2. The numerical modeling of a conventional basin-type solar still

Dunkle [11] was the first to investigate the heat and mass transfer relationships in a solar still under steady-state conditions. Based on the widely used relations from Dunkle, this study has analyzed the transient performance of the solar still in which all coefficients and still parameters are calculated using equations within the model. The weather data used for simulation will be either from actual measured data or data generated from the computer program developed by Nguyen [12].

The heat and mass transfer processes in the still are shown in Figure 1. The following assumptions are made in order to develop the equations for the energy balances in the still:

Factors Affecting the Yield of Solar Distillation Systems and Measures to Improve Productivities http://dx.doi.org/10.5772/intechopen.75593 153

Figure 1. The heat and mass transfer processes in a conventional solar still.

There are many research and review papers that focus on solar stills and the factors that affect the output of solar distillation. Manchanda and Kumar [1] comprehensively reviewed and analyzed the designs and performance parameters of passive solar stills, while Sampathkumar et al. [2] reviewed in detail different types of active distillation systems. Velmurugan and Srithar [3] appraised certain modifications to solar still systems and their resulting respective performance enhancement. Focusing on the single-basin passive solar still, Murugavel et al. [4] evaluated the progress in improving the effectiveness of this type of still. Similarly, Kabeel and El-Agouz [5] examined single-type passive solar stills, with emphasis on performance enhancing modifications. Badran [6] studied another aspect experimentally—the performance of a single-slope solar still using different operational parameters. Other researches by Kaushal and Varun [7] evaluated the effect of different designs and methods on solar still output. Muftah et al. [8] comprehensively reviewed the performance of existing active and passive basin-type solar stills and investigated the effects of climatic, operational and design parameters on the output of these stills. Recently, Sharshir et al. [9] reviewed in details factors affecting solar still productivity and improvement techniques, while Kabeel et al. [10] introduced, explained and discussed the effectiveness of different solar stills into which different condenser arrangements

All the above-mentioned papers, although comprehensive and thorough, have the same drawbacks that all previous researches and papers reviewed had, namely, they were from countries with different climatic conditions and different levels of technology and manufacturing expertise. This would lead to inconsistencies and differences in improvements to the named stills' output and performance as compared to those outputs and performances claimed or reported. Furthermore, there has been very little information relating to factors affecting forced circula-

Therefore this chapter will present the results of the numerical and experimental research carried out in one location so that there is consistency in the factors affecting solar stills' production as well as the gains of the stills' outputs due to the measures taken to optimize these factors. In addition, there will be a focus on the factors affecting the performance of

Dunkle [11] was the first to investigate the heat and mass transfer relationships in a solar still under steady-state conditions. Based on the widely used relations from Dunkle, this study has analyzed the transient performance of the solar still in which all coefficients and still parameters are calculated using equations within the model. The weather data used for simulation will be either from actual measured data or data generated from the computer program

The heat and mass transfer processes in the still are shown in Figure 1. The following assump-

tions are made in order to develop the equations for the energy balances in the still:

forced circulation solar stills with enhanced water recovery improvement techniques.

2. The numerical modeling of a conventional basin-type solar still

were integrated.

152 Desalination and Water Treatment

tion solar stills with enhanced water recovery.

developed by Nguyen [12].


Based on these assumptions and from Figure 1, the energy balances for the glass, for the basin water, and for the basin are:

$$
\eta\_{cw} + \eta\_{ew} + \eta\_{rw} + \alpha\_{\mathcal{g}} Q\_T = \left(\eta\_{ra} + \eta\_{ca}\right) + M\_{\mathcal{g}} \frac{dT\_{\mathcal{g}}}{dt}.\tag{1a}
$$

$$
\alpha\_w Q\_T' = q\_{cw} + q\_{cw} + q\_{rw} + q\_{w-b} + M\_w \frac{dT\_w}{dt} \,. \tag{2a}
$$

$$
\alpha\_b \mathbf{Q}\_T'' + q\_{w-b} = q\_b + M\_b \frac{dT\_b}{dt} \,. \tag{3a}
$$

where

• qcw is the convective heat transfer rate between the basin water and the cover (in W/m<sup>2</sup> ) and can be calculated by using Dunkle's equation:

$$q\_{cw} = 0.884 \left[ \left( T\_w - T\_\S \right) + \frac{\left( p\_w - p\_\S \right) \left( T\_w + 273.15 \right)}{\left( 268.9 \times 10^3 - p\_w \right)} \right]^{1/3} \left( T\_w - T\_\S \right). \tag{4}$$

with pw and pg being the partial pressure of water vapor at the temperatures of the basin water and the cover, respectively (in Pa).

• qew is the evaporative heat transfer rate between the basin water and the cover (in W/m<sup>2</sup> ):

$$q\_{ew} = 16.276 \times 10^{-3} q\_{cw} \frac{\left(p\_w - p\_\mathcal{g}\right)}{\left(T\_w - T\_\mathcal{g}\right)}.\tag{5}$$

• qb is the heat transfer rate between the basin and the ambient surroundings (in W/m<sup>2</sup>

where hb is the heat transfer coefficient between the basin and the ambient surroundings (in

<sup>¼</sup> <sup>δ</sup>insul kinsul þ 1 hi

• δinsul (m) and kinsul (W/m.�C) are the thickness and thermal conductivity of the basin

• hi is the combined convective and radiative heat transfer coefficient between the insulation

<sup>T</sup> is the total solar radiation incidence on the water surface, after transmittance through

<sup>T</sup> is the total solar radiation incidence on the basin, after transmittance through the basin

• αg, α<sup>w</sup> and α<sup>b</sup> are the absorptance of the cover, of the water and of the basin for solar

• Mg, Mw and Mb are the heat capacities per unit area of the cover, of the water and of the

• Tg, Tw and Tb are, respectively, the transient temperatures of the cover, of the water and of

common total solar incidence of the sloped cover, QT, which is readily calculated [3]. If τg, τ<sup>w</sup> and τ<sup>b</sup> are defined as the fractions of solar insolation incident absorbed by the cover, basin

1 hb

and ambient and can be computed by the derivation of Eqs. (6) and (7).

• QT is the total solar radiation incidence on the cover, in W/m<sup>2</sup>

. �C.

dt <sup>¼</sup> <sup>α</sup>wQ<sup>0</sup>

Mb dTb dt <sup>¼</sup> <sup>α</sup>bQ<sup>00</sup>

water and basin liner, respectively, Eqs. (1b), (2b) and (3b) may be written as:

W/m<sup>2</sup> . �C):

• Q<sup>0</sup>

• Q<sup>00</sup>

insulation, respectively.

the cover, in W/m<sup>2</sup>

radiation, respectively.

water, in W/m<sup>2</sup>

.

.

basin for solar radiation, in J/m<sup>2</sup>

the basin for solar radiation, in �C.

Equations (1a), (2a) and (3a) can be rewritten as:

Mg dTg

Mw dTw

It is convenient to present all solar components QT, Q<sup>0</sup>

qb ¼ hbð Þ Tb � Ta : (10a)

Factors Affecting the Yield of Solar Distillation Systems and Measures to Improve Productivities

.

dt <sup>¼</sup> <sup>α</sup>gQT <sup>þ</sup> qcw <sup>þ</sup> qew <sup>þ</sup> qrw- qra <sup>þ</sup> qca : (1b)

<sup>T</sup> and Q<sup>00</sup>

: (2b)

<sup>T</sup> <sup>þ</sup> qw�<sup>b</sup> � qb: (3b)

<sup>T</sup> in the above equations by the

<sup>T</sup> � qcw <sup>þ</sup> qew <sup>þ</sup> qrw <sup>þ</sup> qw�<sup>b</sup>

: (10b)

http://dx.doi.org/10.5772/intechopen.75593

):

155

• qrw is the radiative heat transfer rate between the basin water and the cover (in W/m<sup>2</sup> ), expressed as:

$$\eta\_{rw} = \varepsilon\_w \sigma \left[ (T\_w + 273.15)^4 - \left( T\_\S + 273.15 \right)^4 \right]. \tag{6}$$

with ε<sup>w</sup> being the emissivity of water surface and σ the Stefan-Boltzmann constant, 5.67 � 10�<sup>8</sup> W/m<sup>2</sup> .K<sup>4</sup> .

• qca is the convective heat transfer rate between the cover and the ambient surroundings (in W/m<sup>2</sup> ), computed from [13]

$$
\eta\_{\rm ct} = (5.7w + 3.8) \left( T\_{\rm g} - T\_{\rm a} \right). \tag{7}
$$

where w is the wind speed (m/s) and Ta is the ambient temperature (�C).

• qra is the radiative heat transfer rate between the cover and the ambient surroundings (in W/m<sup>2</sup> ):

$$
\sigma\_{ra} = \varepsilon\_{\mathcal{S}} \sigma \left[ \left( T\_{\mathcal{S}} + 273.15 \right)^{4} - \left( T\_{a} + 261.15 \right)^{4} \right]. \tag{8}
$$

where ε<sup>g</sup> is the emissivity of the cover

• qw�<sup>b</sup> is the heat transfer rate between the water and the basin (in W/m<sup>2</sup> ):

$$q\_{w-b} = h\_{w-b}(T\_w - T\_b). \tag{9}$$

where hw�<sup>b</sup> is the heat transfer coefficient between the water and the basin absorbing surface (in W/m<sup>2</sup> . �C).

• qb is the heat transfer rate between the basin and the ambient surroundings (in W/m<sup>2</sup> ):

$$
\eta\_b = h\_b (T\_b - T\_a). \tag{10a}
$$

where hb is the heat transfer coefficient between the basin and the ambient surroundings (in W/m<sup>2</sup> . �C):

$$\frac{1}{h\_b} = \frac{\delta\_{insul}}{k\_{insul}} + \frac{1}{h\_i}.\tag{10b}$$


Equations (1a), (2a) and (3a) can be rewritten as:

where

154 Desalination and Water Treatment

• qcw is the convective heat transfer rate between the basin water and the cover (in W/m<sup>2</sup>

pw � pg � �

with pw and pg being the partial pressure of water vapor at the temperatures of the basin water

• qew is the evaporative heat transfer rate between the basin water and the cover (in W/m<sup>2</sup>

• qrw is the radiative heat transfer rate between the basin water and the cover (in W/m<sup>2</sup>

qrw <sup>¼</sup> <sup>ε</sup>w<sup>σ</sup> ð Þ Tw <sup>þ</sup> <sup>273</sup>:<sup>15</sup> <sup>4</sup> � Tg <sup>þ</sup> <sup>273</sup>:<sup>15</sup> � �<sup>4</sup> h i

with ε<sup>w</sup> being the emissivity of water surface and σ the Stefan-Boltzmann constant, 5.67 �

• qca is the convective heat transfer rate between the cover and the ambient surroundings (in

qca ¼ ð Þ 5:7w þ 3:8 Tg � Ta

• qra is the radiative heat transfer rate between the cover and the ambient surroundings (in

qra <sup>¼</sup> <sup>ε</sup>g<sup>σ</sup> Tg <sup>þ</sup> <sup>273</sup>:<sup>15</sup> � �<sup>4</sup> � ð Þ Ta <sup>þ</sup> <sup>261</sup>:<sup>15</sup> <sup>4</sup> h i

where hw�<sup>b</sup> is the heat transfer coefficient between the water and the basin absorbing surface

where w is the wind speed (m/s) and Ta is the ambient temperature (�C).

• qw�<sup>b</sup> is the heat transfer rate between the water and the basin (in W/m<sup>2</sup>

qew <sup>¼</sup> <sup>16</sup>:<sup>276</sup> � <sup>10</sup>�<sup>3</sup>

ð Þ Tw þ 273:15

pw � pg � �

Tw � Tg

3 5

1=3

Tw � Tg

� � : (5)

� �: (7)

� �: (4)

: (6)

: (8)

):

qw�<sup>b</sup> <sup>¼</sup> hw�<sup>b</sup>ð Þ Tw � Tb : (9)

<sup>268</sup>:<sup>9</sup> � <sup>10</sup><sup>3</sup> � pw � �

qcw

and can be calculated by using Dunkle's equation:

� � <sup>þ</sup>

qcw ¼ 0:884 Tw � Tg

and the cover, respectively (in Pa).

expressed as:

.K<sup>4</sup> .

), computed from [13]

where ε<sup>g</sup> is the emissivity of the cover

10�<sup>8</sup> W/m<sup>2</sup>

W/m<sup>2</sup>

W/m<sup>2</sup> ):

(in W/m<sup>2</sup>

. �C). 2 4 )

):

),

$$M\_{\mathcal{g}} \frac{dT\_{\mathcal{g}}}{dt} = a\_{\mathcal{g}} Q\_T + q\_{cw} + q\_{cw} + q\_{rw} \cdot (q\_{ra} + q\_{ca}) \,. \tag{1b}$$

$$M\_w \frac{dT\_w}{dt} = \alpha\_w Q\_T^\prime - \left(q\_{cw} + q\_{ew} + q\_{rw} + q\_{w-b}\right). \tag{2b}$$

$$M\_b \frac{dT\_b}{dt} = \alpha\_b Q\_T'' + q\_{w-b} - q\_b. \tag{3b}$$

It is convenient to present all solar components QT, Q<sup>0</sup> <sup>T</sup> and Q<sup>00</sup> <sup>T</sup> in the above equations by the common total solar incidence of the sloped cover, QT, which is readily calculated [3]. If τg, τ<sup>w</sup> and τ<sup>b</sup> are defined as the fractions of solar insolation incident absorbed by the cover, basin water and basin liner, respectively, Eqs. (1b), (2b) and (3b) may be written as:

$$M\_{\mathcal{g}} \frac{dT\_{\mathcal{g}}}{dt} = \tau\_b Q\_T + q\_{cw} + q\_{ew} + q\_{rw} \cdot (q\_{ra} + q\_{ca}) \,. \tag{1c}$$

$$M\_w \frac{dT\_w}{dt} = \tau\_w Q\_T - \left(q\_{cw} + q\_{ew} + q\_{rw} + q\_{w-b}\right). \tag{2c}$$

$$M\_b \frac{dT\_b}{dt} = \tau\_b Q\_T + q\_{w-b} - q\_b. \tag{3c}$$

Tfout and moisture content wout. This air flow goes through the dehumidifying coil, which acts a condenser. The hot air-vapor mixture from the still is passed over the coil and attached fins,

Factors Affecting the Yield of Solar Distillation Systems and Measures to Improve Productivities

http://dx.doi.org/10.5772/intechopen.75593

157

Figure 2. Schematic diagram of a forced circulation solar still with enhanced water recovery.

The hot air-vapor mixture losses heat to the cooling water and subsequently cools down. When the temperature of the mixture falls below its dew point temperature, the condensation process starts. The air exits the condenser at a temperature of Tc-out and a moisture content of wc-out. Some of the heat extracted from the air flow will be recovered in the preheater, since the air

The heat and mass transfer relationships in this still can be seen from Figure 3. From this figure, the energy and mass balances for the glass, for the flow in the still, for the basin water

dTg

dTf

¼ mfð Þþ wout � win mew�<sup>g</sup> (13)

dTw

dTb

dt (11)

dt (12)

dt (14)

dt (15)

qcfg <sup>þ</sup> qrw <sup>þ</sup> <sup>α</sup>gQT <sup>¼</sup> qra <sup>þ</sup> qca <sup>þ</sup> Mg

qew þ qcwf ¼ qcfg þ mfð Þþ hout � hin Mf

<sup>T</sup> <sup>¼</sup> qcwf <sup>þ</sup> qew <sup>þ</sup> qrw <sup>þ</sup> qw�<sup>b</sup> <sup>þ</sup> Mw

<sup>T</sup> <sup>þ</sup> qw�<sup>b</sup> <sup>¼</sup> qb <sup>þ</sup> Mb

mew <sup>¼</sup> qew hfg

αbQ<sup>00</sup>

αwQ<sup>0</sup>

while the cooling water runs inside the coil.

flow goes through it before going back to the still.

and for the basin are
