Theoretical modeling and experimental analysis of solar still integrated with evacuated tubes

Abstract

In this present research work, theoretical modeling of single slope, single basin solar still integrated with evacuated tubes has been performed based on energy balance equations. Major variables like water temperature, inner glass cover temperature and distillate output has been computed based on theoretical modeling. The experimental setup has been made from locally available materials and installed at Gujarat Power Engineering and Research Institute, Mehsana, Gujarat, India (23.5880°N, 72.3693°E) with 0.04 m depth during 6 months of time interval. From the series of experiments, it is found considerable increment in average distillate output of a solar still when integrated with evacuated tubes not only during daytime but also from night time. In all experimental cases, the correlation of coefficient (r) and root mean square percentage deviation of theoretical modeling and experimental study found good agreement with 0.97 < r < 0.98 and 10.22 < e < 38.4% respectively.

Appendix

Following heat and mass transfer equations have used for the theoretical analysis of solar still integrated with evacuated tubes.

Total heat transfer coefficient is represented by:

$$ {\text{h}}_{\text{t}} = {\text{h}}_{\text{c}} + {\text{h}}_{\text{e}} + {\text{h}}_{\text{r}} $$

(24)

The convective heat transfer coefficient is represented by:

$$ h_{c} = 0.884\left[ {(T_{w} - T_{ci} ) + \frac{{(P_{w} - P_{ci} )(T_{w} )}}{{268.9 \times 10^{2} - P_{w} }}} \right]^{{\frac{1}{3}}} $$

(25)

The evaporative heat transfer coefficient is represented by:

$$ h_{e} = 0.016273 \times h_{cw} \times \left( {\frac{{P_{w} - P_{ci} }}{{T_{w} - T_{ci} }}} \right) $$

(26)

The radiative heat transfer coefficient is represented by:

$$ h_{rw} = \varepsilon_{eff} \bullet \sigma \left[ {\left( {T_{w} } \right)^{2} - (T_{ci} )^{2} } \right] \times \left[ {T_{w} + T_{ci} + 546} \right] $$

(27)

The main design parameters of the present solar still have been computed by following equations:

$$ I_{eff} = A_{T} F_{R} (\alpha \tau )_{c} + (\alpha \tau )_{eff} I(t)_{s} $$

(28)

$$ (\alpha \tau )_{eff} = \alpha^{\prime}_{b} \frac{{h_{w} }}{{h_{w} + h_{b} }} + \alpha^{\prime}_{w} + \alpha^{\prime}_{g} \frac{{h_{1} }}{{h_{1} + U_{cg - a} }} $$

(29)

Overall heat transfer coefficient from glass cover to Ambient:

$$ U_{cg - a} = \frac{{h_{2} \frac{{k_{g} }}{{L_{g} }}}}{{h_{2} + \frac{{k_{g} }}{{L_{g} }}}} $$

(30)

$$ {\text{Where,}}\,\,h_{b} = \left[ {\frac{1}{{\frac{{K_{i} }}{{L_{i} }}}} + + \frac{1}{{h_{cb} + h_{rb} }}} \right]^{ - 1} $$

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$$ {\text{and}}\,U_{cg - a} = \frac{{h_{2} \frac{{K_{g} }}{{L_{g} }}}}{{h_{2} + \frac{{K_{g} }}{{L_{g} }}}} $$

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$$ U_{eff} = (U_{LS} + F_{R} A_{L} U_{{_{c} }}^{{}} ),{\text{ where}} $$

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$$ U_{L} = U_{b} + U_{t} , $$

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$$ U_{b} = \frac{{h_{w} h_{b} }}{{h_{w} + h_{b} }}\quad U_{t} = \frac{{h_{1} U_{cg - a} }}{{h_{a} + U_{cg - a} }} $$

(35)

1.1 Error analysis

Thermocouples error analysis:

The accuracy of the thermocouple = ±1 °C

The minimum experimental value measured = 20 °C

Therefore the maximum possible error is 0.1/20 = 0. 05%

Error = 0.005 × 100 = 5%

Anemometer error analysis:

Accuracy of anemometer = ± 0.1 m/s

Minimum wind velocity measured = 1 m/s

Maximum possible error = 0.1/1 = 0.1%

Error = 10%

Solarimeter error analysis:

The accuracy of the meter = ± 1 W/m²

The minimum value measured = 40 W/m²

Maximum possible error = 1/40 = 0.025%

Error = 2.5%

Measuring jar error analysis:

Accuracy of collection tank = ± 10 mL

Minimum value measured = 100 mL

Maximum possible error = 10/100 = 0.01%

Error = 10%.