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Unsteady numerical modeling, experimental validation and optimization of a solar air heater based on the second law of thermodynamics using genetic algorithm

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Abstract

Solar air heaters have a low thermal performance and it is necessary to improve their efficiency. The objective is to find operating conditions with the minimum losses of useful energy by selecting optimal design parameters. For this purpose, an unsteady mathematical model was developed based on six coupled differential equations from the energy balances of six collector components. The equations were solved numerically using Runge-Kutta-Fehlberg method with an iterative code in MATLAB. In the solution procedure, unlike most previous works, the solar heater was divided into differential volume elements of length ∆x and optimal time step size was determined at each integration step. The numerical results were validated with experimental data of a built prototype and good agreements were obtained. The results revealed that the exergy efficiency was improved up to 1.1 times when the absorber thickness decreased from 0.001 to 0.0005 m, while the highest value of efficiency increased 3 times when the side frame thickness varied from 0.015 to 0.035 m. Also, for a mass flow of 0.0017 kg s−1, the useful exergy and outlet temperature reached their maximum values of 6.7 W and 58 °C, respectively. Moreover, the genetic algorithm technique was used to obtain an optimal set of heater geometric parameters with maximum exergy gain. An optimal heater area of 1.72 m2 was found. Finally, three models were defined to quantify the effects of different combinations of geometric parameters and materials. It was found that model III improved the highest value of exergy efficiency by 6 and 4% compared to models I and II, respectively. A constant maximum value of 7% between 10 and 16 h was achieved.

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Abbreviations

\(A\) :

Heater area [m2]

\(C\) :

Specific heat at constant pressure [J kg−1 °C−1]

\({D}_{{\rm h}}\) :

Equivalent hydraulic diameter [m]

E :

Exergy [W]

E d :

Exergy destruction [W]

f :

Friction factor

g :

Gravitational acceleration [m s−2]

\({G}_{{\rm T}}\) :

Solar radiation intensity [W m−2]

h r :

Radiation heat transfer [W m−2 °C−1]

h c :

Convection heat transfer [W m−2 °C−1]

\(K\) :

Extinction coefficient [m−1]

\(k\) :

Thermal conductivity [W m−1 °C−1]

\(L\) :

Channel length [m]

\(\dot{m}\) :

Mass flow [kg s−1]

\(m\) :

Mass [kg]

\(n\) :

Refractive index

\(\mathrm{Nu}\) :

Nusselt number

\(Q\) :

Conduction heat transfer [W m−2 °C−1]

\(R\) :

Particular constant of air [J kg−1 °C−1]

\(\mathrm{Ra}\) :

Rayleigh number

\(\mathrm{Re}\) :

Reynold number

\(\mathrm{Sgen}\) :

Entropy generation [W °C−1]

\(t\) :

Time [s]

\(T\) :

Temperature [°C]

\(U\) :

Total heat loss coefficient [W m−2 °C−1]

\(V\) :

Volume [m3]

\({V}_{{\rm w}}\) :

Wind velocity

\(W\) :

Channel width [m]

\(\alpha\) :

Absorptance

\({\alpha }_{{\rm T}}\) :

Thermal diffusivity [m2 s−1]

\(\beta\) :

Surface tilt angle from the horizontal

\({\beta }_{{\rm v}}\) :

Volumetric expansion coefficient [K−1]

\(\delta\) :

Thickness [m]

\(\varepsilon\) :

Emittance

\({\eta }_{{\rm II}}\) :

Efficiency of second law

\({\theta }_{1}\) :

Incidence angle of solar radiation

\({\theta }_{2}\) :

Refraction angle of cover material

\(\mu\) :

Dynamic viscosity [kg ms−1]

\(\nu\) :

Cinematic viscosity [m2 s−1]

\(\rho\) :

Density [kg m−3]

\(\sigma\) :

Stefan Boltzmann constant [W m−2 K−4]

\(\tau\) :

Transmittance

\({\tau }_{{\rm cs},{\rm a}}\) :

Cover transmittance with only absorption losses

c:

Upper cover

bp:

Base plate

in:

Insulation

ap:

Absorber plate

sf:

Side frame

f:

Working fluid

a:

Ambient

in:

Input or inlet

out:

Output or outlet

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Authors and Affiliations

  1. Universidad de Ciencias y Artes de Chiapas, Libramiento Norte Poniente No. 1150, Col. Lajas Maciel, C.P. 29000, Tuxtla Gutiérrez, Chiapas, Mexico

    Gustavo Espinosa, Guillermo Ibáñez, Aracely López, Orlando Lastres & Juan Reyes-Nava

  2. Universidad Juárez Autónoma de Tabasco, Villahermosa, Tabasco, Mexico

    Joel Pantoja

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  1. Gustavo Espinosa
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Contributions

GE: Software, Validation, Writing original draft. GID: Supervision, Conceptualization, Methodology, Formal analysis, Writing original draft. AL: Validation, Formal analysis, Writing—review and editing. OL: Formal analysis, Writing—review and editing. JR-N: Conceptualization, Writing—review and editing. JP: Methodology, Writing—review and editing.

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Correspondence to Guillermo Ibáñez.

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Espinosa, G., Ibáñez, G., López, A. et al. Unsteady numerical modeling, experimental validation and optimization of a solar air heater based on the second law of thermodynamics using genetic algorithm. J Therm Anal Calorim 148, 7163–7183 (2023). https://doi.org/10.1007/s10973-023-12222-0

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