*Corr. Author’s Address: Czestochowa University of Technology, 42201 Czestochowa, Poland, winczek@gmail.com 369
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379 Received for review: 2021-03-09
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-05-18
DOI:10.5545/sv-jme.2021.7156 Original Scientific Paper Accepted for publication: 2021-06-28
Experimental Investigation and Mathematical Modelling  
of Heat Transfer Coefficient in Double Slope Solar Still
Patel, R.V . – Yadav, A. – Winczek, J.
Raj Vardhan Patel
1,2
 – Anshul Y adav
1,2
 – Jerzy Winczek
3*
1
Kamla Nehru Institute of Technology, India 
2
CSIR-Central Salt and Marine Chemicals Research Institute, India 
3
Czestochowa University of Technology, Poland
In this study, a double slope solar still has been designed and fabricated with the help of locally available materials for the climatic condition of 
Sultanpur, India. The experimental study was performed to investigate the effect of basin water, wind velocity on the heat transfer coefficient 
(convective, evaporative, and radiative) and yield of solar still. A mathematical model is developed to understand the impact of wind velocity 
and basin water depth in the double slope solar still on the heat transfer coefficient. It was found that the convective heat transfer coefficient 
depends upon the water mass and the temperature of basin mass, and glass cover temperature. The maximum value of h
ew
 (55.05 W/(m²K) 
and 31.80 W/(m²K)) and h
cw 
, (2.48 W/(m²K) and 2.38 W/(m²K)) found for depths of 2 cm and 5 cm, respectively. The radiative heat transfer 
coefficient found to be a maximum of 8.31 W/(m²K) for 2 cm depth, and it increases as the condensation increases, because the glass 
surface temperature increases as vapour transfers its energy to the surface. On increasing the depth from 2 cm to 5 cm, the yield from the 
solar still decreases by 25.45 %. The maximum yield of 2.5 l/m²/day was found for a 2 cm water depth. The theoretical and experimental yield 
agreed with an error of 7.5 %, 3.25 %, 7.4 %, and 8.4 % for water depths of 2 cm, 3 cm, 4 cm, and 5 cm, respectively. It was also found that the 
yield from the solar still increases as the wind speed increase because this leads the faster condensation at the glass surface.
Keywords: double slope solar still; solar energy; distillation; heat transfer coefficient
Highlights
• 	 A mathematical model is developed to find the yield and heat transfer coefficient for double slope solar still with the experimental 
findings on the yield and heat transfer coefficient.
• 	 Convective and evaporative heat transfers were the most critical parameters for a solar distillation unit. 
• 	 The radiative heat transfer coefficient increases as the condensation increase because, due to condensation, the glass surface 
temperature increases as vapour transfers its energy to the glass surface.
• 	 The yield from the still increases as the basin water depth decreases. The evening time production is higher for higher basin 
mass because of the heat-storing capacity of basin mass.
• 	 The yield of solar still increases as the wind speed increases because this leads to higher condensation on the glass surface.
0  INTRODUCTION
Currently, energy and fresh water supplies are major 
challenges in remote areas. Only 1 % of the total water 
available on the earth can be used for drinking. Current 
distillation methods use conventional fuel, which are a 
limited resource, and there is environmental pollution 
when such fuels are used to generate power. Solar 
stills are simple devices that can be used to produce 
potable water. They can be an effective solution for 
providing potable water in remote areas [1] and [2].
Solar stills are generally classified into two 
categories: active and passive [3] and [4]. Solar stills 
require only solar energy for their operation, which 
is freely available and eco-friendly, and work on the 
simple principle of evaporation and condensation. 
Solar distillation removes salts and other impurities 
[5] and [6]. It is used to produce potable or pure water 
for hospitals, laboratories, and commercial products 
[7] and [8]. 
The yield of a conventional solar still depends 
on the water mass in the basin. The effect of that 
water mass on the solar heat transfer still has been 
investigated by various researchers [9] to [11]. The 
studies concluded that as the mass of basin water 
increases, the yield from the system decreases. Dev et 
al. [9] investigated the inverted absorber single slope 
solar still, and found higher production of freshwater 
with 1 cm depth compared to 2 cm and 3 cm depths. 
Phadatare and Verma [10] studied water depth on 
the internal heat and mass transfer in the single-
basin double-slope solar still (DSSS). Tripathi and 
Tiwari [11] concluded that the yield from the system 
decreases as the mass of basin water increases. The 
experimental and analytical study performed by 
Feilizadeh et al. [12] reported that the production from 
the solar still increases as the water depth and distance 
between the water basin and the condensing cover is 
lower.
The radiative and convective heat transfer 
decrease as the water mass in the basin increases. 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
370 Patel, R.V. – Yadav, A. – Winczek, J.
The influence of wind on the production of solar 
stills was investigated by El-Sebaii [13] and [14], 
who determined that the increase in wind speed up 
to a critical value increases the yield of still. Higher 
wind speed decreases the yield because it decreases 
the basin temperature. An experiment conducted by 
Danish et al. [15]
 
to enhance the performance of the 
solar still by using a vacuum pump and geothermal 
energy found that the increases in wind speed have a 
detrimental effect on the yield of solar still, because 
the increase in speed increases the heat loss from the 
basin water. 
The production rate of solar stills is low; therefore, 
they cannot be used as a conventional water purifier. 
The yield from a solar desalination unit increased 
by incorporating phase change materials (PCM) [16] 
and [17] and nanofluids [18] and [19] to the basin 
water. Mathematical modelling has been as subject 
of some interest as it can optimize the efficiency and 
production by changing the different operational and 
geometrical parameters without losing its inherent 
feature of low cost; the main advantage associated 
with modelling analysis that much effort and cost 
can be minimized for carried out the experimentation 
[20] and [21]. Rahbar and Esfahani [22] proposed a 
numerical correlation to determine the productivity 
of a solar still by assuming the fixed water depth and 
glass temperature. The trends of water production are 
similar to the convective heat transfer coefficients. 
Madhlopa [23] modelled the radiative heat transfer 
inside a solar still with and without considering the 
view factor, and the numerical model with view factor 
involving provides better yield. Keshtkar et al. [24]
proposed a novel transient model to calculate transient 
temperature and concentration distribution and also 
production from a solar still without specifying the 
water and glass surface temperatures as the boundary 
condition.
The production of a solar still is dependent on the 
rate of heat transfer in the solar still, basin water, and 
wind velocity (which provides glass cover cooling), 
and similar factors. The present study focuses on 
studying the variation of the heat transfer coefficient 
with basin water temperature and wind velocity for the 
acrylic solar still for the summer climatic condition of 
Sultanpur, India. The different heat transfer coefficient 
associated with DSSS is compared for different water 
depths, and the comparisons have been made for the 
orientations (i.e., east and west sides).
1  EXPERIMENTS
1.1  Solar Distillation Unit
The schematic diagram and the experimental setup of 
the DSSS are shown in Figs. 1 and 2, respectively. A 
passive DSSS is designed and fabricated to investigate 
the effect of climatic and operational parameters 
on a solar still for the summer climatic condition 
of Sultanpur (latitude: 26.2648° N and longitude: 
82.0727° E) Uttar Pradesh, India. The basin of the 
solar still is fabricated frin a black acrylic sheet of a 
thickness of 4 mm. The basin size of the still is 1 m × 
1 m × 0.1 m. Plywood of 12 mm thickness is used for 
support and insulation of solar still basin in order to 
reduce the heat transfer from the bottom and side of 
solar still basin. The acrylic material has been selected 
due to its low thermal conductivity and high water-
resistant nature. The still is designed for the maximum 
water depth of 10 cm. Glass of 3.5 mm thickness 
used as the condensing cover, which is inclined at 
an angle of 30°. The condensing cover inclination is 
equal to the latitude of Sultanpur to receive maximum 
radiation from the sun. The basin of the still is painted 
black to enhance the capacity of the basin to receive 
the maximum solar radiation. A V-shaped trough of 
length 1.02 m is provided below the condensing cover 
to collect the condensed water from the glass surface. 
M-seal and putty were used to make still airtight and 
prevent water leakage.
Fig. 1.  A schematic diagram of solar still
1.2  Experimental Measurements
The experiments were performed in March and 
April 2016. The solar still was placed in the east-
west orientation for the experiments. Seven digital 
temperature sensors were used to record the 
temperature reading at the different locations of solar 
still. Global solar radiation, ambient temperature, and 
wind speed data were taken from the solar radiation 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
371 Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 
resource assessment (SRRA) station installed at the 
KNIT, Sultanpur, India. A digital anemometer was 
used for measuring the wind velocity. The temperature 
readings were recorded at a one-hour interval. The 
experiments were carried out for different water 
depths, of which 2 cm, 3 cm, 4 cm, and 5 cm are 
presented in this study.
Fig. 2.  Experimental setup of solar still
1.3 Error Analysis of Experimental Measurements
The errors associated with the different measuring 
instruments (solarimeter, digital thermometer, digital 
anemometer, and measuring jar) have been calculated 
based on the least count and the least value measured 
from that instrument during the experimentation. The 
minimum error is the ratio of the least value that an 
instrument can measure to the least value measured 
from that instrument. Table 1 shows the error 
percentages associated with the different measuring 
instruments.
Table 1.  List of measuring devices and their accuracy and error
Instrument Range Accuracy Error [%]
Solarimeter 0 W/m² to 2500 W/m² ±1 W/m² 0.707
Thermometer –50 °C to 150 °C ±0.1 °C 0.37
Anemometer 0 m/s to 15 m/s ±0.1 m/s 9.17
Measuring jar 0 ml to 1500 ml ±1 ml 10
2  THERMAL CALCULATION FOR THE MODEL
2.1  Mathematical Model for Heat Transfer in Solar Still
The heat transfer can be classified into two categories: 
internal and external heat transfer in a solar distillation 
system. The different heat interactions in the solar 
distillation unit are explained below.
2.1.1  Internal Heat Transfer
The internal heat transfer is the heat transfer 
between basin water and glass cover by convection, 
evaporation, and radiation.
2.1.2  Convective Heat Transfer
The heat transfer is taking place across the air, which 
is inside the solar still. As the system is airtight, there 
is no external velocity provided to the inside air to 
cause heat transfer. The air is humid because of vapour 
evaporating from the water surface; the heat transfer is 
due to the buoyancy only, meaning that free 
convection heat transfer occurs inside the still casing. 
The rate of convective heat transfer (  q
cw
) from the 
water surface to condensing glass cover is given by:
  qh TT
cw cw wg


. (1)
The convective heat transfer coefficient depends 
on the operating temperature range of still and physical 
properties of the fluid at this operating temperature, 
condensing cover geometry and flow characteristics 
of the fluid. Dunkle [25] developed an equation for 
evaluation of the internal heat transfer coefficient:
 hT
cw
 0 0884
1
3
.( ),
*
 (2)
where TT T
PPT
P
wg
wgw
w
*
.
.
. 




 










273 15
268 91 0
3
2.1.3  Evaporative Heat Transfers
The evaporative heat transfer occurs between the 
water surface and the inner glass surface of the DSSS.
The rate of evaporative heat transfer (  q
ew
) from 
the water surface to glass cover surface is given by:
  qh TT
ew ew wg


, (3)
and the evaporative heat transfer from the water 
surface to the glass surface is given by:
  qh PP
ew cw wg


0 0162 .. (4)
The above equation can be rearranged as:
  qh
PP
TT
TT
ew cw
wg
wg
wg








16 273 10
3
., (5)
where hh
PP
TT
ew cw
wg
wg






16 273 10
3
.,

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
372 Patel, R.V. – Yadav, A. – Winczek, J.
where P
w
 and P
g
 are partial saturation pressures  
[W/m
2
] and given by [26]:
 P
T
P
T
g
gi
w
w












exp.
.
,
exp.
25 317
5144
273 15
25 317
5144
273 31 5 .
.






 (6)
 
P
T
P
T
g
gi
w
w












exp.
.
,
exp.
25 317
5144
273 15
25 317
5144
273 31 5 .
.






 (7)
2.1.4  Radiative Heat Transfer Coefficient
The rate of radiative heat transfer (  q
rw
) from the 
water surface to glass cover for these infinite parallel 
surfaces is given by:
      qT T
rw effw g
  







 273 15 273 15
4
4
.. . (8)
The rate of radiative heat transfer is also given by:
  qh TT
rw rw wg


. (9)
The (h
rw
) is the radiative heat transfer coefficient 
from the water surface to the glass cover and is given 
by (by comparing Eqs. (8) and (9)):
   
hT T
TT
rw effw g
wg
  







  



 273 15 273 15
546 30
2
2
..
.. (10)
where e
ff
 is effective emissivity of water and glass 
surface, σ Stefan-Boltzmann constant (5.67×10
–8
 
W/(m
2
K
4
)).
2.1.5  External Heat Transfers
The external heat transfer is primarily governed by 
conduction, convection, and radiation process, which 
are independent of each other. These heat transfers 
occur outside the solar distiller, from the glass cover 
and the bottom and side insulation.
2.1.6  Top Loss Coefficient
Due to the small thickness of the glass cover, the 
temperature of the glass may be assumed to be 
uniform. The external rate of heat transfer radiation 
(  q
rg
), convection (  q
cg
) and total heat (  q
tg
) losses from 
the glass to the ambient surroundings are expressed 
as:
 
  qqq
tg rg cg
 ,
 (11)
     qT T
rg gg sky










 273 15 273 15
44
.. , (12)
  qh TT
rg rg ga


. (13)
Comparing the above Eqs. (12) and (13), we 
obtain:
  h
TT
TT
rg
gg sky
ga













 273 15 273 15
44
..
, (14)
where T
sky
 = T
a
 – 6 [27], ε
g
 emissivity of the glass 
surface. The ambient emissivity is assumed to be 1, 
as it behaves as a black body [8]. (In case of clear 
and cloudy sky, the difference between ambient 
temperature and effective sky temperature was 
assumed to be 6 °C) and the rate of convective heat 
transfer from the glass surface to ambient is given by:
  qh TT
cg cg ga


. (15)
On substituting the value of (  q
rg
) and (  q
cg
) in Eq. 
(11), we obtain:
  qh TT
tg tg ga


, (16)
where h
tg
 = h
rg
 + h
cg
.
The expression for (h
tg
) and (h
cg
) is given by 
Watmuff and Charters [27]:
 h
tg
 = 5.7 + 3.8 V, (17)
 h
cg
 = 2.8 + 3 V, (18)
where V is wind velocity [m/s], h
tg
 is, h
rg
 and h
cg
 total, 
radiative, and convective heat transfer coefficient 
[W/m²] from the top glass surface, respectively.
2.1.7  Bottom and Side Loss Coefficient
Heat is also lost from the water in the basin to the 
ambient through the insulation, subsequently by 
convection and radiation from the bottom or side 
surface of the basin. The bottom loss coefficient (U
b
) 
can be written as:
 U
hh
b
wb








11
1
. (19)
The side loss coefficient (U
e
) can be expressed as:
 U
UA
A
e
bS S
S
= , (20)
where A
SS
 is a sidewall surface area [m
2
] in contact 
with basin water and A
S
 area of the basin of the 
distiller [m
2
]. A
SS
 is very small in comparison to A
S
, 
for small water depth. Therefore, it can be neglected. 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
373 Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 
The rate of heat loss per m
2
 from the basin liner 
to ambient can be written as:
  qhTT
bw a
  , (21)
where h
t
Khh
b
i
ic br b









1
1
, where h
w
 and h
b
 are 
convective and overall heat transfer coefficient from 
basin liner to ambient through the bottom, t
i
 thickness, 
K
i
 thermal conductivity of the insulation material at 
the bottom, h
cb
 and h
rb
 convective and radiative heat 
transfer coefficient basin liner to ambient through the 
bottom.
2.1.8  Determination of Distillate Output
The hourly distillate output per m
2
 from the solar still 
can be obtained as:
    m
L
q
ew
ew
=

3600, or m
hTT
L
ew
ew wg



3600, (22)
where L is latent heat of vaporization [J/kg] for less 
than 70° and given by [27]:
 
LT
TT
 







2 4935 10 19 4779 10
1 3132 10 4 7974 10
64
72 93
..
.. ,, 
where temperatures are in °C and heat transfer 
coefficients are in W/(m
2
K). The heat transfers rate 
presented in the thermal modelling are in W/m
2
. The 
subscripts w, g, a, and i indicate the basin water, glass 
surface, ambient and insulation respectively.
3  RESULTS AND DISCUSSIONS
The present experimental work has been carried out 
for heat transfer analysis of the east-west orientation 
of DSSS for various basin water depths (2 cm, 3 cm, 
4 cm and 5 cm). The east-west orientation has been 
chosen because the still gives maximum yield for this 
orientation. The experimental measurements were 
recorded and accurately from 8:00 h to 17:00 h. The 
mathematical equations which are used in the thermal 
model have solved analytically. As the difference 
between basin water and glass cover increases, the 
rate of heat transfer, as well as the production from the 
DSSS increases.
3.1  Variation of Basin Water Temperature with Basin Water Depth 
In Fig. 3, the variation of basin water temperature 
with the depth of basin water and wind velocity 
are represented. It can be seen that the basin water 
temperature for 2 cm water depth is higher compared 
to 3 cm, 4 cm, and 5 cm water depths. This is 
because the basin water with 3 cm, 4 cm and 5 cm 
depths have high thermal inertia compared to 2 cm 
water depth. Therefore, the basin filled with 2 cm 
water depth will be heated faster than other water 
depths. During the experiments, it was found that the 
Fig. 3.  Variation of basin water temperature with basin water depth and wind velocity

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
374 Patel, R.V. – Yadav, A. – Winczek, J.
maximum temperature for 2 cm, 3 cm, 4 cm, and 5 
cm depths are 69.0 °C, 62.6 °C, 58.5 °C, and 54.4 °C, 
respectively, between 13:00 h and 14:30 h. The peak 
starts shifted towards the right side as basin water 
depth increases from 2 cm to 5 cm. This is because 
5 cm water depth requires more time to be heated, 
due to the higher mass present in the basin. The basin 
water temperature was found to be maximum for 2 cm 
depth. The temperature decrease for 2 cm water depth 
was higher than other higher water depth after 14:00 
h because of lower heat storage capacity. During the 
experimentation, the average wind velocity was found 
to vary between 2 m/s to 3 m/s.
3.2  Variation of Heat Transfer Coefficients with Basin 
Water Depth
Figs. 4 to 6 show the variation of heat transfer 
coefficients (convective, evaporative, and radiative, 
respectively) for DSSS for the east and west glass. The 
curves are drawn for the positive value of temperature 
difference between basin water and glass cover 
surface ( δT). The yield from the solar still increases 
either increase in evaporation temperature or decrease 
in condensing surface temperature. In both cases, the 
( δT) increases and the heat transfer rate increases.
Fig. 4 shows the variation of the convective 
heat transfer coefficient obtained from Eq. (2). The 
convective heat transfer rate is strongly dependent 
on the temperature difference between the water and 
glass cover surface. Fig. 4 shows that the average heat 
transfer coefficient for 2 cm water depth is maximum 
because of the higher temperature difference than 
higher water depths. This is because the lesser mass 
present in the basin with 2 cm depth requires less 
time to be heated. The maximum value of h
cw
 were 
2.48 W/(m²K), 2.25 W/(m²K), 2.21 W/(m²K), and 
2.38 W/(m²K) for 2 cm, 3 cm, 4 cm, and 5 cm depths, 
respectively. The heat transfer coefficients are higher 
than the results obtained in the experimental studies 
by Shukla and Rai [28]. The maximum heat transfer 
occurs around 13:00 to 14:00 h, while in the case with 
5 cm depth, the maximum value of h
cw
 occurs at 16:00 
h. This is because of the higher wind speed, which 
leads to faster cooling of the glass. Thus, the heat 
transfer of convection increases. The heat transfer 
coefficient is lower for 2 cm depth compared to 5 
cm depth after 16:00 h. This is because of the higher 
thermal storage capacity of 5 cm water depth, which 
leads to higher basin water temperature.
Fig. 5 shows the variation of the evaporative heat 
transfer coefficient (calculated from Eq. (5)) with 
basin water depth for the experimental setup. It can 
be observed from Fig. 5 that the h
ew
 is high for west 
glass because there is no direct sun heating of it in the 
morning, but as the evaporation starts and vapour start 
condensing on the west glass surface, the heat released 
during condensation heated the glass surface which 
leads the increase in the surface temperature of the 
glass. Thus, as the process continued, the temperature 
of west glass approaches saturation temperature, and 
due to this, condensation starts decreasing after 13:00 
h, 13:30 h and 14:00 h, and 14:30 h for 2 cm, 3 cm, 4 
cm, and 5 cm water depths.
It is seen that from Figs. 4a and 5a that in the 
morning for 2 cm water depth, the rate of h
cw
 and h
ew
 
is maximum for the west glass because basin water, 
as well as the east glass, is heated; therefore, the δT 
is higher for the west glass as compared to the east 
glass. After 13:00 h, the variation becomes closer 
for east and west glass because solar radiation does 
not directly fall on one glass only. This is also due 
to the higher basin water temperature as it absorbs 
solar energy since morning. However, in the case of 
higher water depths (i.e., 3 cm, 4 cm, and 5 cm), the 
east and west variation is almost eliminated because 
of the heating due to solar radiation and cooling due 
to wind. While 2 cm depth variation of heat transfer 
is faster than other depths, the wind velocity is higher 
with the 5 cm water depth; this is because of higher 
thermal energy storing capacity with the 5 cm depth 
consequent the slower cooling of the basin water. The 
h
cw
 of east and west surfaces for the present solar still 
is higher for the period of 15:00 to 17:00, compared 
to Shukla and Rai [28]. This is because of the higher 
basin temperature and low thermal conductivity of 
acrylic material of solar still, which reduces the heat 
loss of the basin water. 
The average evaporative heat transfers were 
higher for 2 cm depth than other water depths (3 cm, 
4 cm, and 5 cm). Therefore, the yield in the case of 2 
cm water depth is maximum as the evaporation rate 
is the main driving parameter for the production from 
the solar still. From Fig. 5, the h
ew
 starts decreasing at 
a faster rate for 2 cm depth compared to other water 
depths. This is not only because of low heat-storing 
capacity for 2 cm water depth but also because of the 
lower heating rate for the other higher depths; thus, 
from the evening, the production rate starts decreasing 
faster for lower and nocturnal production is more for 
higher depths.
The maximum value of h
ew
 is found to be 
55.05 W/(m²K), 49.23 W/(m²K), 31.25 W/(m²K) 
and 31.80 W/(m²K) for 2 cm, 3 cm, 4 cm and 5 cm 
water depths. The peak of h
ew
 shifted to the right as 
the mass in the basin starts increasing; this is due 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
375 Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 
to lower thermal inertia for 2 cm depths compared 
to others depth. The maximum value of h
cw
 and h
ew
 
are found to be 2.48 W/(m²K) and 55.05 W/(m²K) 
for the west glass, respectively, for 2 cm depth. 
          
Fig. 4.  Variation of the convective heat transfer coefficient with basin water depth for: a) east glass, and b) west glass
           
Fig. 5.  Variation of evaporative heat transfer coefficient with basin water depth for a) east glass b) west glass
          
Fig. 6.  Variation of radiative heat transfer coefficient with basin water depth for a) east glass b) west glass

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
376 Patel, R.V. – Yadav, A. – Winczek, J.
2 cm, 3 cm, 4 cm and 5 cm water deptha for the 
experimental setup for the east and west glass of 
DSSS. The radiation heat transfer mainly depends 
on the basin water and glass surface temperature and 
the emissivity of basin water and glass surface. As 
the evaporation increases, the surface temperature of 
the glass surface increases due to the condensation of 
vapour on the glass surface. Therefore, the radiation 
heat transfer coefficient increases. The maximum heat 
transfer coefficients are found to be 8.32 W/(m²K), 
8.21 W/(m²K), 7.47 W/(m²K) and 7.41 W/(m²K) for 
2 cm, 3 cm, 4 cm and 5 cm water depths, respectively. 
Shukla and Rai [28] showed a lower radiative heat 
transfer coefficient than the present study did. This is 
because of the higher evaporation and condensation 
associated with the design of DSSS. In the present 
There are some fluctuations in heat transfer because 
of uncontrolled wind speed over the DSSS glass 
surfaces. From Fig. 5, it can be seen that the heat 
transfer coefficient increases for higher water depths. 
This is due to an increase in wind speed which leads 
to better evaporation as well as condensation. When 
the results are compared with those of Shukla and 
Rai [28], the maximum and average evaporative heat 
transfer coefficients are found to be higher in this 
study. This is due to the higher temperature difference 
obtained with the present experimental setup. This 
higher temperature difference is because of higher 
basin temperature also due to the insulating nature of 
acrylic.  
Fig. 6 shows the variation of radiation heat 
transfer’s coefficient (calculated from Eq. (8)) for 
 Fig. 7.  Hourly yield from per m
2
 area of the solar still at 2 cm, 3 cm, 4 cm and 5 cm water depth; a) theoretical, and b) experimental

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
377 Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 
study, the radiative heat transfer coefficient for 2 cm 
and 3 cm depth are higher because of the high basin 
temperature and higher evaporation associated with 
these depths, leading to increases in glass temperature 
as the h
rw
 is the function of both glass and basin water 
temperature. It was also observed that the h
ew
 (west 
surface) was much higher for 3 cm compared to h
rw
, 
but the variation in h
rw
 for 2 cm and 3 cm (Fig. 6b) 
is closer due to higher evaporation compensated by 
higher basin temperature for 2 cm depth. 
Fig. 7 shows the theoretical (calculated from 
Eq. (17)) and experimental yield from the still for 2 
cm, 3 cm, 4 cm, and 5 cm water depths in the basin. 
The theoretical yield from the still is higher than the 
experimental yield, but sometimes it is lower than 
experimental because of the atmospheric condition 
like wind speed; due to this, the vapour is condensed 
rapidly, whereas the theoretical yield depends on the 
temperature difference between the glass and basin 
water; also. the data recorded are average data. The 
yield for 2 cm water depth is higher than 3 cm, 4 cm. 
and 5 cm water depths. This proves that the yield is 
higher for a lower basin mass. After 15:00 h, it can be 
seen that the yield for 2 cm depth is decreasing at a 
faster rate compared to other higher depts. This is due 
to the heat-storing capacity of the basin mass. This 
proves that the evening and off-sun time production 
is higher for higher basin mass. Before the afternoon, 
the yield rate is higher for 2 cm depth because of the 
higher evaporation rate as compared to other water 
depths.
The wind has a positive effect on yield with higher 
depth compared to a lower depth. This is because 
the lesser depth (2 cm) of basin water’s temperature 
decreases faster, which enhances the yield. While for 
higher depth (4 cm), this has a less negative effect due 
to the higher energy storing capability of water mass. 
It can be seen from Figs. 3 and 7b that the yield is 
higher when wind speed increases. This is because 
of the higher temperature gradient between the basin 
water condensing glass cover for 4 cm compared to 
the 2 cm depth water depth. The yield from the still is 
higher for the 4 cm depth between 13:00 h and15:00 h 
not only because of the wind speed but also due to the 
higher water mass, which stores more thermal energy 
and release during this time period. From Fig. 7b, it 
can be seen that the rate of production increases for 
2 cm as well as 4 cm depths at a very high rate. This 
is due to an increase in wind speed and the high solar 
radiation during this period.
4  CONCLUSIONS
The DSSS of acrylic with basin area 1 m² with an 
inclination angle of 30° was fabricated for the climatic 
condition of Sultanpur, Uttar Pradesh, India. Various 
experiments were performed on this setup to analyze 
the effect of parameters, including different depths (2 
cm, 3 cm, 4 cm and 5 cm), the wind velocity effect 
on the yield, and heat transfers. The experimental and 
theoretical yields have been compared. The following 
conclusions have been drawn from the present study.
1. Convective and evaporative heat transfers are the 
most critical parameter for a solar distillation unit. 
The maximum value of h
ew 
(55.05 W/(m²K), 49.2 
W/(m²K), 31.25 W/(m²K) and 31.80 W/(m²K)) 
and h
cw
 (2.48 W/(m²K), 2.25 W/(m²K), 2.19 W/
(m²K) and 2.38 W/(m²K)) was found for 2 cm, 3 
cm, 4 cm, and 5 cm depths, respectively. 
2. The radiative heat transfer coefficient is found 
to be a maximum of 8.39 W/(m²K) for 2 cm 
depth, and it increases as the rate of condensation 
increases on the glass surface.
3. The yield from the still increases as the basin 
water depth decreases because the lower basin 
water requires less time to come into steady-state, 
and due to this, the evaporation starts earlier. 
4. On increasing the depth from 2 cm to 4 cm, the 
yield decreases by 17.62 %. In comparison, it 
decreases by 25.45 % when the water depth is 
5 cm. The maximum yield of 2.5 l/m² per day is 
found for 2 cm water depth. The theoretical and 
experimental yield from solar still agreed with an 
error of 7.5 %, 3.25 %, 7.4 % and 8.4 % for 2 cm, 
3 cm, 4 cm and 5 cm water depths, respectively.
5. The afternoon production is higher for the higher 
basin mass because of the heat-storing capacity of 
basin mass.
6. During the initial time duration of still (i.e. 1 h 
to 2 h of operations), the rate of convective, 
evaporative, and radiative heat transfer 
coefficients is less. This is due to the slow heating 
of water mass in the basin because of the outer 
glass surface at a higher temperature than the 
lower surface.
7. The yield of DSSS increases as the wind speed 
increase because this leads to faster condensation 
at the glass surface. The higher basin mass 
temperature is less affected by the variation in 
wind velocity.

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
378 Patel, R.V. – Yadav, A. – Winczek, J.
5  NOMENCLATURES
 q
cw
 rate of convective heat transfer from water to 
glass cover, [W/m
2
]
h
cw
 convective heat transfer coefficient from water to 
condensing cover, [W/(m
2
K)]
 q
ew
 rate of evaporative heat transfer from water to 
glass cover, [W/m
2
]
h
ew
 evaporative heat transfer coefficient, [W/(m
2
K)]
 q
rw 
rate of radiative heat transfer from water to glass 
cover, [W/m
2
]
h
rw
 radiative heat transfer coefficient, [W/(m
2
K)]
ε
eff
 effective emissivity of glass and water, [-]
ε
g
 emissivity of glass, [-]
ε
w
 emissivity of water, [-]
ρ	 Stefan Boltzmann constant, [W/(m
2
K
4
)]
 q
g 
rate of total heat transfer from glass cover to 
ambient, [W/m
2
]
 q
rg
 rate of radiative heat transfer from glass cover to 
ambient, [W/m
2
]
h
rg
 radiative heat transfer coefficient from glass 
cover to ambient, [W/(m
2
K)]
 q
cg
 rate of convective heat transfer from glass cover 
to ambient, [W/m
2
]
h
cg
 convective heat transfer coefficient from glass 
surface to ambient, [W/(m
2
K)]
 q
tg
 rate of total heat transfer from glass cover to 
ambient, [W/m
2
]
h
tg
 total heat transfer coefficient from glass surface 
to ambient, [W/(m
2
K)]
U
b
 bottom heat loss coefficient, [W/(m
2
K)]
U
e
 side heat loss coefficient, [W/(m
2
K)]
h
w
 convective heat transfer coefficient from basin 
liner to water, [W/(m
2
K)]
h
cb
 convective heat transfer coefficient from basin 
liner to ambient, [W/(m
2
K)]
h
rb
 radiative heat transfer coefficient from basin liner 
to ambient, [W/(m
2
K)]
h
b
 overall heat transfer coefficient from basin liner 
to ambient through bottom, [W/(m
2
K)]
T
g
 temperature of condensing cover, [°C]
T
b
 temperature of basin, [°C]
T
w
 water temperature, [°C]
T water vapour temperature, [°C]
T
sky
 temperature of sky, [°C]
T
a
 ambient temperature, [°C]
V wind velocity, [m/s]
t
i
 thickness of insulation material, [m]
K
i
 thermal conductivity of insulation material, 
[W/(m·K)]
P
w
 partial vapour pressure at water temperature, 
[N/m
2
]
P
g
 partial vapour pressure at glass temperature, 
[N/m
2
]
m
ew
 distillate output, [kg/m
2
/h]
L latent heat of vaporization, [J/kg]
h
b
 overall heat transfer coefficient from basin liner 
to ambient through bottom insulation, [W/(m
2
K)]
ASS surface area in contact with water, [m
2
]
AS area of the basin of the distiller, [m
2
]
6  REFERENCES
[1] Kannan, N., Vakeesan, D. (2016). Solar energy for future 
world: A review. Renewable and Sustainable Energy Reviews. 
vol. 62, p. 1092-105, DOI:10.1016/j.rser.2016.05.022.
[2] Patel, R.V.P., Kumar, A. (2017). Experimental investigation of 
double slope solar still for the climatic condition of Sultanpur. 
International Journal of Engineering and Technology, vol. 9, no. 
6, p. 4019-4033, DOI:10.21817/ijet/2017/v9i6/170906309.
[3] Patel, R.V., Bharti, K., Singh, G., Mittal, G., Singh, D.B., Yadav, 
A. (2021). Comparative investigation of double slope solar 
still by incorporating different types of collectors: A mini 
review. Materials Today: Proceedings, vol. 38, p. 300-304, 
DOI:10.1016/j.matpr.2020.07.338.
[4] Misra, S., Patel, R.V., Kumar, A., Yadav, A., Patel, V. (2021) 
Effect of Climatic Conditions and Water Depth on Yield of 
Single Slope Solar Still. Current Advances in Mechanical 
Engineering: Select Proceedings of ICRAMERD 2020, p. 137-
147, DOI:10.1007/978-981-33-4795-3_14.
[5] Sharshir, S.W., Ellakany, Y.M., Algazzar, A.M., Elsheikh, A.H., 
Elkadeem, M.R., Edreis, E.M.A., Waly, A.S., Sathyamurthy, R., 
Panchal, H., Elashry, M.S. (2019). A mini review of techniques 
used to improve the tubular solar still performance for solar 
water desalination. Process Safety and Environmental 
Protection, vol. 124, p. 204-212, DOI:10.1016/j.
psep.2019.02.020.
[6] Tiwari, A.Kr., Tiwari, G.N. (2006). Effect of water depths on 
heat and mass transfer in a passive solar still: in summer 
climatic condition. Desalination, vol. 195, no. 1-3, p. 78-94, 
DOI:10.1016/j.desal.2005.11.014.
[7] Zarasvand Asadi, R., Suja, F., Ruslan, M.H., Jalil, N.A. (2013). 
The application of a solar still in domestic and industrial 
wastewater treatment. Solar Energy, vol. 93, no. 63-71, 
DOI:10.1016/j.solener.2013.03.024.
[8] Ali, M.T., Fath, H.E.S., Armstrong, P.R. (2011). A comprehensive 
techno-economical review of indirect solar desalination. 
Renewable and Sustainable Energy Reviews, vol. 15, no. 8, p. 
41874199, DOI:10.1016/j.rser.2011.05.012.
[9] Dev, R., Abdul-Wahab, S.A., Tiwari, G.N. (2011). Performance 
study of the inverted absorber solar still with water depth and 
total dissolved solid. Applied Energy, vol. 88, no. 1, p.252-
264, DOI:10.1016/j.apenergy.2010.08.001.
[10] Phadatare, M.K., Verma, S.K. (2007). Influence of water depth 
on internal heat and mass transfer in a plastic solar still. 
Desalination, vol. 217, no. 1-3, p. 267-275, DOI:10.1016/j.
desal.2007.03.006.
[11] Tripathi, R., Tiwari, G.N. (2006). Thermal modeling of passive 
and active solar stills for different depths of water by using the 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379
379 Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 
concept of solar fraction. Solar Energy, vol. 80, p. 956-967, 
DOI:10.1016/j.solener.2005.08.002.
[12] Feilizadeh, M., Karimi Estahbanati, M.R., Ahsan, A., Jafarpur, 
K., Mersaghian, A. (2016). Effects of water and basin depths 
in single basin solar stills: An experimental and theoretical 
study. Energy Conversion and Management, vol. 122, p. 174-
181, DOI:10.1016/j.enconman.2016.05.048.
[13] El-Sebaii, A.A. (2011). On effect of wind speed on passive solar 
still performance based on inner/outer surface temperatures 
of the glass cover. Energy, vol. 36, no. 8, p. 4943–4949. 
DOI:10.1016/j.energy.2011.05.038.
[14] El-Sebaii A.A. (2004). Effect of wind speed on active and 
passive solar stills. Energy Conversion and Management, 
vol. 45, no. 7-8, p. 1187–1204, DOI:10.1016/j.
enconman.2003.09.036.
[15] Danish, S.N., El-Leathy, A., Alata, M., Al-Ansary, H. (2019). 
Enhancing solar still performance using vacuum pump and 
geothermal energy. Energies, vol. 12, no. 3, art. ID 539, 
DOI:10.3390/en12030539.
[16] Thalib, M.M., Manokar, A.M., Essa, F.A., Vasimalai, N., 
Sathyamurthy, R., Garcia Marquez, F.P. (2020). Comparative 
study of tubular solar stills with phase change material and 
nano-enhanced phase change material. Energies, vol. 13, no. 
15, art. ID. 3989, DOI:10.3390/en13153989.
[17] Singh, R., Kumar, A., Yadav, A. (2019). Performance analysis 
of the solar photovoltaic thermal system using phase change 
material. IOP Conference Series: Materials Science and 
Engineering, vol. 577, art. ID 012166, DOI:10.1088/1757-
899X/577/1/012166.
[18] Safaei, M.R., Goshayeshi, H.R., Chaer, I.. (2019). Solar 
still efficiency enhancement by using graphene oxide/
paraffin nano-PCM. Energies, vol. 12, no. 10, art. ID 2002, 
DOI:10.3390/en12102002.
[19] Nazari, S., Safarzadeh, H., Bahiraei, M. (2019). Performance 
improvement of a single slope solar still by employing 
thermoelectric cooling channel and copper oxide nanofluid: An 
experimental study. Journal of Cleaner Production, vol. 208, p. 
1041-1052, DOI:10.1016/j.jclepro.2018.10.194.
[20] El-Sebaey, M.S., Ellman, A., Hegazy, A., Ghonim, T. (2020). 
Experimental analysis and CFD modeling for conventional 
basin-type solar still. Energies, vol. 13, no. 21., art. ID 5734, 
DOI:10.3390/en13215734.
[21] Rahbar, N., Esfahani, J.A. (2013). Productivity estimation 
of a single-slope solar still: Theoretical and numerical 
analysis. Energy, vol. 49, no. 289-297, DOI:10.1016/j.
energy.2012.10.023.
[22] Setoodeh, N., Rahimi, R., Ameri, A. (2011). Modeling and 
determination of heat transfer coefficient in a basin solar 
still using CFD. Desalination, vol. 268, no. 1-3, 103-110, 
DOI:10.1016/j.desal.2010.10.004.
[23] Madhlopa, A. (2014). Modelling radiative heat transfer inside 
a basin type solar still. Applied Thermal Engineering, vol. 73, 
no. 1, p. 707-711, DOI:10.1016/j.applthermaleng.2014.07.065.
[24] Keshtkar, M., Eslami, M., Jafarpur, K. (2020). A novel 
procedure for transient CFD modeling of basin solar stills: 
Coupling of species and energy equations. Desalination, vol. 
481, art. ID 114350, DOI:10.1016/j.desal.2020.114350.
[25] Dunkle, R.V. (1961). Solar wter distillation: the roof type still 
and a multiple effect diffusion still. International Developments 
in Heat Transfer, ASME, Proceeding of International Heat 
Transfer, part V, p. 895.
[26] Fernández, J., Chargoy, N. (1990). Multi-stage, indirectly 
heated solar still. Solar Energy, vol. 44, no. 4, p. 215-223, 
DOI:10.1016/0038-092X(90)90150-B.
[27] Watmuff, J.H., Charters, W.W.S., Proctor, D. (1977). Solar and 
wind induced external coefficients-solar collectors. CMES, p. 
56.
[28] Shukla, K.S., Rai, A.K. (2008). Analytical thermal modeling of 
double slope solar still by using inner glass cover temperature. 
Thermal Science, vol. 12, no. 3, p. 139-152, DOI:10.2298/
TSCI0803139S.