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Examination of the theoretical model for flat-plate solar collectors and integration with solar radiation decomposition/transposition models

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Abstract

Water heating and climatization are important segments of the residential energy consumption. In this regard, solar thermal energy is a great prospect for promoting energy sustainability. An experimental and theoretical examination of the classical model to evaluate the thermal performance of flat-plate solar collector (FPSC) was conducted in this work. The experimental data were obtained between the months of March and May in Porto Alegre city, Brazil. The model was also integrated with a solar radiation model, for which sixteen combinations of decomposition/transposition models were evaluated. The three best combinations of decomposition/transposition models were identified. The experimental data were compared with the classical model, called M1, obtaining a relative error (RE) between 1.98 and 11.48% and a mean relative error (MRE) of 6.38%. Afterward, two correction factors were identified by the theoretical examination of the classical model. These factors were implemented to correct the determined value of the useful energy. Moreover, two new models, which incorporate the correction factors, were tested, namely, models M2 and M3, respectively. These models were compared with experimental data. The results show a MRE of 4.35 and 3.38%, respectively. Therefore, model M3 showed better results than the classical model M1. A case study was carried out implementing the model M3 to study the FPSC performance in Porto Alegre, Brazil.

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Abbreviations

\(A\) :

Area (\({\mathrm{m}}^{2}\))

AM:

Air mass

C b :

Bond conductance

C p :

Specific heat [J/(kg K)]

D :

Diameter of the tube (m)

E :

Thickness (m)

F :

Efficiency of a straight fin

f :

Friction factor

F′:

Efficiency factor

F″:

Collector flow factor

F R :

Collector heat removal factor

FPSC:

Flat-plate solar collector

G T :

Incident irradiance (W/m2)

h :

Heat transfer coefficient (W/m2 K)

I :

Global horizontal irradiance (W/m2)

I b,n :

Direct normal irradiance (W/m2)

I d :

Diffuse horizontal irradiance (W/m2)

I b :

Direct horizontal irradiance (W/m2)

I T :

Global tilted irradiance (W/m2)

\({I}_{T,b}\) :

Beam radiation on tilted surface (W/m2)

\({I}_{T,d}\) :

Diffused radiation on tilted surface (W/m2)

\({I}_{T,d,\mathrm{iso}}\) :

Isotropic diffuse component on inclined surface (W/m2)

\({I}_{T,d,\mathrm{cs}}\) :

Circumsolar component on inclined surface (W/m2)

\({I}_{T,d,\mathrm{hb}}\) :

Horizon brightening component on inclined surface (W/m2)

\({I}_{T,r}\) :

Ground reflected radiation on tilted surface (W/m2)

\({I}_{o}\) :

Extraterrestrial horizontal irradiance (W/m2)

\({I}_{o,n}\) :

Extraterrestrial direct beam irradiance

\(k\) :

Thermal conductivity (W/m K)

\({k}_{t}\) :

Clearness index

\({k}_{d}\) :

Diffuse fraction

\({k}_{n}\) :

Direct transmittance

\({k}_{n,c}\) :

Clear-sky direct transmittance

\({f}_{xx}\) :

Brightness coefficients

\({f}_{k}\) :

Correction factor from Klucher

\(\dot{m}\) :

Mass flow rate (kg/s)

\(\left(\alpha \tau \right)\) :

Transmittance–absorbance product

\({\alpha }_{s}\) :

Solar altitude angle (degree)

\(\beta\) :

Tilt angle (degree)

\(\varepsilon\) :

Emittance

\(\zeta\) :

Clearness parameter

\(\eta\) :

Thermal efficiency

\(\theta\) :

Angle of incidence (degree)

\({\theta }_{z}\) :

Zenith angle (degree)

\(\mu\) :

Viscosity (kg/m s)

\(\rho\) :

Density (kg/m3)

\({\rho }_{g}\) :

Ground reflectance albedo

\(\sigma\) :

Stefan–Boltzmann constant (W/m2 K4)

\(\tau\) :

Reduce temperature (°C m2/W)

\(\Delta\) :

Brightness parameter

\(\Delta {k}_{n}\) :

Deviation from clear-sky direct transmittance

MBE:

Mean bias error

MRE:

Mean relative error

N :

Number of experimental data

\(\mathrm{Nu}\) :

Nusselt number

\(p\) :

Local air pressure (Pa)

\(P\) :

Perimeter (m)

\(\mathrm{Pr}\) :

Prandtl number

\({Q}_{u}\) :

Useful energy gain (\(W\))

RE:

Relative error

\(\mathrm{Re}\) :

Reynold number

rMBE:

Relative mean bias error

RMSE:

Root-mean-square error

rRMSE:

Relative root-mean-square error

\({R}^{2}\) :

R squared

\(S\) :

Solar energy absorbed (W/m2)

\(T\) :

Temperature (°C and K)

\({U}_{x}\) :

Loss coefficient (W/m2 °C)

\(V\) :

Speed (m/s)

\(w\) :

Distance between tubes (m)

\({W}_{A}\) :

Calibration uncertainty

\({W}_{D}\) :

Uncertainty associated with an instrument

\({W}_{G}\) :

Measurement uncertainty

\({W}_{S}\) :

Data acquisition system uncertainty

\({x}_{i}\) :

Observed measures

\(\overline{x }\) :

Measured mean value

\({y}_{i}\) :

Predict (calculated) value

\({y}_{i}\) :

Predict (calculated) value

\(a\) :

Ambient

\(\mathrm{ave}\) :

Average

\(b\) :

Bottom

\(c\) :

Collector

\(e\) :

Edge

\(\mathrm{exp}\) :

Experimental

\(f\) :

Fluid

\(g\) :

Glass

\(i\) :

Inlet

\(\mathrm{in}\) :

Inner

\(\mathrm{iso}\) :

Insulation

\(L\) :

Overall

\(m\) :

Mean

\(\mathrm{num}\) :

Numerical

\(o\) :

Outlet

\(p\) :

Plate

\(t\) :

Top

\(\mathrm{wa}\) :

Water

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Acknowledgements

The authors are grateful to CNPq, Brazil (Conselho Nacional de Desenvolvimento Científico e Tecnológico), for supporting this work through Project 308915/2022-4.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Rio Grande do Sul (UFRGS), R. Sarmento Leite 425, Porto Alegre, RS, CEP, 90050-170, Brazil

    Leonardo Geovo, Crissiane A. Ancines, Arno Krenzinger & Andrés Z. Mendiburu

  2. Department of Electrical Engineering, National University of Mar del Plata (UNMdP), Diagonal J. B. Alberdi 2695, CEP 7600, Mar del Plata, Argentina

    Justo J. Roberts

  3. School of Science and Engineering, Department of Chemistry and Energy, São Paulo State University (UNESP), Av Ariberto P. da Cunha, 333, Guaratinguetá, SP, CEP 12510410, Brazil

    Diego J. Mariños Rosado

  4. Department of Mechanical Engineering, Institute of Engineering and Technology, GLA University, Mathura, 281406, India

    Sujit Verma

  5. School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab, 144001, India

    Rahul Kumar

  6. International Research Group for Energy Sustainability (IRGES), R. Sarmento Leite 425, Porto Alegre, RS, CEP 90050-170, Brazil

    Leonardo Geovo, Justo J. Roberts, Diego J. Mariños Rosado, Sujit Verma, Rahul Kumar & Andrés Z. Mendiburu

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  1. Leonardo Geovo
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Correspondence to Andrés Z. Mendiburu.

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Geovo, L., Ancines, C.A., Krenzinger, A. et al. Examination of the theoretical model for flat-plate solar collectors and integration with solar radiation decomposition/transposition models. J Braz. Soc. Mech. Sci. Eng. 45, 606 (2023). https://doi.org/10.1007/s40430-023-04524-z

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