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Energy and exergy analyses of nanofluid-filled parabolic trough solar collector with acentric absorber tube and insulator roof

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Abstract

Increasing the energy demands has encouraged the development of novel archetypes solar receiver employed in sustainable energies. Parabolic trough solar collectors (PTSCs) attract researchers due to high thermo-hydraulic performance. The main goal of the present investigation is to design an efficient PTSC filled with nanofluid numerically using the finite volume method. The other aim is to compare the obtained numerical results of nanofluid simulation in PTSC the using single-phase mixture model (SPM) and the two-phase mixture model (TPM). In the first step, influences of using SPM or TPM on nanofluid simulation in absorber tube are investigated. Then, the influences of using an insulator roof and an acentric absorber tube on energy and exergy efficiency are studied. Consequently, in this step the optimum configuration is introduced. In the last step, effect of different nanofluid parameters (different volume fraction and various nanoparticles diameters) on the optimum configuration is investigated using TPM. Based on obtained results, for both conventional and novel PTSC, the obtained Nusselt number employing TPM simulation is more than that of SPM simulation. Also, it is found that using the novel PTSC leads to higher Nusselt number, energy efficiency, performance evaluation criteria, and outlet temperature for all studied Reynolds numbers. According to the results, the energy and exergy efficiencies of novel PTSC with an insulator arc angle of 70° and acentric value of 20 mm filled with nanofluid having a diameter of 20 mm and nanoparticles volume fraction of 1% are about 73.10 and 31.55% and are the maximum obtained efficiencies in the present study.

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Abbreviations

\( A_{\text{a}} \) :

Absorber tube surface

\( {\mathcal{A}}_{\text{PTSC}} \) :

Aperture of PTSC

a :

Radiation constant (\( a = 7. 5 6 1\times 10^{ - 19} {\text{kJ}}\;{\text{m}}^{ - 3} {\text{K}}^{ - 4} \))

a i :

Coefficients in thermal properties of Syltherm 800 oil estimations

b :

Exergy transfer

b q :

Exergy of the heat receiver

\( C_{\mu } \) :

Standard constant in the turbulent model

\( c_{\text{p}} \) :

Constant specific heat capacity

\( c_{1} \) :

Standard constant in the turbulent model

\( c_{2} \) :

Standard constant in the turbulent model

C.PTSC:

Conventional PTSC

c :

Speed of light in vacuum (2.998 × 108 m s−1)

\( D \) :

Coefficient of Einstein diffusion

\( d_{\text{a}} \) :

Absorber tube outer diameter

\( d_{\text{g}} \) :

Glass cover outer diameter

\( d_{\text{np}} \) :

Nanoparticle mean diameter

\( \dot{E}_{\text{dest}} \) :

Destruction exergy

\( \dot{E}_{{{\text{dest}},\Delta {\text{p}}}} \) :

Destruction exergy due to the pressure gradient

\( \dot{E}_{\text{dest, heat}} \) :

Destruction exergy due to heat transfer

\( \dot{E}_{\text{loss}} \) :

Exergy loss

\( \dot{E}_{\text{loss, heat}} \) :

Exergy loss due to heat transfer

\( \dot{E}_{{{\text{loss}},\Delta {\text{p}}}} \) :

Exergy loss due to pressure gradient

\( \dot{E}_{\text{loss,opt}} \) :

Exergy loss due to optical error

\( \dot{E}_{\text{solar, in}} \) :

Inlet solar exergy

\( \dot{E}_{\text{loss,opt}} \) :

Optical error exergy

\( \dot{E}_{\text{loss, heat}} \) :

Heat transfer loss exergy

e :

Emission energy

\( f_{\text{av}} \) :

Friction factor for enhanced PTSC

\( f_{{{\text{av}},0}} \) :

Friction factor for the reference PTSC

\( G \) :

The production rate of \( k \)

\( \vec{g} \) :

Fluid gravitational acceleration

GM:

Gray model

HTF:

Heat transfer fluid

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

Convective heat transfer of air-filled annular space

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

Convective heat transfer of surrounding air with outer glass tube

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

Base fluid enthalpy

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

Solid particles enthalpy

\( I_{\text{b}} \) :

Direct normal irradiance is

\( k_{\text{np}} \) :

Nanoparticle thermal conductivity

\( k_{\text{bf}} \) :

Base fluid thermal conductivity (W mK−1)

\( k \) :

Thermal conductivity

\( k_{\text{b}} \) :

Boltzmann’s constant

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

Length of PTSC

M :

Molecular mass

N :

Avogadro number

\( {\text{Nu}}_{\text{av}} \) :

Averaged Nusselt number of enhanced PTSC

\( {\text{Nu}}_{{{\text{av}},0}} \) :

Averaged Nusselt number of reference PTSC

NPTSC:

Nanofluid-based parabolic trough solar collectors

N.PTSC:

Novel PTSC

p :

Pressure

\( { \Pr } \) :

Base fluid Prandtl number

\( { \Pr }_{\text{W}} \) :

Wall temperature Prandtl number

PEC:

Performance Evaluation Criterion

PTSC:

Parabolic trough solar collector

\( \dot{Q}_{\text{rad,r} - \text{a}} \) :

Transmitted solar irradiance across glass cover by radiation

\( \dot{Q}_{\text{conv,a} - \text{nf}} \) :

Heat exchange among heat transfer nanofluid and absorber tube by convection

\( \dot{Q}_{\text{conv,a} - \text{anna}} \) :

Heat exchange among absorber tube and annulus-air (anna) by convection

\( \dot{Q}_{\text{rad,g} - \text{sky}} \) :

Radiation heat loses with the lower part of the glass cover

\( \dot{Q}_{\text{rad,a} - \text{sky}} \) :

Radiation heat loses with the lower part of the absorber tube

\( \dot{Q}_{\text{cond,a} - \text{ins}} \) :

Heat exchange among absorber tube and insulation part by conduction

\( \dot{Q}_{\text{cond,a} - \text{nf}} \) :

Heat exchange among absorber tube and nanofluid

\( \dot{Q}_{\text{conv,g} - \text{env}} \) :

Heat exchange among glass cover and surrounding by convention

\( \dot{Q}_{\text{j, loss}} \) :

Heat loss

\( {\text{Re}}_{\text{np}} \) :

Nanoparticle Reynolds number

\( {\text{Re}}_{\text{s}} \) :

Particle Reynolds number

S2S:

Surface-to-surface transfer mode

SPM:

Single-phase model

T :

Nanofluid temperature

\( T_{\text{a}} \) :

The temperature of air-filled annular space

\( T_{\text{g}} \) :

Surrounding air temperature

\( T_{\text{a,j}} \) :

Absorber tube temperature

\( T_{\text{i,j}} \) :

Inlet absorber tube fluid temperature

\( T_{\text{e,j}} \) :

Exit absorber tube fluid temperature

\( T_{\text{env}} \) :

Ambient (environment) temperature

\( T_{\text{in}} \) :

Inlet nanofluid temperature

\( T_{\text{fr}} \) :

Base fluid freezing point

\( T_{0} \) :

Surrounding temperature

\( T_{\text{s}} \) :

Surface temperature

TPM:

Two-phase model

\( u_{\text{B}} \) :

Nanoparticle mean Brownian velocity

\( \vec{U}_{\text{m}} \) :

Mixture velocity or mass-averaged velocity

\( \vec{U}_{\text{s}} \) :

Solid particles velocity

\( \vec{U}_{\text{bf}} \) :

The velocity of the base fluid

\( \vec{U}_{\text{dr,bf}} \) :

Base fluid drift velocity

\( \vec{U}_{\text{dr,s}} \) :

Particles drift velocity

\( V_{\text{w}} \) :

Wind velocity

\( V_{\text{nf}} \) :

Nanofluid velocity

\( \vec{\alpha } \) :

Particle’s gravitational acceleration

α :

Absorptance

\( \delta \) :

Half of the sun’s cone angle

\( \delta_{\text{a}} \) :

Absorber tube thickness

\( \delta b \) :

Irreversibility of exergy

ε :

Emittance

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

Exergy efficiency

\( \Lambda \) :

Acentric values

\( \mu \) :

Dynamic viscosity

\( \mu_{\text{t,m}} \) :

Turbulent viscosity

\( \mu_{\text{m}} \) :

Mixture viscosity

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

Nanofluid viscosity

\( \sigma_{\text{k}} \) :

Standard constants in the turbulent model

\( \sigma_{\varepsilon } \) :

Standard constants in the turbulent model

\( \sigma_{\text{t}} \) :

Standard constants in the turbulent model

\( \rho_{\text{m}} \) :

Density for a two-phase mixture

ρ :

Density

τ :

Transmittance

\( \rho_{{{\text{f}}0}} \) :

Base fluid density was evaluated at temperature \( T_{0} = 293\;{\text{K}} \)

\( \tau_{\text{D}} \) :

Time request to the distance between two molecules

\( \varrho \) :

Refractive index

\( \phi \) :

Volume fraction

\( \varsigma_{\text{Rim}} \) :

Rim angle

\( \varsigma_{\text{NP}} \) :

Non-parallelism angle

\( \psi \) :

Highest available solar work

Ψ:

Arc angle

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  1. Department of Mechanical Engineering, University of Kashan, Kashan, Iran

    Ali Akbar Abbasian Arani & Farhad Monfaredi

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  1. Ali Akbar Abbasian Arani
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Abbasian Arani, A.A., Monfaredi, F. Energy and exergy analyses of nanofluid-filled parabolic trough solar collector with acentric absorber tube and insulator roof. J Therm Anal Calorim 145, 787–816 (2021). https://doi.org/10.1007/s10973-020-10267-z

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