{\mathrm{\partial }T}{\mathrm{\partial }y}|}_{y=0}\mathrm{dx}$(11) L_w is the width of the water surface.

2.4. Boundary conditions

The boundary conditions of our model are illustrated in Table 1.

Table 1. Boundary conditions for non-dimensional form.

Border	Condition on U	Condition on V	Condition on θ	Condition on C
Tubular shell	0	0	0	0
Seawater surface	0	0	1	1
Trough wall	0	0	${\displaystyle \frac{\mathrm{\partial }\theta }{\mathrm{\partial }n}}=0$	${\displaystyle \frac{\mathrm{\partial }C}{\mathrm{\partial }n}}=0$

3. Results and discussion

In this part and after the validation of our code, our numerical model is utilized to investigate how the rib, radius and vertical elevation of both the rectangular and cylindrical trough affect heat and mass transmission inside the tubular solar still, particularly concerning the productivity of fresh water.

3.1. Numerical method and validation

Using Comsol Multiphysics 5.5, the flow structure within the tubular solar still was modelled. It was decided to use a second-order upwind discretization technique. The species transport model for the air-vapour mixture was implemented in this simulation.

The density was changed to reflect that of an ideal, incompressible fluid. The mixing law was applied to calculate the specific heat capacity. The mass-weighted mixing equation was used to determine the viscosity and thermal conductivity.

The solution was deemed convergent when the scaled residuals for the energy equation were less than 10⁻⁶ and 10⁻⁴ for the others.

On 26 June 2016, in Ha'il, Saudi Arabia, Elashamwy [55] conducted experimental work that is utilized to validate this model. The evolution of the water productivity is numerically determined for each hour of this day by our code, which is shown in Figure 2, based on the temporary temperature conditions of the trough, inside tube surface, and ambient. With the help of this graph, we can observe how well our code’s numerical findings and Elashamawy’s experimental findings [55] agree on several key points. So, the mesh used is extremely fine.

Figure 2. Comparison of experimental and numericalwater productivity.

3.2. Effect of the geometry of rectangular and cylindrical trough

We examine the impact of the radius of the cylindrical trough on heat and mass transport inside the tubular solar still in this section. To do this, we change this radius from 20 to 50 mm in the centre of the tubular shell while maintaining the same operating pressure, glass cover temperature and beginning seawater temperature, as shown in Table 2.

Table 2. Initial parameters of tubular solar still.

The radius of the tubular shell (R)	0.8 m
Rib of the square trough	60 mm
Operating pressure (pop)	101 kPa
Seawater temperature (Tw)	60°C
Thermal Rayleigh number (RaT)	1.3 10^5
Buoyancy ratio (Br)	2.4

Figure 3 displays the velocity contours for several radii of the cylindrical trough (0.02 m; 0.03 m; 0.04 mm and 0.05 m). This figure shows that the velocity reduces as the radius of the trough increases. In fact, the greatest velocity for a radius of 0.02 mm is 0.40 m/s. However, the velocity does not surpass 0.23 m/s in the case of the radius of the trough of 0.05 m. The highest velocities are 0.40, 0.35, 0.29 and 0.23 m/s, which are equivalent to the radius of the cylindrical trough of 0.02 m; 0.03 m; 0.04 mm and 0.05 m, respectively.

Figure 3. Contours of vorticity (left), velocity (middle) and temperature (right) for various radii of the cylindrical trough at Tw = 60°C and Pop = 101 kpa. (a) −20 mm; (b) −30 mm; (c) −40 mm; (d) −50 mm.

The vorticity contours for various trough radiuses (20 mm; 30 mm; 40 and 50 mm) are shown in Figure 3. This image shows that there are two cells sandwiched between the cylindrical troughs. Additionally, as the radius of the cylindrical trough grows, there is a notable increase in vorticity between the upper rib of the square and the upper tubular shell.

The temperature contours for various trough radiuses (20; 30; 40 and 50 mm) are shown in Figure 3. It is evident from the figure that the hot zone is restricted to the area between the upper face of the cylindrical trough and the upper surface of the tubular shell. This is a result of the seawater evaporation phase. The lower part is cold because that is where condensed water is recovered after cooling.

To compare the effectiveness of the two types of cylindrical and rectangular troughs, we took the same volume of seawater corresponding to the studied radii (0.02 m; 0.03 m; 0.04 mm and 0.05 m) and we deduced the corresponding dimensions of the square trough, which will be 0.026; 0.038; 0.051 and 0.063 m.

Figure 4 shows the contours of vorticity, velocity and temperature for various ribs (26; 38; 51 and 63 mm) of the rectangular trough at Tw = 60°C and Pop = 101 kpa.

Figure 4. Contours of vorticity (left), velocity (middle) and temperature (right) for various ribs of the rectangular trough at Tw = 60°C and Pop = 101 kpa. (a) −26 mm; (b) −38 mm; (c) −51 mm; (d) −63 mm.

According to this figure, we see the same physical phenomenon as in the case of a cylindrical trough while it is very remarkable that the maximum velocity is lower than the case of the cylindrical trough of the same seawater volume.

To examine the impact of distillate rate, or the productivity of distillate water from the tubular solar still with both cylindrical and rectangular troughs, we plot the distillate rate according to each radius (20; 30; 40 and 50 mm) and each square rib of the trough (26; 38; 51 and 63 mm) at Tw = 60°C and Pop = 101 kpa, as shown in Figure 5. We can see from this graph that when the radius and rib of the two types of troughs are increased, so does the production of distillate water.

Figure 5. Evolution of the Water Productivity according to square rib/Radius of the trough at Tw = 60°C and Pop = 101 kpa.

Indeed, the distillate rate is 0.38122 kg/(m²*h) for the case of the radius of the cylindrical trough is 20 mm. This quantity increases by 5.77; 18.96; 46.47% when the radius of the cylindrical trough is 0.030; 0.04 and 0.05 m, respectively.

For the case of the rectangular trough, the productivity is 0.23432 kg/(m²*h) when the rib square trough is 26 mm. This amount of fresh water increases by 20.77; 46.65; 82.67% when the rib of the square trough becomes 0.038; 0.051 and 0.063 m, respectively.

In addition, we deduce that the water productivity of the cylindrical trough is better than the rectangular trough case for the same volume of seawater from the start. Indeed, the efficiency of the water productivity in the cylindrical case is between 30.4 and 62.69% when the trough is placed in the middle of the tubular shell.

3.3. Effect of the vertical elevation of the rectangular and cylindrical trough

This section looks into the effects of vertical elevation on heat and mass transfer in cylindrical and rectangular troughs inside a tubular solar still. To maintain consistent working pressure, glass cover temperature and beginning seawater temperature, we move them through the position of the centre of the tubular shell from 5 to 30 mm vertically and upwards.

Figures 6 and 7 show the contours of the velocity of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) and four square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kPa for different vertical elevation of the trough (5–30 mm with a gap of 5 mm).

Figure 6. Contours of the velocity of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

Figure 7. Contours of the velocity of four various square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

These 2 figures show that the velocity reduces when the two types of troughs are elevated from the tubular shell'’s centre to its upper surface.

Indeed, when the cylindrical trough is in the centre of the tubular trough and its radius is 0.05 m, the maximum velocity is 0.23 m/s while it is 0.14 m/s for the same volume corresponding to a rectangular trough.

However, when it is raised to the upper surface of 5; 10; 15; 20; 25 and 30 mm, the maximum velocity drops by 8.7; 21.47; 34.78; 47.83; 56.52 and 65.22% for the case of the cylindrical trough, respectively. It dropped by 21.43; 35.71; 50; 67.14; 78.57 and 87.86% in rectangular trough case.

We conclude that the increase of the velocity in the case of rectangular is more significant than that for the cylindrical trough. Therefore, the trough geometry is a determining factor for the velocity and the heat transfer effect inside the tubular shell.

Figures 8 and 9 show the contours of vorticity of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) and four square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kPa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

Figure 8. Contours of vorticity of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

These figures show that there are two cells situated in between the rectangular and cylindrical troughs. The vorticity between the upper rib of the square/circular trough and the upper tubular shell both greatly increases when the two types of troughs travel up and reduce in the lower region.

Figures 10 and 11 show the contours of the temperature of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) and four square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kPa for different vertical elevation of the trough (5–30 mm with a gap of 5 mm).

Figure 9. Contours of vorticity of four various square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

Figure 10. Contours of Temperature of four various radii of the cylindrical trough (r = 0.02; 0.03; 0.04 and 0.05 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

In these figures, there is a distinct hot zone between the top of the rectangular and cylindrical troughs and the top of the tubular shell. The seawater’s evaporation is to blame for this because purified water is recovered after condensation in the bottom section, it is cold Figure 11.

Figure 11. Contours of Temperature of four various square ribs of the rectangular trough (SR = 0.026; 0.038; 0.051 and 0.063 m) at Tw = 60°C and Pop = 101 kpa for different vertical elevations of the trough (5–30 mm with a gap of 5 mm).

To study the effect of the productivity of fresh water of the tubular solar still with both rectangular and cylindrical troughs, we plot the distillate rate for each type of trough according to the vertical elevation of the trough (5–30 mm with a gap of 5 mm) at Tw = 60°C and Pop = 101 kpa shown in Figures 12 and 13, respectively. From these figures, we see that the productivity of distillate water rises with the increase of the vertical elevation of the trough in the two cases. This can be understood by the fact that as the trough dimension grows, the space between the hot and cold zones closes, allowing for more substantial convective transfer. In addition, when the rectangular trough is vertically offset from the centre by 30 mm; water production improves much better than for the cylindrical trough case. Indeed, the efficiency of production water for a rectangular trough of dimensions 0.026; 0.038; 0.051 and 0.063 m is respectively: 17.42, 30.31, 53.22 and 105.82%. Whereas for the case of the cylindrical trough and the same conditions, these percentages are 12.43, 17.14, 22.05 and 27.12%.

Figure 12. Evolution of Water productivity according to the vertical elevation of the trough for different radii of the cylindrical trough at Tw = 60°C and Pop = 101 kpa.

Figure 13. Evolution of Water productivity according to the vertical elevation of the trough for the different square ribs of the rectangular trough at Tw = 60°C and Pop = 101 kpa.

We conclude that the vertical elevation of the trough is a crucial factor in improving distillate water productivity. It is much more significant in the case where the trough is rectangular.

4. Conclusion

The purpose of this research is to study the tubular solar still with a rectangular trough by comparing it with the cylindrical trough. After the validation of the code with the experimental results using Comsol Multiphysics, it’s used to examine the effect of the dimensions and the vertical elevation of the two types of the trough on water productivity.

The significant findings are summarized as follows:

• ✓ The velocity reduces when the two types of troughs are elevated from the tubular shell’s centre to its upper surface.

• ✓ The productivity of distillate water is significantly increased with the increase of the dimensions of the 2 types of trough situated in the middle of the tubular shell.

• ✓ The productivity of distillate water increases as the vertical elevation of the trough moves towards the upper surface.

• ✓ The enhancement of the water productivity in the tubular solar still with rectangular trough improves much better than with the cylindrical trough.

Disclosure statement

No potential conflict of interest was reported by the author(s).