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Insulator roof, acentric absorber tube and nanofluid effect on parabolic trough collector efficiency via two-phase flow simulation

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Abstract

Current study aims to present an effectual parabolic trough collector (PTC), which is employed from nanofluid up to 4% as working fluid numerically using the finite volume scheme. Another propose is comparing the responses using the single-phase mixture (SPM) method and two-phase mixture (TPM) method. In this study, the effects of employing acentric absorber tube up to 20mm and an insulator roof from 30° to 150° are investigated. Subsequently, the best arrangement is established. Also, various nanofluid constraints (nanoparticles diameter and volume fraction) for the best arrangement is examined by TPM method. For proposed and conventional PTC configurations, the average Nusselt number by TPM method is higher than by SPM method. Furthermore, it is shown that employing proposed PTC provide higher energy efficiency, Nusselt number, outlet temperature, and performance evaluation criteria (PEC) in studied range of Reynolds numbers from 3000 to 11,500. Finally, the proposed PTC provide the energy efficiency equal to 73.10% having the acentric value of 20mm and arc-angle of \(70^\circ \) occupying by nanofluid considering nanoparticles diameter of 20nm and nanoparticles volume fraction of 1%.

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Abbreviations

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

Absorber tube surface

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

Aperture of PTSC

a,:

Radiation constant (a=7.561·10−19 kJm−3 K−4)

a i :

Coefficients in thermal properties of Syltherm 800 oil estimations

\(C_{{\upmu }}\) :

Standard constant in the turbulent model

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

Constant specific heat capacity

C.PTSC:

Conventional PTSC

\(D\) :

Coefficient of Einstein diffusion

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

Absorber tube outer diameter

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

Glass cover outer diameter

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

Nanoparticle mean diameter

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

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

Nanoparticle thermal conductivity,

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

Base fluid thermal conductivity (W m−1 K−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

NPTC:

Nanofluid based parabolic trough solar collectors

N.PTC:

Novel PTC

\(p\) :

Pressure

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

Base fluid Prandtl number

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

Wall temperature Prandtl number

PEC:

Performance evaluation criterion

PTC:

Parabolic trough solar collector

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

Transmitted solar irradiance across glass cover by radiation

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

Heat exchange among heat transfer nanofluid and absorber tube by convection

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

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

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

Radiation heat loses with the lower part of the glass cover

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

Radiation heat loses with the lower part of the absorber tube

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

Heat exchange among absorber tube and insulation part by conduction

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

Heat exchange among absorber tube and nanofluid

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

Heat exchange among glass cover and surrounding by convention

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

Nanoparticle Reynolds number

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

Particle Reynolds number

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

\(\alpha\) :

Absorptance

\(\delta\) :

Half of the sun’s cone angle

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

Absorber tube thickness

\(\delta b\) :

Irreversibility of exergy

\(\varepsilon\) :

Emittance

\({\Lambda }\) :

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

\(\sigma_{{\upvarepsilon }}\) :

Standard constants in the turbulent model

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

Standard constants in the turbulent model

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

Density for a two-phase mixture

\(\rho\) :

Density

\(\tau\) :

Transmittance

\(\rho_{{{\text{f0}}}}\) :

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

\(\psi\) :

Arc-angle

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

    Ali Akbar Abbasian Arani & Farhad Monfaredi

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Abbasian Arani, A.A., Monfaredi, F. Insulator roof, acentric absorber tube and nanofluid effect on parabolic trough collector efficiency via two-phase flow simulation. J Therm Anal Calorim 148, 12481–12499 (2023). https://doi.org/10.1007/s10973-023-12603-5

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