# Energy and Exergy Analyses of a Flat Plate Solar Collector Using Various Nanofluids: An Analytical Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}O

_{3}/water, MgO/water, TiO

_{2}/water, and CuO/water, and compared with water as a flowing medium (traditional base fluid). The analysis considered nanofluids made of nanomaterials’ volume fractions of 1–4% with water. The volume flow rates of nanofluids and water were 1 to 4 L/min. The solar collector′s highest EnE efficiency values were obtained for CuO/water nanofluid among the four types of nanofluids mentioned above. The EnE efficiencies of the CuO nanofluid-operated solar collector were 38.21% and 34.06%, respectively, which is significantly higher than that of water-operated solar collectors. For the same volume flow rate, the mass flow rate was found to be 15.95% higher than water for the CuO nanofluid. The EnE efficiency of FPSC can also be increased by increasing the density and reducing the specific heat of the flowing medium.

## 1. Introduction

_{2}O

_{3}/water and CuO/water to investigate the performance efficiency of FPSC. Their result showed CuO/water nanofluid achieved maximum efficiency compared to the other two nanofluids. The reason for these results may be because of differences in TC coefficients of the nanoparticles. Said et al. [16,17] experimentally and theoretically investigated the impact of utilising different sized Al

_{2}O

_{3}nanoparticles (20 nm and 13 nm) suspended into a base fluid (water) on the EnE efficiencies of the FPSC. They performed their experiments with nanofluid of 0.3 vol % and 0.1 vol %, varying the mass flow rate from 0.5 to 1.8 kg/min. They reported that the nanoparticle size has an impact on the performance of FPSC. They found a 3% higher thermal performance enhancement when the size varies from 20 nm to 13 nm. Additionally, they recorded 83.5% theoretical thermal efficiency at 0.3 vol % and 1.8 kg/min of a mass flow rate. An overview of the literature analysis is presented in Table 1.

_{2}O

_{3}/water as a heat transfer fluid inside the FPSC improved the effectiveness of FPSC by 2–31.6% when nanoparticle concentrations of 0.1 to 3 wt.% and mass flow rates of 0.5 to 7.5 kg/min were maintained. In addition, Cu/water and CuO/water nanofluids improve the efficiency of 6.3 to 27.3% when the experiments were employed at a volume fraction that varies from 0.025 to 0.5 vol % and the mass flow rate changes from 1 to 8.8 kg/min, when compared to traditional fluids.

_{2}O

_{3}, MgO, TiO

_{2}, and CuO nanoparticles in water were considered in this study. The first law of thermodynamics was used to calculate energy efficiency, while the second law of thermodynamics was used to determine exergy efficiency.

## 2. Analytical Approach

#### 2.1. The First Law of Thermodynamics for Energy Efficiency

_{u}) may be expressed as,

_{o}) [42].

_{R}can be defined by,

_{R}(τα), F

_{R}, and U

_{1}were constant at the tested temperatures [5]. However, it should be remembered that different types of energy have additional chances of generating work. As a result, efficiency specification was limited to a comparison of quantities that were metrically equivalent but not conceptually equivalent.

#### 2.2. The Second Law of Thermodynamics for Exergy Efficiency

_{f}in at the inlet to T

_{f}out at the outlet. The exergy collection rate can be expressed without considering the mechanical exergy if the fluid is incompressible by using the following Equation:

**⮕**plate): when solar light at Ts is absorbed by the absorber at Tc, an exergy annihilation event occurs.

**⮕**ambient): a process of exergy loss followed by heat leaking from the absorber into its environs.

**⮕**fluid): heat conduction between the absorber and the heat transfer fluid causes exergy annihilation.

_{1}) and the heat transfer coefficient distribution; these equations may be approximated using the mean absorber temperature as shown below:

- ✓
- e
_{opt}: Optical loss percent solar energy absorbed owing to glazing transmissiveness and amorphous absorption. - ✓
- e
_{rp}: When solar radiation at Ts is absorbed by the absorber at Tc, there is a loss fraction. (Absorption at low temperatures degrades the high-quality energy). - ✓
- e
_{pa}: A portion of the exergy lost by the absorber to the environment. - ✓
- e
_{pf}: The heat transfer from the absorber to the fluid is accompanied by a heat-conduction loss percentage.

_{l}(Tc − Ta)/IT in the well-known formulation of energy efficiency correspond to two of the aforementioned loss fractions, e

_{opt}and e

_{pa}; it is worth mentioning that the word e

_{pf}is quite close to the collector efficiency factor, which stands for loss of heat conduction. The following link is discovered using the temperature distribution correlations in the collector [45]:

## 3. Input Data and Methodology

#### 3.1. Input Data

#### 3.2. Methodology

## 4. Results and Discussions

_{2}/water, TiO

_{2}/water, Al

_{2}O

_{3}/water, CuO/water, and Gr/water, were experimentally investigated by Verma et al. [53]. They found the CuO/water nanofluids achieved maximum efficiencies. A group of nanofluids (SiO

_{2}/water, TiO

_{2}/water, Al

_{2}O

_{3}/water, GNP/water, and SWCNT/water) were also examined and compared their efiiciencied by Elcioglu et al. [54]. Additionally, they verified that, the increase in volume fraction of nanofluids enhanced the absorber’s efficiency for all nanofluids investigated.

- ✓
- As nanofluids replace water as an absorbing medium, the nanofluids’ viscosity, density, and TC increase, but its specific heat decreases compared to the base fluid (water). Interestingly, these findings are in agreement with those of Pandey et al. [50].
- ✓
- To gain exergy, the entropy generation number is typically expected to decrease. The entropy generation number decreases when nanofluids are used as agent fluids [51].
- ✓
- With an increase in particle concentration, the heat transfer rate is increased [56].

_{2}O

_{3}/water MgO/water and TiO

_{2}/water nanofluids compared to the base fluid. These results satisfactorily agree with the results of Yousefi et al. [12] and Tyagi et al. [11].

_{2}O

_{3}, MgO and TiO

_{2}nanofluids for a given volume fraction. The relative heat of Al

_{2}O

_{3}and TiO

_{2}nanofluid was nearly identical. Even though the specific heat of these nanofluids varied, they were all above the specific heat of the base fluid. These findings are consistent with those of Kamyar et al. [57] and Sohel et al. [58].

_{2}nanofluid, and 9.35% for Al

_{2}O

_{3}and 9.53% for MgO nanofluid compared to base fluid (water).

_{2}O

_{3}and MgO show approximately equal exergy efficiency but higher than water. On the other hand, TiO

_{2}provides slightly better exergy efficiency compared to base fluid, Al

_{2}O

_{3}and MgO nanofluids. Thus, the analytical results indicate that the maximum exergy efficiency can be achieved with collectors using nanofluids as an agent medium. This improvement was most likely aided by the following factors: At a fixed Reynolds number, (I) the suspension TC increases as the volume fraction of nanoparticles, and (II) the nanofluids’ convective heat transfer coefficient is higher than that of the base fluid. Those similar conclusions were reported by Duangthongsuk and Wongwises [60], Xuan and Li [61], and He et al. [62]. When the collector absorbent surface area is identical, the mass flow rates and the specific heat may have a considerable effect on the exergetic efficiency of solar collectors, according to the exergy efficiency Equation (30).

_{2}O

_{3}, TiO

_{2}, MgO, and CuO nanofluids, respectively for 3.2% nanoparticles volume concentration. This indicates that about an 11.45% increase in the mass flow rate is possible for CuO nanofluid than water. These findings are in agreement with the results published by Sohel et al. [58].

## 5. Conclusions

- The analytical result shows CuO nanofluid increased the EnE efficiency of a FPSC by 38.21% and 14.86%, respectively.
- Additionally, the study demonstrated that increasing volume fraction, mass flow rate, and density could improve EnE efficiency. Whenever the volume flow rate remains constant, the mass flow rate can be increased by adding nanoparticles into the base fluid, which has higher efficiency. Specific heat is one of the essential parameters for efficiency improvement. By reducing the specific heat of a fluid, the efficiency of a FPSC can be improved. It is simple to do so by suspending a small number of nanoparticles.
- CuO nanofluid is a better option for increasing both the EnE efficiency of FPSC.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A_{p} | absorption area, m^{2} |

C_{p} | specific heat, J/kg·K |

e | exergy loss |

$\dot{{E}_{g}}$ | exergy gain rate per unit area, W/m^{2} |

F_{R} | heat removal factor |

F’ | collector efficiency factor |

g | gravitational acceleration, m/s^{2} |

I_{T} | incident solar energy per unit area, W/m^{2} |

k | heat conductivity, W/m·K |

ṁ | mass flow rate, kg/s |

P | mechanical power, W |

$\dot{Q}$ | thermal energy rate, W |

$\dot{{Q}_{u}}$ | energy gain rate, W |

s | entropy per unit mass, J/kg·K |

S | absorbed irradiation, W/m^{2} |

T | temperature, K |

T_{c} | absorber plate temperature, K |

U_{1} | overall heat loss, W/m^{2} K |

V | volume flow rate, L/min |

z | height from reference level, m |

EnE | energy and exergy |

FPSC | flat plate solar collector |

DAC | directive solar collector |

CNT | carbon nanotube |

TC | Thermal conductivity |

η_{En} | energy efficiency |

η_{Ex} | exergy efficiency |

η_{o} | optical efficiency |

τ | transmittance |

α | absorptance |

φ | nanoparticles volume fraction, % |

ρ | density, kg/m^{3} |

σ | overall entropy production, J/kg·K |

Subscript | |

a | ambient |

bf | base fluid |

d_{est} | destruction |

f_{in} | inlet fluid |

f_{out} | outlet fluid |

np | nanoparticles |

nf | nanofluid |

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References | Model | Base Fluid | Nanoparticles’ Specification | Optimum Parameters | |||||
---|---|---|---|---|---|---|---|---|---|

Particle Name | Volume Fractions (Vol %) | Size (nm) | Mass Flow Rate (kg/min) | Improvement of Efficiency (%) | Flow Regime | FPSC Surface Area (m^{2}) | |||

Sundar et al. [18] | Experimental | Water | Al_{2}O_{3} | 0.1 and 0.3 | 20 | 5 | 18 | Turbulent | 2 |

Hawwash et al. [19] | Experimental and Numerical (CFD ansys fluent) | DW | Al_{2}O_{3} | 0.1 and 0.3 | 20 | 5.51 | 18 | Turbulent | 2.1 |

Mogahadam et al. [20] | Experimental | Water | CuO | 0.4 | 40 | 1 | 21.8 | Laminar | 1.88 |

Genc et al. [21] | Numerical (Matlab) | Water | Al_{2}O_{3} | 0.1, 0.2 and 0.3 | 3.6 | 9.5 | Laminar | 1.99 | |

Nasrin and Alim [22] | Experimental | DW | Al_{2}O_{3}, CuO and TiO_{2} | 0.2, 0.4 and 0.8 | 50, 50 and 25 | 4 | 71, 87.8 and 52.5 | Laminar | 1.51 |

Shojaeizadeh et al. [23] | Experimental and Numerical | DI water | Al_{2}O_{3} SDBS | 0.090696, 0.094583, 0.10293, 0.11057, 0.117686, 0.1244, 0.13082, 0.137, and 0.1423 | 15 | 2.5 | 70 | Turbulent | 1.51 |

Kilic et al. [24] | Experimental | Water | TiO_{2} Triton X-100 | 0.2 | 44 | 2 | 34.43 | Turbulent | 1.82 |

Said et al. [25] | Experimental | PEG-400 | TiO_{2} | 0.1 and 0.3 | 21 | 0.5 | 76.6 | Laminar | 1.84 |

Jouybari et al. [26] | Experimental | Water | SiO_{2} | 0.2, 0.4, and 0.6 | 7 | 1.5 | 8 | Laminar | 0.8 |

Faizal et al. [27] | Experimental | Water | SiO_{2} | 0.2, 0.4, and 0.6 | 10 | 3 | 23.5 | Turbulent | 2 |

Meibodi et al. [28] | Experimental | EG–water | SiO_{2} | 0.5, 0.75, and 1 | 10 | 2.7 | 8 | Turbulent | 1.59 |

Nanoparticles | Specific Heat, Cp (J/kg·K) | Thermal Conductivity, k (W/m·K) | Density, ρ (kg/m ^{3}) |
---|---|---|---|

Alumina (Al_{2}O_{3}) | 773 | 40 | 3960 |

Copper oxide (CuO) | 551 | 33 | 6000 |

Titanium oxide (TiO_{2}) | 692 | 8.4 | 4230 |

Magnesium oxide (MgO) | 955 | 45 | 3560 |

Water (H_{2}O), base fluid | 4182 | 0.60 | 997 |

**Table 3.**Characteristic parameters for two kinds of solar collector [45].

Solar Collector Type | Optical Efficiency, η_{o} | Overall Heat Loss, U _{1} (W/m^{2} K) | Collector Efficiency Factor, F′ |
---|---|---|---|

Evacuated tube | 0.47 | 1.1 | 0.99 |

Flat plate | 0.82 | 5.0 | 0.97 |

Parameters of Collector | Value |
---|---|

Type | Black paint flat plate |

Glazing | Single glass |

Agent fluids | Water, Al_{2}O_{3}, MgO_{2}, TiO_{2} and CuO nanofluids |

Absorption area (m^{2}) | 1.44 |

Wind speed (m/s) | 20 |

Collector till (°) | 20 |

Fluid inlet and ambient temperature (K) | 300 |

Apparent sun temperature (K) | 4350 |

Optical efficiency | 84% |

Emissivity of the absorber plate | 0.95 |

Emissivity of the covers | 0.90 |

Glass thickness (mm) | 4 |

Insulation TC (W/m∙K) | 0.06 |

Incident solar energy per unit area of the absorber plate (W/m^{2}) | 500 |

Inner diameter of pipes (m) | 0.005 |

Absorbing Medium | Maximum ηEn Enhancement, (%) | Maximum ηEx Enhancement, (%) | ||
---|---|---|---|---|

φ = 2% and Diff. Volume Flow Rate | φ = 3.20% and V = 1 L/s | φ = 2% and V = 2.40 L/s | φ = 3.20% and V = 1 L/s | |

CuO nanofluid | 38.21 | 16.80 | 14.86 | 11.45 |

TiO_{2} nanofluid | 34.17 | 9.25 | 12.64 | 9.70 |

MgO nanofluid | 34.77 | 9.71 | 12.56 | 9.53 |

Al_{2}O_{3} nanofluid | 35.32 | 9.18 | 11.11 | 9.35 |

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**MDPI and ACS Style**

Mostafizur, R.M.; Rasul, M.G.; Nabi, M.N.
Energy and Exergy Analyses of a Flat Plate Solar Collector Using Various Nanofluids: An Analytical Approach. *Energies* **2021**, *14*, 4305.
https://doi.org/10.3390/en14144305

**AMA Style**

Mostafizur RM, Rasul MG, Nabi MN.
Energy and Exergy Analyses of a Flat Plate Solar Collector Using Various Nanofluids: An Analytical Approach. *Energies*. 2021; 14(14):4305.
https://doi.org/10.3390/en14144305

**Chicago/Turabian Style**

Mostafizur, R. M., M. G. Rasul, and M. N. Nabi.
2021. "Energy and Exergy Analyses of a Flat Plate Solar Collector Using Various Nanofluids: An Analytical Approach" *Energies* 14, no. 14: 4305.
https://doi.org/10.3390/en14144305