Effect of cost-free energy storage material and saline water depth on the performance of square pyramid solar still: a mathematical and experimental study

Abstract

Low productivity of single-slope solar still is the main barrier for its worldwide usability. An attempt has been conducted to enhance the distillate yield of single basin square pyramid solar still using thermal storage material in basin. The experiments were conducted with two identical single basin square pyramid solar stills under the climate of location (20.61° N 72.91° E), one with small pieces of black granite as a thermal storage material and other without black granite. With and without thermal storage, the effect of saline water depth (30 and 20 mm) was investigated on the performance of still. Compared to still without thermal storage, yield of 1430.40 mL m⁻² (13.96% higher) and 1380.40 mL m⁻² (6.63% higher) was obtained at water depth of 30 mm and 20 mm for the still with thermal storage. The daily average efficiency of 18.69% (11.35% higher) and 18.58% (5.09% higher) was obtained at water depth of 30 mm and 20 mm for the still with thermal storage. The higher yield was achieved at water depth of 30 mm than the 20 mm for the still with thermal storage, whereas the higher yield was achieved at water depth of 20 mm than the 30 mm for the still without thermal storage. Transient model for the still with and without thermal storage was developed, and the results were compared with experimental outcomes and good agreement was observed.

Appendix

In Eqs. (4) to (8), various heat transfer coefficients can be calculated using correlation as mentioned below,

Convective and evaporative heat transfer coefficient between saline water and glass cover (h_{c, w–g} and h_{e, w–g}) suggested by Dunkle [60]:

$$\begin{aligned} h_{{{\text{c}},{\text{w}} - {\text{g}}}} & = 0.884 \times \left[ {\left( {T_{\text{w}} - T_{\text{g}} } \right) + \frac{{\left( {p_{\text{w}} - p_{\text{g}} } \right) \times T_{\text{w}} }}{{268900 - p_{\text{w}} }}} \right]^{{\frac{1}{3}}} \\ h_{{{\text{e}},{\text{w}} - {\text{g}}}} & = 16.273 \times 10^{ - 3} \times h_{{{\text{c}},{\text{w}} - {\text{g}}}} \times \frac{{\left( {p_{\text{w}} - p_{\text{g}} } \right)}}{{\left( {T_{\text{w}} - T_{\text{g}} } \right)}} \\ \end{aligned}$$

Various radiative heat transfer coefficient:

$$\begin{aligned} h_{{{\text{r}},{\text{w}} - {\text{g}}}} & = \varepsilon_{\text{eff}} \sigma \left( {T_{\text{w}} + T_{\text{g}} } \right)\left( {T_{\text{w}}^{2} + T_{\text{g}}^{2} } \right) ;\quad \varepsilon_{\text{eff}} = \left( {\frac{1}{{\varepsilon_{\text{w}} }} + \frac{1}{{\varepsilon_{\text{g}} }} - 1} \right)^{ - 1} \\ h_{{{\text{r}},{\text{g}} - {\text{sky}}}} & = \varepsilon_{\text{g}} \sigma \left( {T_{\text{g}} + T_{\text{sky}} } \right)\left( {T_{\text{g}}^{2} + T_{\text{sky}}^{2} } \right) \\ \end{aligned}$$

Heat transfer coefficient between basin and the surrounding through insulation [52]:

$$h_{\text{b}} = \left( {\frac{{y_{\text{ins}} }}{{k_{\text{ins}} }} + \frac{1}{{h_{{{\text{t}},{\text{b}} - {\text{a}}}} }}} \right)^{ - 1} ; \quad h_{{{\text{t}},{\text{b}} - {\text{a}}}} = 5.7 + 3.8 V$$

Overall heat transfer coefficient between basin and surroundings through insulation:

$$U_{\text{b}} = \left( {1 + \frac{{A_{\text{s}} }}{{A_{\text{b}} }}} \right) \times \left( {\frac{{h_{\text{b}} \times h_{{{\text{c}},{\text{b}} - {\text{w}}}} }}{{h_{\text{b}} + h_{{{\text{c}},{\text{b}} - {\text{w}}}} }}} \right)$$

Convective heat transfer coefficient between glass cover and atmosphere (h_c,g–a) [52]:

$$h_{{{\text{c}},{\text{g}} - {\text{a}}}} = 2.8 + 3 V$$

Saturation vapor pressure at water or at glass cover temperature [61]:

$$p_{\text{w or g}} = e^{{\left[ {25.317 - \frac{5144}{{{\text{T}}_{\text{w or g}} }}} \right]}}$$

Specific heat capacity of saline water based on salinity and temperature (°C) [52]:

$$C_{\text{w}} = a_{1} + a_{2} T_{\text{w}} + a_{3} T_{\text{W}}^{2} + a_{4} T_{\text{W}}^{3}$$

where

$$\begin{aligned} a_{1} & = 4206.8 - 6.6197{\text{s}} + 1.2288 \times 10^{ - 2} {\text{s}}^{2} \\ a_{2} & = - 1.1262 + 5.4178 \times 10^{ - 2} {\text{s}} - 2.2719 \times 10^{ - 4} {\text{s}}^{2} \\ a_{3} & = 1.2026 \times 10^{ - 2} - 5.5366 \times 10^{ - 4} {\text{s}} + 1.8906 \times 10^{ - 6} {\text{s}}^{2} \\ a_{4} & = 6.8774 \times 10^{ - 7} + 1.5170 \times 10^{ - 6} {\text{s}} - 4.4268 \times 10^{ - 9} {\text{s}}^{2} \\ \end{aligned}$$

Latent heat of vaporization of saline water dependent on temperature (°C) [52]:

$$\begin{aligned} h_{\text{fg}} & = 2.4935 \times 10^{6} \left( {1 - 9.4779 \times 10^{ - 4} T_{\text{w}} + 1.3132 \times 10^{ - 7} T_{\text{w}}^{2} } \right. \\ & \quad \left. { - \;4.7974 \times 10^{ - 9} T_{\text{w}}^{3} } \right) {\text{J}}\;{\text{kg}^{ - 1}}\quad {\text{for}}\; T_{\text{w}} \le 70 \;^{ \circ } {\text{C}} \\ \end{aligned}$$

In Eqs. (1) to (3) and (14 and 15), $\alpha_{\text{b}}^{'} , \alpha_{\text{R}}^{'} , \alpha_{\text{w}}^{'} \;{\text{and}} \;\alpha_{\text{b}}^{'}$ can be calculated as [50]

$$\begin{aligned} \alpha_{\text{b}}^{'} & = \alpha_{\text{b}} \left( {1 - \alpha_{\text{g}} } \right)\left( {1 - R_{\text{g}} } \right)\left( {1 - R_{\text{w}} } \right)\left( {1 - \alpha_{\text{w}} } \right)\left( {1 - R_{\text{b}} } \right) \\ \alpha_{\text{gr}}^{'} & = \alpha_{\text{gr}} \left( {1 - \alpha_{\text{g}} } \right)\left( {1 - R_{\text{g}} } \right)\left( {1 - R_{\text{w}} } \right)\left( {1 - \alpha_{\text{w}} } \right)\left( {1 - R_{\text{gr}} } \right) \\ \alpha_{\text{w}}^{'} & = \alpha_{\text{w}} \left( {1 - \alpha_{\text{g}} } \right)\left( {1 - R_{\text{g}} } \right)\left( {1 - R_{\text{w}} } \right) \\ \alpha_{\text{g}}^{\prime } & = \left( {1 - R_{\text{g}} } \right)\alpha_{\text{g}} \\ \end{aligned}$$