Improvement of the tilted wick solar still by using a flat plate reflector

Abstract 

Desalination 216 (2007) 139–146 

Improvement of the tilted wick solar still by using 

a flat plate reflector 

Hiroshi Tanaka*, Yasuhito Nakatake 

Mechanical Engineering Department, Kurume National College of Technology, Komorino, 

Kurume, Fukuoka 830-8555, Japan 

Tel. +81 (942) 35-9359; Fax: +81 (942) 35-9321; email: tanakad@kurume-nct.ac.jp 

Received 12 April 2006; Accepted 25 December 2006 

This paper presents a numerical analysis to investigate the effect of the vertical flat plate external reflector on the 

distillate productivity of the tilted wick solar still. We propose a geometrical method to calculate the solar radiation 

reflected by the external reflector and absorbed on the evaporating wick, and also performed numerical analysis of 

heat and mass transfer in the still to predict the distillate productivity on four days (spring and autumn equinox and 

summer and winter solstice days) at 30EN latitude. We found that the external reflector can increase the distillate 

productivity in all but the summer seasons, and the increase in the daily amount of distillate averaged over the four 

days is predicted to be about 9%. 

Keywords: Solar desalination; Solar distillation; Solar still; Tilted wick; Reflector 

1. Introduction 

Many attempts have been made to increase the 

distillate productivity of the tilted wick solar still 

[1–7]. Among the modifications, an external 

reflector can be a useful one to increase the distillate 

productivity for the tilted wick still as 

indicated by Malik et al. [8], Tsumura et al. [9] 

and Al-Karaghouli and Minasian [10], but a 

detailed and quantitative analysis of the effect of 

*Corresponding author. 

0011-9164/07/$– See front matter © 2007 Published by Elsevier B.V. 

doi:10.1016/j.desal.2006.12.010 

the external reflector has not been presented. For 

the basin still, El-Swify and Metias [11] presented 

a useful geometrical method to calculate 

the solar radiation reflected by the internal 

reflector and then absorbed on the basin liner, and 

Tripathi and Tiwari [12] proposed a new concept 

of solar fraction to evaluate the effectiveness of 

an internal reflector in absorbing solar radiation 

on the basin liner. We also presented [13,14] a 

geometrical method for evaluating the effect of an 

external reflector in addition to an internal

140 

reflector on the solar radiation absorbed on the 

basin liner of the basin still. 

Furthermore, we proposed a newly designed 

solar still [15], which consists of a vertical 

multiple-effect diffusion still and a flat plate 

reflector, and we presented a geometrical method 

for calculating the direct and diffuse solar radiation 

directly absorbed on the vertical surface as 

well as the radiation reflected by the flat plate 

reflector and absorbed on the vertical surface. We 

performed outdoor experiments [16] under solar 

isolation in Kurume (33EN latitude), Japan, to 

validate the geometrical method, and the results 

show that direct, diffuse and reflected radiation 

absorbed on the vertical surface can be adequately 

calculated with the geometrical method 

we presented. 

The geometrical method for calculating the 

effect of external reflector for the basin still as 

well as the vertical still can be easily modified to 

the tilted wick still. Therefore, in this paper, the 

objective of the study is to theoretically find the 

effect of the vertical flat plate external reflector 

on the amount of solar radiation absorbed on the 

evaporating wick as well as the distillate productivity 

of a single slope tilted wick still at 30EN 

latitude. Finally, we give the optimum inclination 

of the tilted wick still with and without an external 

reflector. 

2. Solar radiation absorbed on the evaporating 

wick of a single slope tilted wick still with a 

vertical flat plate external reflector 

The proposed still is shown in Fig. 1. The still 

consists of a glass cover, evaporating wick and a 

vertical flat plate external reflector of highly 

reflective materials such as a mirror finished 

metal plate. Saline water is fed to the wick constantly. 

The direct and diffuse solar radiation and 

also the reflected solar radiation from external 

reflector are transmitted through the glass cover 

and absorbed onto the wick. 

H. Tanaka, Y. Nakatake / Desalination 216 (2007) 139–146 

Fig. 1. Schematic diagram of tilted wick still with vertical 

flat plate external reflector. 

To simplify the following calculation to determine 

the absorption of solar radiation on the 

wick, the walls of the still are disregarded, since 

the height of the walls (10 mm) is negligible in 

relation to the still’s length (1 m) and width 

(1 m). 

Fig. 2 shows a schematic diagram of the 

shadows of the glass cover (as well as the evaporating 

wick) and the external reflector on a 

horizontal surface caused by direct solar radiation. 

Since the walls disregarded as mentioned 

above, the shadows of the glass cover and the 

evaporating wick would be exactly the same. l s is 

the length of the still (ABCD), l m is the height of 

the external reflector (ADEF), w is the width of 

both the still and reflector and θ is the angle of 

the still from horizontal. γ is the azimuth angle of 

the still and is always set as 0 o (still is oriented 

due south) in this paper, and ϕ and φ are the 

azimuth and altitude angle of the sun. 

The direct solar radiation absorbed on the 

evaporating wick, Q sun,dr, can be determined as the 

product of the direct solar radiation on a horizontal 

surface, G dr, the shadow area of the still on

H. Tanaka, Y. Nakatake / Desalination 216 (2007) 139–146 141 

Fig. 2. Shadows of the still and reflector on a horizontal surface. 

a horizontal surface (shown as ANBCDN), transmissivity 

of the glass cover, τ g(β), and absorptivity 

of the wick, α w, and this may be expressed 

as 

Qsun, dr = Gdrτg( 

β) αw 

⎛ cos( ϕ −γ 

) ⎞ 

× wls 

⎜cosθ + sinθ 

⎟ 

⎝ tanφ 

⎠ 

(1) 

The shadow of the external reflector (ADEF) on 

a horizontal surface is shown as ANDNENFN, and 

plane ADGH is the mirror symmetric plane of the 

glass cover to the reflector, and its shadow is 

shown as ANDNGH. The solar radiation reflected 

from the external reflector and absorbed on the 

wick, Q sun,re, can be determined as the product of 

the direct solar radiation on a horizontal surface, 

the overlapping area of shadows of the mirror 

symmetric glass cover plane (ANDNGH) and the 

external reflector (ANDNENFN) shown as ANDNIFN, 

reflectivity of the external reflector, ρ re, transmissivity 

of the glass cover and absorptivity of 

the wick, and this may be expressed as 

Q = G τ ( β) ρ α × l 

sun, re dr g re w m 

⎛ 1 sin| ϕ −γ 

| ⎞ 

× ⎜w− lm 

⎟ 

⎝ 2 tanφ⎠ 

cos( ϕ −γ 

) 

tanφ 

(2) 

In Eqs. (1) and (2), β is the incident angle of 

sunrays to the glass cover, and can be expressed 

as [19]:

142 

C For Eq. (1) 

cos β = sinφcosθ + cosφsinθcos( ϕ −γ) 

C For Eq. (2) 

cos β = sinφcosθ −cosφsinθcos( ϕ −γ) 


(3) 

(4) 

Diffuse solar radiation absorbed on the wick, 

Q sun,df, can be determined with the assumption that 

diffuse radiation comes uniformly from all 

directions in the sky dome, and may be expressed 

as 

Q , = G ( τ ) α × wl 

sun df df g df w s 

(5) 

where G df is the diffuse solar radiation on a 

horizontal surface, and (τ g) df is a function of the 

angle of the still, θ, and is calculated by integrating 

the transmissivity of the glass cover for 

diffuse radiation from all directions in the sky 

dome. This may be expressed as 

−3 

−5 

2 

( τ ) =− 2.03× 10 × θ 

g df 

− 2.05× 10 × θ + 0.667 θ [ ] 

 

(6) 

During the months of April to August, the sun 

moves north in the morning and evening, and the 

external reflector would obstruct the sunrays and 

shade the wick. This causes a decrease in the 

direct solar radiation absorbed on the wick, Q sun,dr. 

In the calculation, the effect of the shadow is 

taken into account, and the solar radiation 

absorbed on the wick Q sun,dr and Q sun,re when the 

sun moves north may be expressed as: 

Q = G τ ( β) α × 

sun, dr dr g w 

2 

+ lm 

2 ⎥ 

2 tan φ ⎦ 

(7) 

⎡ ⎧ ⎛ cos( ϕ −γ) ⎞ cos( ϕ −γ) 

⎫ 

⎢w⎨ls⎜cosθ −sinθ ⎟−lm 

⎬ 

⎢⎣ ⎩ ⎝ tanφ ⎠ tanφ 

⎭ 

1 cos( ϕ −γ)sin| ϕ −γ 

| ⎤ 

Q = 0 

sun, re 

3. Heat and mass transfer in the still 

(8) 

Heat and mass transfer in the still are shown in 

Fig. 3. The energy balance for the glass cover and 

the evaporating wick may be expressed as 

Q + Q + Q + Q = Q 

sun, g r, w−g d, w−g e, w−g r, g−a + Q + ( mc ) 

cg , −a 

p g 

dT 

d t 

Q = Q + Q + Q 

sun, w r, w−g d, w−g e, w−g g 

(9) 

dT 

(10) 

w 

+ Qdw , −a 

+ Qf+ ( mcp) 

d t 

where Qsun,g and Qsun,w are the solar radiation 

absorbed on the glass cover and the evaporating 

wick, and Qr, Qd, Qc and Qe are the heat transfer 

rates by radiation, conduction, convection, and 

evaporation and condensation. Qf is the increase 

in the enthalpy of the saline water fed to the wick. 

mcp is heat capacity, T is temperature and t is 

time. 

The solar radiation absorbed on the glass 

cover (Qsun,g) and the evaporating wick (Qsun,w) can be determined as follows: 

C For a still with an external reflector: 

αg 

Qsun, g = ⎡( 

Qsun, dr Qsun, 

re ) / τ g ( β ) 

α ⎣ 

+ 

w 

(11) 

+ Qsun, 

df /( τ g ) df ⎤ 

⎦ 

Q = Q + Q + Q 

sun, w sun, dr sun, re sun, df 

C For a still without the external reflector: 

α 

Q Q Q 

(12) 

( / τ ( β) /( τ ) ) 

g 

sun, g = sun, dr g + sun, df g df 

αw 

(13)

Table 1 

Design, weather conditions, physical properties and 

constants 

w = 1 m, ls = 1 m, lm = 0.5 m, θ = 30 o , 

γ = 0 o (still is orienting due south) 

Diffusion gap between wick and glass cover 

= 10 mm, (mcp) g = 6.4 kJ/K 

αw = 0.9, αg = 0.08, ρre = 0.85 

τg(β) = 2.642cosβ ! 2.163cos 2 β ! 0.320cos 3 β 

+ 0.719cos 4 β [18] 

T a = 25 o C, 33 o C, 30 o C and 20 o C in spring, 

summer, autumn and winter 

G dr: Bouguer’s Eq. (19) with transmissivity of 

atmosphere is 0.7 and 30EN latitude 

G df: Berlage’s Eq. (19) with the solar radiation incident 

on the atmosphere of 1370 W/m 2 at 30EN latitude 

Thermal conductivity and thickness of bottom insulation 

= 0.04 W/mK and 50 mm. 

Q = Q + Q 

sun, w sun, dr sun, df 


(14) 

Heat and mass transfer (Q c, Q d, Q e, Q f and Q r) 

in Eqs. (9) and (10) are basically the same in 

Fig. 3. Heat and mass transfer in the still. 

content as the one by Elsayed [17] and Tanaka et 

al. [18]. Eqs. (1)–(14) were solved together to 

find the solar radiation absorbed on the evaporating 

wick, temperatures in the still and the distillate 

production rate at time t+Δt. Temperatures 

of the evaporating wick and the glass cover were 

set to be equal to T a at t = 0, just before sunrise as 

the initial conditions. The weather and design 

conditions and physical properties and constants 

employed in the calculations are listed in Table 1. 

4. Results 

Fig. 4 shows the theoretical predictions of 

hourly variations of (a) the global solar radiation 

on a horizontal surface (global) and the distillate 

production rates of the tilted wick still with an 

external flat plate reflector (called RS) and one 

without a reflector (called NS), (b) the solar 

radiation absorbed on the evaporating wick of RS 

and NS and (c) the absorption of direct and diffuse 

solar radiation and reflected solar radiation

144 

Fig. 4. Time variation of (a) distillate production rate, 

(b) solar radiation absorbed on the wick and (c) absorption 

of direct, diffuse and reflected solar radiation on a 

spring equinox day at θ = 30E. 


from the reflector on the wick on a spring equinox 

day at θ = 30E latitude. Distillate production 

rate as well as the solar radiation absorbed on the 

wick is greater for RS (the still with a reflector) 

than for NS (the still without a reflector) from 

8 am to 4 pm since the evaporating wick could 

receive the reflected radiation from the reflector 

during the period. The daily global solar radiation 

on a horizontal surface is about 23.3 MJ/m 2 day, 

and the daily amount of distillate of RS 

(6.5 kg/m 2 day) is about 14% greater than that of 

NS (5.7 kg/m 2 day). 

The daily amounts of distillate varying with 

the angle of the still from horizontal, θ, on the 

spring equinox and summer and winter solstice 

days are shown in Fig. 5. Here, the results for the 

autumn equinox are not shown in Fig. 5, but the 

results for the autumn equinox are almost the 

same as those for the spring equinox since the 

loci of the sun on these days would be almost the 

same. On the spring equinox, the daily amounts 

of distillate of RS and NS have gentle peaks 

around θ = 30 o , since the tilted surface in which 

the inclination is equal to the latitude (30EN) 

would maximize the solar radiation on the tilted 

surface on the day. On the summer solstice, the 

daily amounts of distillate of RS and NS decrease 

inversely with an increase in the angle θ since the 

solar altitude angle becomes nearly vertical 

around noon and this causes a smaller projecting 

area on a horizontal surface for the still with a 

larger angle θ. Further, the daily amount of distillate 

is smaller for RS than for NS. This is 

because the external reflector would obstruct the 

sunrays and shade the wick during the early 

morning (until about 9 am) and the late afternoon 

(after about 3 pm), and the reflected radiation 

absorbed on the wick would be very small even 

around noon. On the winter solstice, the daily 

amount of distillate of NS increases directly with 

an increase in the angle θ, while an RS still has a 

gentle peak around θ = 20E, and the daily 

amounts of distillate of RS and NS would be 

approximately the same when the angle θ is

Fig. 5. Variation of daily amount of distillate with angle 

of still on the spring equinox and the summer and winter 

solstices. 

Fig. 6. Variation of average daily amount of distillate for 

four days (spring and autumn equinox and summer and 

winter solstice days) with angle of still. 

larger than 35E. The reason is that the reflected 

radiation from the reflector which can be absorbed 

on the wick decreases with an increase in 

the angle θ and would be negligible when the 

angle θ is larger than 35 o , since the portion of 

sunrays that would be reflected by the reflector 

but cannot hit the wick and would escape to the 

ground, would increase with an increase in the 

angle θ. 

Variations of the averaged daily amount of 

distillate for four days (spring and autumn equinox 

and summer and winter solstice days) with an 


angle of the still, θ, is shown in Fig. 6. The 

averaged daily amount of distillate for NS has a 

gentle peak around θ = 30E (equal to the latitude) 

while the average for RS peaks at around 20E. 

This is mainly caused by the fact that the daily 

amount of distillate of RS on the summer solstice 

decreases considerably with an increase in the 

angle θ, but on the spring and autumn equinox 

and winter solstice days it is almost the same at 

θ = 20E and 30E, as shown in Fig. 5. 

The averaged daily amount of distillate of RS 

at θ = 20E is about 9% greater than that of NS at 

θ = 30E. Recently, we theoretically analyzed the 

effect of the vertical flat plate external reflector 

on the distillate productivity of the basin still 

[13], and the increase in the daily amount of 

distillate by using external flat plate reflector was 

predicted to average about 26% for the entire 

year. Therefore, the vertical flat plat external 

reflector would be less effective for the tilted 

wick still than for the basin still. 

5. Conclusions 

We theoretically predicted the effect of a 

vertical flat plate external reflector for the tilted 

wick still on the solar radiation absorbed on the 

evaporating wick as well as the distillate productivity 

of the still at 30EN latitude, and the 

results of this work are summarized as follows: 

1. The averaged daily amount of distillate for 

four days (spring and autumn equinox and summer 

and winter solstice days) peaks when the 

angle of the still θ is 20E for the still with the 

reflector, and peaks at θ = 30E for the still 

without the reflector. 

2. The average daily amount of distillate of 

the still with the reflector is predicted to be about 

9% larger than that of the still without the 

reflector, and the vertical flat plate external 

reflector would be less effective for the tilted 

wick still than for the basin still.

146 

6. Symbols 

G df — Diffuse solar radiation, W/m 2 

G dr — Direct solar radiation, W/m 2 

l m — Height of reflector, m 

l s — Length of still, m 

mc p — Heat capacity, J/K 

m f — Feed rate of saline water, kg/m 2 s 

Q c — Convective heat transfer rate, W 

Q d — Conductive heat transfer rate, W 

Q e — Heat transfer rate of evaporation and 

condensation, W 

Q f — Enthalpy increase of feeding saline 

water, W 

Q r — Radiative heat transfer rate, W 

Q sun,df — Absorption of diffuse solar radiation, 

W 

Q sun,dr — Absorption of direct solar radiation, 

W 

Q sun,g — Absorption of solar radiation on 

glass cover, W 

Q sun,re — Absorption of reflected solar radiation, 

W 

Q sun,w — Absorption of solar radiation on 

wick, W 

T — Temperature, K 

t — Time, s 

w — Width of still, m 

Greek 

α — Absorptivity 

β — Incident angle 

φ — Solar altitude angle 

γ — Azimuth angle of still 

ϕ — Solar azimuth angle 

θ — Angle of still 

ρ re — Reflectivity of reflector 

τ g — Transmissivity of glass cover 

Subscripts 

a — Ambient air 


g — Glass cover 

w — Wick 

References 

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(2007) 70–82. 

[17] M.M. Elsayed, J. Solar Energy Engineering, Trans. 

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[19] Japan Solar Energy Soc., Solar Energy Utilization 

Handbook, Tokyo, 1985, pp. 2, 20.

Improvement of the tilted wick solar still by using a flat plate reflector

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