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Eco-design requisites for solar desaltification still augmented evacuated annular tube collectors with parabolic concentrator: an optimum-environ-economic viability

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Abstract

In this paper, an eco-design criterion for a novel solar desaltification setup (SDS) with evacuated annular tube collector (EATC) and a specific set of modified combination of parabolic concentrator has been examined for maximum performance with environmental and economic circumstances. This technique approaches to rectify the irregular utilization of EATC for optimum performance with environ-economic viabilities, which evidently satisfies the eco-design requirements and boosts the solar absorption capabilities uniformly along the periphery of vacuum tubes, and results improved thermo-syphon loom significantly more than in typical applications. The suggested unit is being refined and improved water temperature by 11.4% while keeping the basin lid and annular tubes at the same direction (30°). An incremental improvement in thermo-syphon circulation of 28.1% obtained through the present study. The average solar intensity of the respective clear day has been found as 401.8 kW and the overall energy and exergy efficiency on a daily basis are 50.8%, and 3.8%, correspondingly. At a minimal retail price of 0.07 $/l, and improved daily output by 12.3 kg per day than the typical SDS-EATC system taken for comparison into consideration are determined to be more satisfactory. 131.97 and 67.44 tons alleviates for $1318.36 and $673.77 from environmental generated money based on energy-exergy are there for CO2, respectfully. The setup cost is noticeably reduced by 9.15% to the comparative system, and its productivity is determined to be 940.8% (> 100%), and this indicates that the present system is highly viable and appreciable for the feasible adaptation with the positive environ-economic possibilities.

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Abbreviations

\(A_{a}\) :

MCPC aperture area (m2)

\(A_{g}\) :

Glass area (m2)

\(A_{b}\) :

Liner area (m2)

\(A_{rc}\) :

Collector area of EATC (m2)

\(C_{w} , C_{f}\) :

Water heat capacity (J/kg K)

\(d\) :

EATC interior diameter (m)

\(E_{e}\) :

Energy get (kWh)

\(E_{x}\) :

Exergy get (kWh)

\(F^{^{\prime}}\) :

Tube collector efficiency aspect

\(G_{r}\) :

Grashof No.

\(h_{ba}\) :

Net heat transport coefficient (liner-atmosphere) (W/m2 K)

\(h_{bw}\) :

Convective heat transport coefficient (liner-water) (W/m2 K)

\(h_{t - g} , h_{o}\) :

Thermal thrashing coefficient (glaze-atmosphere) (W/m2 K)

\(h_{t - wg}\) :

Net heat transport coefficient (water-top glass) (W/m2 K)

\(h_{c - wg}\) :

Convection heat transport coefficient (water-top glass) (W/m2 K)

\(h_{e - wg}\) :

Evaporation heat transport coefficient (water-top glass) (W/m2 K)

\(h_{r - wg}\) :

Radiation heat transport coefficient (water-top glass) (W/m2 K)

\(h_{r - ev}\) :

Radiation thermal thrashing coefficient of EATC (W/m2 K)

\(h_{{{\text{saf}}}}\) :

Net heat transport coefficient from EATC absorber to water (W/m2 K)

\(I_{d} \left( t \right)\) :

Imitated radiation of ground (W/m2)

\(I_{s} \left( a \right)\) :

Absorbed sun’s ray energy (W/m2)

\(I_{s} \left( t \right)\) :

Sun’s ray energy of instance (W/m2)

\(I_{b} \left( t \right)\) :

Irradiated solar beam radiation (W/m2)

\(K_{g}\) :

Glaze conductivity (thermal) (W/m K)

\(K_{b}\) :

Lining conductivity (thermal) (W/m K)

\(K_{w}\) :

Medium (water) conductivity (thermal) (W/m K)

L:

Heat latent (vaporization) (J/kg)

\(L_{{{\text{EATC}}}}\) :

Tube length (m)

\(\dot{m}_{{{\text{ewg}}}}\) :

Hour yielding (kg/h)

\(\dot{m}_{f}\) :

Water circulation rate (kg/s)

\(m_{w}\) :

Basin water amount (kg)

\(m_{f}\) :

EATC water amount (kg)

\(n_{o}\) :

Air index (refractive)

\(n_{g}\) :

Glass index (refractive)

\(n_{w}\) :

Water index(refractive)

\(N_{u}\) :

Nusselt No.

\(N_{sh}\) :

Sunshine hours

\(P_{r}\) :

Prandtl No.

\(p_{w}\) :

Fractional vapor pressure (water surface) (Pa, N/m2)

\(p_{gi}\) :

Fractional vapor pressure (top glaze) (Pa, N/m2)

\(\dot{Q}_{{N - {\text{EATC}}}}\) :

Heat gain rate from EATC (kJ/s)

\(R_{a}\) :

Rayleigh No.

\(R_{e}\) :

Reynold No.

\(R_{g}\) :

Glass reflectivity

\(R_{i1}\) :

Internal tube ID (m)

\(R_{i2}\) :

Internal tube OD (m)

\(R_{o2}\) :

External tube OD (m)

\(R_{sc}\) :

Absorber reflectivity

\(T_{a}\) :

Air temperature (°C)

\(T_{b}\) :

Lining temperature (°C)

\(t_{b}\) :

Lining thickness (m)

\(t\) :

Time (s)

\(t_{g}\) :

Glass thickness (m)

\(T_{sa}\) :

Temperature of EATC absorber (°C)

\(T_{f}\) :

EATC fluid temperature (°C)

\(T_{fo1}\) :

EATC outlet water (brackish) temperature (°C)

\(T_{w}\) :

Still water (brackish) temperature (°C)

\(T_{go}\) :

Outer glass facade temperature (°C)

\(T_{gi}\) :

Inner glaze facade temperature (°C)

\(U_{saa}\) :

EATC tube overall heat transmit coefficient

V:

Averaged air speed (m/s)

SDS:

Solar desaltification scheme

EATC:

Evacuated annulled tube collector

CPC:

Combination of parabolic concentrator

OCPC:

Orient combination of parabolic concentrator

MCPC:

Modified combination of parabolic concentrator

CCPC:

Cusp combination of parabolic collector

\(\nu\) :

Viscosity (kinematic) (m2/s)

\(\beta^{^{\prime}}\) :

Volumetric expansion (thermal) (K−1)

\(\alpha\) :

Absorptivity (absorber)

\(\mu\) :

Viscosity (dynamic) (N.s/m2)

\(\alpha_{g}\) :

Glass absorptivity

\(\alpha_{w}\) :

Water absorptivity

\(\alpha_{b}\) :

Liner absorptivity

\(\eta_{i}\) :

Instantaneous efficiency (%)

\(\eta_{e}\) :

Energy efficiency (%)

\(\eta_{x}\) :

Exergy efficiency (%)

\(\tau\) :

Transmissivity

\(\sigma\) :

Stefan–Boltzmann constant (W/m2 K4)

\(\rho\) :

Density (kg/m3)

\(\varepsilon_{{{\text{eff}}}}\) :

Effective emissivity

\(\varepsilon_{g}\) :

Glass emissivity

\(\varepsilon_{w}\) :

Water emissivity

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Delhi Technological University, Delhi, 110042, India

    Ashok Kumar Singh &  Samsher

  2. Mechanical Engineering Department, Galgotias College of Engineering and Technology, Greater Noida, Uttar Pradesh, 201306, India

    Ashok Kumar Singh

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  1. Ashok Kumar Singh
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  2. Samsher
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Contributions

AKS: Conceptualization, Data curation, Formal analysis, Validation, Investigation, Methodology, Software, Writing—original draft. SG: Supervision, Resources, Visualization, Project administration.

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Correspondence to Ashok Kumar Singh.

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Appendix

Appendix

Relationships employed to resolve Eq. (1), (2) (Duffie & Beckman, 2006; Singh & Gautam, 2022)

$${U}_{saa}={\left(\frac{{R}_{o2}\mathrm{ln}\left(\frac{{R}_{i2}}{{R}_{i1}}\right)}{{K}_{g}}+\frac{1}{{h}_{r-v}}+\frac{{R}_{o2}\mathrm{ln}\left(\frac{{R}_{o2}}{{R}_{o1}}\right)}{{K}_{g}}+\frac{1}{{h}_{o}}\right)}^{-1}$$
$${I}_{s}\left(a\right)={I}_{b}\left(t\right).{(\propto \tau )}_{eff}$$
$${(\propto \tau )}_{eff}={R}_{sc}\alpha {\tau }^{2}\left({A}_{a}/{A}_{rc}\right)$$
$${h}_{o}={h}_{c-wg}+{h}_{r-wg}=3.8V+5.7$$
$${h}_{r-v}={\varepsilon }_{eff}.\sigma \left[{\left({T}_{f}+273.15\right)}^{2}+{\left({T}_{sa}+273.15\right)}^{2}\right]\times \left[{T}_{f}+{T}_{sa}+546.30\right]$$
$${\varepsilon }_{\mathrm{eff}}={\left(1/{\varepsilon }_{g}+1/{\varepsilon }_{w}-1\right)}^{-1}$$

Terminologies utilized in Eqs. (7), (10), and (17) as stated,

$$F_{1} = \frac{{F^{\prime}.h_{{{\text{saf}}}} }}{{\left( {F^{\prime}h_{{{\text{saf}}}} + U_{{{\text{saa}}}} } \right)}}$$
$${U}_{L}=\frac{{F}^{^{\prime}}.{h}_{\mathrm{saf}}.{U}_{\mathrm{saa}}}{({F}^{^{\prime}}{h}_{\mathrm{saf}}+{U}_{\mathrm{saa}})}$$
$$F_{2} = 1 - \frac{{\left( {A_{rc} .F_{r} } \right)U_{L} }}{{\dot{m}_{f} C_{f} }}$$
$${F}_{r}=\frac{{\dot{m}}_{f}{C}_{f}}{{A}_{rc}.{U}_{L}}\left\{ 1-\mathrm{exp}\left(-\frac{2\pi {R}_{i1}{L}_{\mathrm{EATC}}.{U}_{L}}{{\dot{m}}_{f}{C}_{f}}\right)\right\}$$
$${h}_{t-g}=5.7+3.8V$$
$${U}_{c}={h}_{t-g}/\left(1+\frac{{h}_{t-g}}{{K}_{g}/{t}_{g}}\right)$$

Relationships utilized for Eq. (18) as expressed (Cooper, 1973; Dunkle, 1961; Singh & Gautam, 2022; Singh & Samsher, 2020),

$${\alpha }_{g}^{A}=\left(1-{R}_{g}\right){\alpha }_{g}$$
$${R}_{g}=1-\frac{4{n}_{o}{n}_{g}}{\left({n}_{o}+{n}_{g}^{2}\right)(1+{n}_{o})}$$
$${h}_{t-wg}={h}_{r-wg}+{h}_{c-wg}+{h}_{e-wg}$$
$${h}_{r-wg}={\varepsilon }_{\mathrm{eff}}.\sigma \left\{{\left({T}_{w}+273.15\right)}^{2}+{\left({T}_{gi}+273.15\right)}^{2}\right\}\left\{{T}_{w}+{T}_{gi}+546.30\right\}$$
$${h}_{c-wg}=0.884{\left\{\left({T}_{w}-{T}_{gi}\right)+\frac{\left({P}_{w}-{P}_{gi}\right)\left({T}_{w}+273.15\right)}{268.9\times {10}^{3}-{P}_{w}}\right\}}^{1/3}$$
$${h}_{e-wg}=16.273 \times {10}^{-3}{h}_{c-wg}\left\{\frac{{P}_{w}-{P}_{gi}}{{T}_{w}-{T}_{gi}}\right\}$$
$${P}_{w}=\mathrm{exp}\left(25.32-\frac{5144}{{T}_{w}+273.15}\right)$$
$${P}_{gi}=\mathrm{exp}\left(25.32-\frac{5144}{{T}_{gi}+273.15}\right)$$

Equations used in Eq. (20) as,

$${\alpha }_{w}^{A}=\left\{\left(1-{R}_{g}\right)\left(1-{\alpha }_{g}\right)(1-{R}_{w}){\alpha }_{w}\right\}$$
$${R}_{w}=\left[1-\left(4{n}_{o}{n}_{w}\right)/\left\{\left({n}_{o}+{n}_{w}^{2}\right)(1+{n}_{o})\right\}\right]$$
$${R}_{a}=\frac{g{\beta }^{^{\prime}}{\rho }^{2}{X}^{3}{C}_{w}\Delta T}{\mu {K}_{w}}$$
$${G}_{r}=\frac{g{\beta }^{^{\prime}}{\rho }^{2}{X}^{3}\Delta T}{{\mu }^{2}}$$
$${P}_{r}=\frac{\mu {C}_{w}}{{K}_{w}}$$

Equations used in Eq. (22) as written (Tiwari, 2014),

$${h}_{ba}={\left\{\left({t}_{b}/{K}_{b}\right)+0.357\right\}}^{-1}$$
$${\alpha }_{beff}=\left({\alpha }_{b}^{A}.{h}_{bw}\right)/\left({h}_{ba}+{h}_{bw}\right)$$
$${U}_{bwa}=\left({h}_{bw}.{h}_{ba}\right)/\left({h}_{bw}+{h}_{ba}\right)$$

Relationships involved in Eqs. (25), (28), and (34) as,

$${U}_{ta}=\left({h}_{t-wg}.{A}_{g}.{U}_{c}\right)/\left({A}_{b}.{h}_{t-wg}+{U}_{c}.{A}_{g}\right)$$
$${h}_{1}^{^{\prime}}=\left({A}_{g}.{h}_{t-wg}\right)/\left({h}_{t-wg}.{A}_{b}+{A}_{g}.{U}_{c}\right)$$
$$a=\left\{{U}_{eff}+{\dot{m}}_{f}{C}_{f}\left(N-1\right)\right\}/\left({m}_{w}{C}_{w}\right)$$
$${U}_{\mathrm{eff}}=\left\{\left({U}_{ta}+{U}_{bwa}\right){A}_{b}+\left({A}_{rc}{F}_{r}\right){U}_{L}\right\}$$
$${\alpha }_{\mathrm{eff}}^{A}=\left({\alpha }_{w}^{A}+{\alpha }_{beff}+{h}_{1}^{^{\prime}}.{\alpha }_{g}^{A}\right)$$
$$f\left(t\right)=\left\{{I}_{s}\left(t\right){A}_{b}.{\alpha }_{eff}^{A}+{T}_{a}.{U}_{eff}+{F}_{1}.{\left(\propto \tau \right)}_{eff}.\left({A}_{rc}{F}_{r}\right){I}_{b}(t)\right\}/\left({m}_{w}{C}_{w}\right)$$
$$\left(Gr.Nu\right)/Pr=\left(g.{d}^{4}.\dot{q}.{\beta }^{^{\prime}}\right)/\left({\nu }^{2}.{C}_{f}.\mu \right)$$
$$Nu=\frac{h.X}{{K}_{w}}$$
$$\nu =\mu /\rho$$

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Singh, A.K., Samsher Eco-design requisites for solar desaltification still augmented evacuated annular tube collectors with parabolic concentrator: an optimum-environ-economic viability. Environ Dev Sustain 25, 11057–11094 (2023). https://doi.org/10.1007/s10668-022-02518-w

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