How Nanofluids May Enhance Energy Efficiency and Carbon Footprint in Buildings?

Abstract

Nanofluids are an innovative working medium in solar hot water installations (DHWs), thanks to their increased thermal conductivity and heat transfer coefficient. The aim of this work was to assess the effect of Al₂O₃ nanofluids in a water–ethylene glycol base (40:60%) and with the addition of Tween 80 surfactant (0.2 wt%) on thermal efficiency (ε) and exergy (η_ex) in a plate heat exchanger at DHW flows of 3 and 12 L/min. The numerical NTU–ε model was used with dynamic updating of thermophysical properties of nanofluids and the solution of the ODE system using the ode45 method, and the validation was carried out against the literature data. The results showed that the nanofluids achieved ε ≈ 0.85 (vs. ε ≈ 0.87 for the base fluid) and η_ex ≈ 0.72 (vs. η_ex ≈ 0.74), with higher entropy generation. The addition of Tween 80 reduced the viscosity by about 10–15%, resulting in a slight increase of Re and h-factor; however, the impact on ε and η_ex was marginal. The environmental analysis with an annual demand of Q = 3000 kWh/year and an emission factor of 0.2 kg CO₂/kWh showed that for ε < 0.87 the nanofluids increased the emissions by ≈16 kg CO₂/year, while at ε ≈ 0.92, a reduction of ≈5% was possible. This paper highlights the need to optimize nanofluid viscosity and exchanger geometry to maximize energy and environmental benefits. Nowadays, due to the growing problems of global warming, the analysis of energy efficiency and carbon footprint related to the functioning of a building seems to be crucial.

1. Introduction

Improving the energy efficiency of buildings is one of the key challenges of contemporary climate and energy policy, aimed at reducing greenhouse gas emissions and achieving global sustainable development goals. As it derives from the newest European Environment Agency reports, in the European Union, the building sector accounts for approximately 40% of total energy consumption in 2021 and 36% of CO₂ emissions in 2022 [1,2]. Consequently, modern technologies supporting the energy transition, including the goal of nearly zero-energy buildings (nZEB), are gaining increasing importance [2].

Solar systems play a vital role in this transformation by enabling the use of renewable energy sources for domestic hot water heating, space heating, and even cooling. However, the efficiency of traditional solar collectors is often limited by the thermophysical properties of the working fluids used, such as water or ethylene glycol. To address these limitations, nanofluids—colloidal suspensions of nanoparticles in base fluids—have attracted growing interest due to their enhanced thermal conductivity, improved heat transfer coefficients, and stability under cyclic temperature variations.

In recent years, numerous experimental and simulation studies have confirmed that applying nanofluids in solar systems can significantly increase their efficiency, directly translating into energy savings in buildings. The most commonly used nanoparticles are metal oxides such as Al₂O₃, TiO₂, and ZnO, as well as carbon materials like graphene and carbon nanotubes. The selection of the appropriate nanofluid composition, particle concentration, and system design parameters is crucial to achieving optimal system performance. Hybrid nanofluids, combining properties of different nanoparticle types such as TiO₂ and SiO₂, are particularly promising. Their synergistic effect allows further enhancement of thermal conductivity, heat transfer, and potential reduction of exergy losses in the energy transfer process within the heat exchanger [3,4].

One promising research direction to improve the thermal efficiency of solar collectors is the use of ionic liquid (IL)-based nanofluids with added graphene oxide (GO). A recent study [5] analyzed flow and thermal properties of IL/GO, IL-H₂O/GO (75:25 and 50:50), and H₂O/GO mixtures, considering advanced heat transfer phenomena such as nonlinear natural convection, thermal radiation, heat absorption, and boundary conditions with velocity slip and temperature jump. The mathematical model, based on actual thermophysical properties (e.g., viscosity, density, heat capacity, thermal conductivity at 20 °C), was solved using the Galerkin weighted residual method. Results indicated a clear advantage of IL/GO nanofluids in heat transfer efficiency—achieving a 36.8% higher efficiency compared to pure water, corroborated by experimental data. Additionally, increases in natural convection and radiation parameters intensified heat transfer, while higher heat absorption could mitigate thermal stresses in the collector. The Nusselt number increased with the Biot number, heat absorption, and temperature jump, but decreased with increased radiation and velocity slip [6]. Notably, despite high energy accumulation efficiency, IL/GO nanofluids exhibited lower maximum temperatures than other fluids, indicating thermal stability and suitability under strong solar irradiation. Water mixtures with GO (lower IL content) perform better under moderate operating conditions where overheating prevention is critical. Thus, nanofluid composition should be tailored to specific applications, collector designs, and environmental conditions [5]. Thermophysical parameters used in the model were drawn from experimental work [7], which first assessed the effectiveness of novel ionic liquid–graphene oxide nanofluids (INF) composed of 1-ethyl-3-methylimidazolium acetate ionic liquid and GO nanoparticles for flat plate solar collectors (FPSC). Four INF variants were developed: IL/GO, IL-H₂O/GO in 75:25 and 50:50 ratios, and water with GO. These fluids were characterized in terms of thermophysical and physicochemical properties. The best results were achieved with pure IL-based INF—the system efficiency increased by 37.4% compared to water, with collector temperatures rising up to 2.5 times. Moreover, IL/GO showed high stability—no degradation or nanoparticle sedimentation was observed even after two years. These findings confirm that IL- and GO-based INF can significantly enhance solar collector performance and represent a promising research direction for solar domestic hot water preparation [7].

While intensive research on ionic liquid salt-based nanofluids [5,6,7] demonstrated their beneficial heat transfer properties, it was natural to analyze the behavior of these working fluids in heat pipes. This allows for further improvements in the efficiency and performance of these systems [8,9,10,11,12,13,14,15,16,17,18,19,20].

The literature extensively describes the application of nanofluids in solar collectors with heat pipes, including pulsating heat pipes (PHPs), thermosiphon tubes, and evacuated tubes [8]. Parabolic concentrator collectors using Al₂O₃ and CuO nanofluids with Syltherm 800 (Dow Chemical Co., Midland, MI, USA) as the base fluid in a Rankine cycle achieved a global efficiency around 24.66% [7]. For example, study [10] demonstrated that a mixture of water, ethanol, and Al₂O₃ nanoparticles in a closed pulsating heat pipe reduced thermal resistance by up to 48% compared to pure water. Ji et al. [11] observed up to 75.8% system efficiency improvement using deionized water with differently shaped and sized Al₂O₃ nanoparticles. Further studies showed that Al₂O₃ nanofluids based on water increased heat absorption coefficients by about 30% in thermosiphon heat pipes [12]. Meanwhile, study [13] reported collector efficiencies rising from 48% (pure water) to 58% (Al₂O₃ + water) and 64% (TiO₂ + water). In [14], Cu and Al₂O₃ nanofluids based on water improved thermal efficiency by 22.7%, 56.3%, and 35.1%, respectively, compared to pure water. Authors of [15] found that Cu + water and Cu + ethylene glycol + water nanofluids in heat pipe collectors could increase energy output by 50% and reduce the required collector area by 34%. In [16], CuO was deemed the most effective among CuO, Al₂O₃, and ZnO nanofluids. Research in [17] showed aqueous MgO nanoparticle suspensions could improve thermal efficiency by 40.5–41.5%, depending on concentration. Silver + water nanofluids showed higher thermal conductivity and stability for at least a year, confirming commercial viability [18]. Carbon nanotube-based nanofluids also showed promise: study [19] demonstrated an 11.86% heat transfer coefficient increase using MWCNT + R141b refrigerant in flat plate collectors, while study [20] confirmed up to 55% energy and 10% exergy efficiency improvements with MWCNT + water in evacuated heat pipes.

To enhance the thermal efficiency of flat plate solar collectors in domestic hot water systems, ref. [21] designed an innovative collector with a corrugated surface and triangular header tubes (CFPSC). They evaluated ethylene glycol (EG) and water-based nanofluids with CuO, Al₂O₃, and TiN nanoparticles. EG-based nanofluids exhibited longer temperature stabilization times (12.4–28.6%) than water-based ones but showed greater temperature variation under radiation—up to 19.2% more than water. Among the tested nanofluids, CuO and Al₂O₃ additives showed the best thermal properties, with negligible differences between them. CuO-EG provided up to 4% higher heat collection efficiency compared to TiN nanofluids at various radiation intensities. Increasing the CuO volumetric concentration in EG improved thermal efficiency, reaching a maximum of 96.6%. For TiN-EG, peak thermal efficiency (93.8%) was observed at 0.075% concentration. Notably, changes in concentration had little impact on thermal stability or efficiency for CuO and Al₂O₃ [21].

Numerous studies have explored nanofluid applications in heat exchangers within solar systems to enhance heat transfer intensification [22]. However, most focus on cooling performance rather than heating, with efficiency differences of a few percent [23]. Therefore, nanofluids are mainly applied as coolants to assess or improve cooling in exchanger systems [24]. Cases analyzing solar installation efficiency with nanofluids at temperatures significantly higher than the working medium on the internal secondary side of PHE (hot water installation) are rare, despite being common in practice [25,26], as noted by Iranmanesh et al. [24]. Nonetheless, solar installations with aqueous graphene nanoplatelet solutions were tested in warm climates. Central Europe’s climate necessitates glycol–water mixtures to prevent freezing.

As reported in [27], synergistic cooperation of nanofluids with PHE is possible and effective; however, there is a lack of sufficient experimental research in this direction, especially when it comes to cooperation with a solar installation. Table 1 presents selected nanofluids available in the literature that cooperate with PHE, along with an analysis of heat exchange efficiency indicators.

The largest percentage increases in the convective heat transfer coefficient (ΔCHT) were observed for propylene glycol-based nanofluids (ZrO₂/PG:W). Under laminar conditions, they reach up to +123%. However, this primarily applies to very low flow rates. In a traditional PHE system with water as the working fluid, the largest increases in ΔCHT were observed for Al₂O₃ (approx. +27%) and graphene-COOH (approx. +28%).

Hybrid nanofluids (Fe₃O₄–SiO₂, Al₂O₃–MWCNT, TiO₂–Al₂O₃) provide a moderate increase in heat transfer efficiency (approx. +12–24% in NTU or ΔCHT), but their key advantage may be improved stability [28] and the ability to dissipate heat over a wider temperature range. Water/EG mixtures dominate solar circuits due to the need to lower the freezing point. Among these media, the hybrid TiO₂:SiO₂/DI:EG fluid performs best, providing +7% U-value and +25–27% NTU improvement compared to the base fluid at realistic flow rates.

Table 1. Heat transfer efficiency of selected nanofluids in the PHE system.

Nanofluid	Concentration	Increased Heat Exchange Efficiency	Source
Al2O3/DI	0.2 vol%	+27% ΔCHT	[29]
Fe3O4–SiO2/DI	1.0 vol%	+13.23% NTU; +24.51% NTU	[30]
Al2O3–MWCNT/DI	0.01 vol%	+15.2% ΔCHT	[31]
TiO2/DI	0.05 wt%	+15.6% ΔCHT	[32]
Graphene-COOH/DI	0.05 wt%	+27.8% ΔCHT	[33]
TiO2–Al2O3/DI	1.0 wt%	+12.3% ΔCHT	[27]
ZrO2/PG:DI (10:90)	0.25–1.0 wt%	up to +123% ΔCHT	[34]
TiO2:SiO2/DI:EG (20:80)	0.5–1.5 vol%	+7% U; +25–27% NTU (lokally to 44%); +3.5% ε; +13–26% ηexergy	[4]
GNP/DI	0.025–0.1 wt%	noticeable increase in PHE thermal efficiency (value not given)	[24]
MWCNTs–SiO2/EG	to 0.86 wt%	+ ~20% h	[27]

Table 1. Heat transfer efficiency of selected nanofluids in the PHE system.

Nanofluid	Concentration	Increased Heat Exchange Efficiency	Source
Al2O3/DI	0.2 vol%	+27% ΔCHT	[29]
Fe3O4–SiO2/DI	1.0 vol%	+13.23% NTU; +24.51% NTU	[30]
Al2O3–MWCNT/DI	0.01 vol%	+15.2% ΔCHT	[31]
TiO2/DI	0.05 wt%	+15.6% ΔCHT	[32]
Graphene-COOH/DI	0.05 wt%	+27.8% ΔCHT	[33]
TiO2–Al2O3/DI	1.0 wt%	+12.3% ΔCHT	[27]
ZrO2/PG:DI (10:90)	0.25–1.0 wt%	up to +123% ΔCHT	[34]
TiO2:SiO2/DI:EG (20:80)	0.5–1.5 vol%	+7% U; +25–27% NTU (lokally to 44%); +3.5% ε; +13–26% ηexergy	[4]
GNP/DI	0.025–0.1 wt%	noticeable increase in PHE thermal efficiency (value not given)	[24]
MWCNTs–SiO2/EG	to 0.86 wt%	+ ~20% h	[27]

The incorporation of nanofluids into solar thermal systems signifies a promising avenue to augment building energy efficiency through the enhancement of heat transfer rates and the reduction of auxiliary energy demand. These advancements may result in substantial decreases in fossil fuel consumption related to water heating and space conditioning, both of which are primary contributors to building energy utilization on a global scale [35]. Recent investigations have conducted comparative analyses of nanofluids with other heat transfer fluids and materials, including phase change materials (PCMs), advanced insulation, and smart glazing technologies, which have elucidated varying levels of performance and economic viability [36,37,38,39]. Although nanofluids present distinct advantages in terms of thermal conductivity and stability, their implementation should be evaluated in conjunction with other advances as part of comprehensive building energy strategies.

This study endeavors to reconcile the improvements in thermal performance of nanofluids with their tangible effects on building energy efficiency and carbon emissions [40]. It offers a comparative framework and pinpoints areas meriting further scholarly investigation.

Based on a thorough literature review, it is concluded that further research and analysis of the use of nanofluids as working fluids, particularly in PHE systems in solar installations, must address the following challenges:

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Cost, stability, and implementation—higher nanoparticle concentrations (above ~0.5%) significantly increase viscosity, which in turn increases pressure losses and pump wear. This is a key trade-off: increased heat transfer vs. rising operating costs.

-

The cost of producing stable suspensions—especially hybrid ones—and ensuring their stable dispersion throughout the continuous solar cycle is a barrier to commercialization.

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Research gaps and recommendations—there is a lack of reliable data on the long-term stability of nanofluids in PHE systems operating throughout the entire heating/cooling season in solar installations. Therefore, research on agglomeration, corrosion, and loss of thermal properties after several months of operation is necessary.

-

Lifecycle Assessment (LCA).

-

Cost–Effectiveness Analysis.

The aim of this article is to evaluate the potential of Al₂O₃-based nanofluids to improve energy efficiency and reduce carbon footprint in solar domestic hot water installations for buildings. This work focuses on analyzing the impact of nanofluid thermophysical properties such as viscosity and thermal conductivity on heat transfer efficiency and exergy performance in plate heat exchangers. Additionally, it aims to develop a correlation model to estimate potential energy savings and CO₂ emission reductions based on nanofluid parameters. This article also discusses limitations of current models and the need for further experimental research and advanced modeling techniques.

What is more, in this paper, it employs a water–ethylene glycol-based nanofluid (40:60 ratio) widely used in HVAC systems for frost protection in the colder climates of Central Europe. This ratio of base fluid components lowers the freezing point to approximately −30 °C, ensuring stable and safe operation of the heating/solar system even during severe frosts down to −20 °C. The addition of nanoparticles (e.g., Al₂O₃ with a diameter of ~50 nm) improves the thermal conductivity of the carrier without compromising the antifreeze properties of the base fluid.

In conclusion, this investigation seeks to explore the following principal research questions:

• Does the application of Al₂O₃-based nanofluids, stabilized by the surfactant Tween 80 (e.g., delivered by Merc), enhance the thermal and exergy efficiency of domestic hot water (DHW) plate heat exchangers compared to traditional base fluids (water–ethylene glycol mixture)?
• In what manner does the integration of Tween 80 affect the viscosity of the nanofluid and subsequently the overall performance of the heat exchanger?

It is further hypothesized that the incorporation of Tween 80 as a surfactant will decrease the viscosity of the nanofluid, thereby augmenting flow characteristics and heat transfer efficiency, which will result in improved thermal and exergy performance of the DHW heat exchanger.

2. Materials and Methods

2.1. Physical Model

The studied system consists of a solar thermal installation connected to a domestic hot water (DHW) system through a plate heat exchanger. On the hot side, a nanofluid circulates—based on a water–ethylene glycol mixture with suspended nanoparticles—while the cold side contains domestic water with an inlet temperature of 20 °C. The nanofluid enters the heat exchanger at a constant temperature of 60 °C. The schematic diagram of the installation is presented in Figure 1.

A real plate heat exchanger with six plates was selected, and its detailed geometric parameters are presented in

Table 2. Technical parameters of the studied PHE.

Parameter	Nomenclature	Value
Plate width between gaskets, m	Lw	0.18
Plate height between ports, m	Lv	0.48
Plate height between gaskets, m	Lp	0.357
Plate width between ports, m	Lh	0.06
Port diameter, mm	Dp	30
Chevron angle, °	β	30
Enhancement factor	ϕ	1.15
Heat transfer area, m2	A	0.3
Effective heat transfer area, m2	Ap = A/Nt	0.05
Corrugation pitch, mm	Pc	14.2
Mean channel spacing, mm	b	2.8
Plate pitch, mm	p	2.8
Plate thickness, mm	t	0.45
Total number of plates	${\mathrm{N}}_{\mathrm{t}}$	6
Pass number	${\mathrm{N}}_{\mathrm{p}}$	3
Thermal conductivity, W/mK	kp	9.5
Hydraulic diameter, mm	Dh = 2b/ϕ	4.87

. A constant volumetric flow rate of 3 L/min was assumed for the solar side, while the DHW side was analyzed across a range of 3 to 12 L/min. The flow was considered steady, incompressible, and single-phase. The flow rates analyzed—3 L/min and 12 L/min—correspond, respectively, to low domestic water demand (e.g., handwashing or low-flow fixtures) and peak domestic demand (e.g., showering or simultaneous use of multiple taps). What is more, the pump in solar circulation is a low-pressure and low-power pump (e.g., Grundfos Alpha2 L, Grundfos Holding A/S, Denmark) with a maximum head of approximately 6 m and power consumption of ~7 W. It provides a steady flow rate of 3 L/min in the solar coil. The piping consists of 15 mm copper tubes. It is insulated with 22 mm polyurethane foam that reduces thermal losses to the environment. The calculated heat losses from insulated coils are ~4 W/m under operating conditions. In order to guarantee a realistic evaluation of performance, these values are taken into account during the thermal and hydraulic calculations.

Six stainless steel plates make up the PHE, each offering a heat transfer area of about 0.05 m², which sums up to a total of 0.3 m² of effective heat transfer surface. These plates incorporate chevron corrugations with a pitch of 2.8 mm and a depth of 14.2 mm, tilted at an angle of 30° to promote turbulence and enhance heat exchange. The hydraulic diameter, Dh, of the flow channels was calculated using a correction factor of ϕ = 1.15 to account for the intricate channel design. Although stainless steel plates exhibit excellent thermal conductivity (k_p = 9.5 W/m·K) and are resistant to corrosion, the possibility of degradation or fouling from interactions with nanofluids remains unconfirmed and deserves additional research [39,41].

2.2. Nanofluids Selection and Thermophysical Data

The Al₂O₃ nanofluid was selected for analysis, based on a water–glycol mixture as the base fluid. Nanofluids based on ethylene glycol (EG) have significantly higher viscosity than those based on water, but they are commonly used in solar installations exposed to low external temperatures. Thermophysical properties (density, thermal conductivity, dynamic viscosity, and specific heat capacity) were taken from the literature and compiled for three mass concentrations, φ: 0.5%, 1.0%, and 2.0%. These values are summarized in

Table 3. Thermophysical properties of chosen solar fluids for 60 °C.

Parameter/Nanofluid	Water 40% + 60% EG	0.5% Al2O3	1% Al2O3	2% Al2O3 *	0.5% Al2O3 + Tween 80	1% Al2O3 + Tween 80	2% Al2O3 + Tween 80 *
Thermal conductivity (W/m·K)	0.34 ± 3%	0.36 ± 5%	0.38 ± 5%	0.40 ± 5%	0.36 ± 5%	0.38 ± 5%	0.40 ± 5%
Viscosity (mPa·s)	3.8 ± 4%	4.0 ± 7%	4.2 ± 7%	4.6 ± 7%	3.5–3.6 ± 7%	3.6–3.8 ± 7%	3.9–4.1 ± 7%
Density (kg/m3)	1075 ± 1%	1080 ± 1%	1085 ± 1%	1090 ± 1%	1080 ± 1%	1085 ± 1%	1090 ± 1%
Specific heat (kJ/kg·K)	3.6 ± 3%	3.5 ± 3%	3.4 ± 3%	3.3 ± 3%	3.5 ± 3%	3.4 ± 3%	3.3 ± 3%
Literature	[43]	[25,26,44]

* estimated values [25,26,44].

with appropriate uncertainty analysis results [42]. Nanofluids are compared with the base fluid, which is a water + EG mixture in the ratio of 40:60%. Additionally, the effect of adding Tween 80 on the thermophysical properties of the nanofluid was examined. A 0.2 wt% concentration of Tween 80 was used, as this concentration effectively stabilizes nanoparticles and reduces viscosity without significantly affecting other thermophysical parameters [24].

Based on these data, it can be concluded that thermal conductivity increases with increasing nanoparticle concentration, but the addition of Tween 80 does not affect this parameter; the viscosity of the nanofluid is significantly higher than that of the base fluid and increases with nanoparticle concentration; the addition of Tween 80 reduces viscosity by approximately 10–15% compared to the nanofluid without surfactant; density and specific heat capacity change only slightly with the addition of nanoparticles and Tween 80.

2.3. Methodology

The simulation was based on established heat transfer and flow equations for plate heat exchangers, considering real geometry and empirical correlations for the Nusselt number:

-

for nanofluids [45]:

$${\mathrm{N}\mathrm{u}}_{\mathrm{h}}={\mathrm{N}\mathrm{u}}_{\mathrm{h}\mathrm{n}\mathrm{f}}=\mathrm{C}{\mathrm{R}\mathrm{e}}^{\mathrm{m}}{\mathrm{P}\mathrm{r}}^{1/3}=0.348{\mathrm{R}\mathrm{e}}^{0.663}{\mathrm{P}\mathrm{r}}^{0.3}$$

(1)

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for the DHW side [46]:

$${\mathrm{N}\mathrm{u}}_{\mathrm{c}}={\mathrm{N}\mathrm{u}}_{\mathrm{D}\mathrm{H}\mathrm{W}}={\mathrm{C}\mathrm{R}\mathrm{e}}^{\mathrm{m}}{\mathrm{P}\mathrm{r}}^{1/3}=0.32673{\mathrm{R}\mathrm{e}}^{0.6125}{\mathrm{P}\mathrm{r}}^{0.3}$$

(2)

The heat exchanger performance was analyzed using the NTU–effectiveness method, allowing for the calculation of real heat transfer [41,47,48]:

$${\dot{\mathrm{Q}}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}}=\mathrm{\epsilon }{\dot{\mathrm{Q}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=\mathrm{\epsilon }{\mathrm{C}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\left({\mathrm{T}}_{\mathrm{h},\mathrm{i}\mathrm{n}}-{\mathrm{T}}_{\mathrm{n}\mathrm{f},\mathrm{i}\mathrm{n}}\right)$$

(3)

where effectiveness ε was determined depending on the number of transfer units (NTU) and the capacity rate ratio ${\mathrm{C}}_{\mathrm{m}\mathrm{i}\mathrm{n}}/{\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, according to classical relationships for multi-pass plate heat exchangers.

The detailed computational algorithm follows the methodology presented in the referenced studies [4,23].

2.4. Numerical and Mathematical Model Assumptions

This paper presents a numerical thermohydraulic simulation model of a solar installation utilizing a nanofluid as the working fluid. The model has been implemented in the Matlab environment R2020a, enabling efficient solution of the system of equations describing heat transfer and fluid flow within the installation. The purpose of the model is to analyze the influence of nanofluids on heat exchange efficiency, thermal conductivity, viscosity, and hydraulic losses in a solar installation equipped with a plate heat exchanger. The model allows for comparison of nanofluids containing Al₂O₃ nanoparticles with a conventional water–glycol mixture and evaluation of the effect of adding the surfactant Tween 80 on thermophysical parameters.

The assumptions of the model are as follows:

▪

The flow is laminar and steady with a constant volumetric flow rate (3 L/min) on the nanofluid side and variable flow rates (3 and 12 L/min) on the domestic water side; for typical DHW flow rates and system configurations examined here, laminar or weakly transitional flows are expected, consistent with previous experimental observations [49]. Nevertheless, future investigations should incorporate turbulence modeling and transient effects to enhance generalizability.

▪

The nanofluid is treated as a homogeneous fluid with effective thermophysical properties dependent on nanoparticle concentration and the presence of surfactant.

▪

The heat exchanger is modeled using an energy balance approach with an effective overall heat transfer coefficient (U), accounting for the thermal conductivity of the nanofluid and viscosity influencing hydraulic resistance.

▪

The inlet temperatures of the nanofluid, cold water, and external conditions are specified as input parameters.

▪

The model is based on energy balance equations describing the temperature changes of the nanofluid and domestic water within the heat exchanger.

▪

The system of ordinary differential equations (ODEs) was solved numerically (e.g., using the ode45 solver with Matlab 2020a), simulating the temperature distribution along the heat exchanger.

▪

Thermophysical properties of the nanofluid are dynamically updated as functions of temperature and concentration.

▪

The input parameter module allows rapid changes of operating conditions and fluid properties for various installation configurations.

As they need to be added, at each integration step of the ODE45 solver that utilizes adaptive time-stepping for maintaining numerical accuracy and stability, the thermophysical properties of the nanofluids are consistently updated. Moreover, this method effectively accounts for changes in properties with temperature, it overlooks the non-uniform distribution of particles that may result from sedimentation and thermophoresis. This limitation is recognized, and upcoming studies aim to investigate multiphase models that account for nanoparticle movement under the gradients of temperature.

▪

The model was validated by comparing results with the literature data and experimental results for conventional water–glycol mixtures.

2.5. Entropy and Exergy Analysis

To evaluate the irreversibility of heat exchange processes, entropy generation was assessed in two components:

• due to flow resistance;
• due to temperature difference during heat transfer (dominant).

In further analysis, the total entropy generation was considered and calculated using [21,45,50], and it is the sum of thermal and frictional entropy:

$${\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n}}={\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n},\mathrm{t}\mathrm{h}}+{\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n},\mathrm{f}},$$

(4)

$${\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n},\mathrm{t}\mathrm{h}}={\displaystyle \frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}\mathrm{v}}}^2}{\mathrm{N}\mathrm{u} \mathrm{R}\mathrm{e} \mathrm{P}\mathrm{r} {\mathrm{T}}_{\mathrm{i}\mathrm{n}} {\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}} {\mathrm{L}}_{\mathrm{v}}}},$$

(5)

$${\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n},\mathrm{f}}={\displaystyle \frac{8\mathrm{f}{{\dot{\mathrm{m}}}^2\mathrm{L}}_{\mathrm{v}}}{{\mathrm{\rho }}^2{\mathrm{\pi }}^2{\mathrm{D}}_{\mathrm{h}}^2\left({\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n},}\right)}}\mathrm{l}\mathrm{n}\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{T}}_{\mathrm{i}\mathrm{n},}}}\right).$$

(6)

Based on this, the exergy efficiency was determined from

$${\mathrm{\eta }}_{\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}=1-{\displaystyle \frac{{{\mathrm{T}}_{\mathrm{a}}\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n}}}{\left(1-\left(\frac{{\mathrm{T}}_{\mathrm{a}}}{{\mathrm{T}}_{\mathrm{w},\mathrm{a}\mathrm{v}}}\right)\right){\dot{\mathrm{Q}}}_{\mathrm{h}}}}$$

(7)

where ${\mathrm{T}}_{\mathrm{a}}$ is the ambient temperature (20 °C), and ${\mathrm{T}}_{\mathrm{w},\mathrm{a}\mathrm{v}}$ is the average temperature of the nanofluid stream.

2.6. Sensivity Analysis Model

A comprehensive sensitivity analysis was performed to examine the primary parameters that affect the thermal and exergy efficiency of the plate heat exchanger. The analysis revealed that viscosity and flow rate were the most influential factors. However, geometric attributes such as corrugation angle and plate spacing, along with environmental variables such as ambient temperature, were recognized as crucial aspects for future research. This chapter discusses these elements and also acknowledges the limitations of the present study. The sensitivity coefficient for individual variables was determined based on the dependence:

$${\mathrm{S}}_i={\displaystyle \frac{{\Delta \mathrm{O}}_{\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}}/{\mathrm{O}}_{\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\_\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}{{\Delta \mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}}_{vary}/{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}$$

(8)

where ${\Delta \mathrm{O}}_{\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}}/{\mathrm{O}}_{\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\_\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$—values of exergy or efficiency taken from calculated models for base and variation parameters, ${\Delta \mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}}_{vary}/{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$—values taken from

Table 4. Proposed range of parameter variation for sensitivity analysis.

Parameter	Baseline Value	Variation Range (%)
Thermal conductivity (W/m·K)	0.34–0.4 (see Table 2)	±10
Viscosity (mPa·s)	3.6–4.6 (see Table 2)	±10
Distance between plates (mm)	2.8	2.5–3.5
Corrugation angle (°)	30	20–40
Nanofluid flow (L/min)	3	2–4
Ambient temperature (°C)	20	0–40

.

2.7. Environmental Analysis of a Solar Installation with Nanofluids

The assumptions for the environmental analysis of the solar installation with nanofluids, aimed at minimizing the carbon footprint, are as follows:

• The installation heats domestic hot water—the energy is supplied by the sun or a renewable source;
• Improving the heat exchanger efficiency means less supplementary energy is needed, thus lower expected CO₂ emissions;
• Knowing the difference in efficiency, it is possible to estimate the reduction in fuel/energy consumption and the corresponding CO₂ emissions;
• The annual heat demand for domestic hot water heating: ${\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}=3000\hspace{0.17em}\mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{r}\mathrm{o}\mathrm{k}$;
• Heat exchanger efficiency for the base fluid (Water + 60% EG): ${\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}=0.87$;
• Heat exchanger efficiency for the nanofluid based on Al₂O₃: ${\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}=0.85$;
• Supplementary energy source: natural gas with an emission factor of $\mathrm{E}\mathrm{F}=0.2\hspace{0.17em}\mathrm{k}\mathrm{g}\mathrm{C}{\mathrm{O}}_2/\mathrm{k}\mathrm{W}\mathrm{h}.$

The supplementary energy needed to heat the water depends on the heat exchanger efficiency [21,45,47]:

$${\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}}{\mathrm{\epsilon }}}.$$

(9)

where ${\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}}$ is the auxiliary energy demand, ${\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}$ is the heat required for heating domestic hot water (DHW), and $\mathrm{\epsilon }$ is the heat exchanger effectiveness.

Difference in energy consumption and CO₂ emissions requires calculation of the additional supplementary energy required when using the nanofluid:

$$\Delta \mathrm{E}={\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}-{\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}.$$

(10)

The reduction (or increase) in CO₂ emissions is obtained as follows:

$$\Delta \mathrm{C}{\mathrm{O}}_2=\Delta \mathrm{E}\times \mathrm{E}\mathrm{F}.$$

(11)

The impact of nanofluid efficiency on CO₂ emission reduction in the installation, expressed as a percentage reduction in emissions, is described by the following formula:

$${\mathrm{CO}}_2 \mathrm{Reduction} \left(\mathrm{\%}\right)=\left(1-{\displaystyle \frac{{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}{{\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}}\right)·100$$

(12)

Equation (12), which is leveraged to compute the reduction percentage of CO₂ emissions, is an approximation obtained from the basic principles of energy balance, specifically for solar water heating systems [21,47]. It stems from the fundamental connection between the supplementary energy requirement, ${\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}}$, and the efficiency of the heat exchanger, ε (see Equation (9)).

Based on the above analysis, the following formula is proposed to calculate the reduction of CO₂ emissions [%]:

$$\mathrm{Reduction}\left(\mathrm{\%}\right)={\displaystyle \frac{\Delta \mathrm{C}{\mathrm{O}}_2}{{\mathrm{E}}_{\mathrm{C}\mathrm{O}2,\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}\times 100={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\times \mathrm{E}\mathrm{F}\times \left(\frac{1}{{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}-\frac{1}{{\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}\right)}{{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\times \mathrm{E}\mathrm{F}\times \frac{1}{{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}}\times 100=\left(1-{\displaystyle \frac{{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}{{\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}}\right)\times 100$$

(13)

where the numerator ${\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\times \mathrm{E}\mathrm{F}\times \left({\displaystyle \frac{1}{{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}-{\displaystyle \frac{1}{{\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}}\right)$ is the difference in emissions between the base fluid and nanofluid; dividing this by the base case emissions in the denominator leads to the final formula expressing relative emission reduction. It is also assumed that the CO₂ emissions are proportional to the auxiliary energy via a fixed emission factor, EF.

Formula (13) is a simplification of classical energy balance and emission estimation methods commonly known in thermal system analyses [21,47]. This is not an entirely original theoretical framework; rather, it refines and condenses these principles into a succinct format specifically designed for the examination of nanofluid-enhanced solar installations. The inherent simplicity enables an objective comparison of emission reductions by focusing exclusively on the relative efficiencies of exchangers, while omitting the complexities associated with system dynamics, such as transient effects or detailed emission modeling.

3. Results and Discussion

Due to differences in viscosity among the various nanofluids, despite the assumed constant flow rate in the solar installation, the Reynolds number will vary slightly between concentrations. The functional relationships Nu(Re) are shown in Figure 2.

The Reynolds number strongly depends on the viscosity of all analyzed nanofluids, as evidenced by the high Pearson correlation coefficient above 0.99 for each nanoparticle concentration, as shown in Figure 2b.

3.1. Influence of DHW Flow Rate on Thermal and Exergy Performance

This section analyzes the effect of domestic hot water (DHW) flow rate on the thermal and exergy performance of a plate heat exchanger (PHE) using three working fluids: base fluid (water + 60% EG), Al₂O₃ nanofluid, and Al₂O₃ nanofluid with Tween 80 additive. The simulations were conducted for two distinct volumetric flow rates on the domestic hot water (DHW) side: 3 L/min and 12 L/min, representing two realistic user scenarios in residential installations:

• Low flow (3 L/min): typical of low-consumption activities such as hand washing or water-saving fixtures.
• High flow (12 L/min): representative of peak demand scenarios like showering or operating multiple taps simultaneously.

Table 5. Energy efficiency of the analyzed solar installation based on nanofluid without stabilizer.

Concentration [%]	DHW Flow [L/min]	Re	Nu	h [W/m2K]	U [W/m2K]	NTU	Efficiency, ε	TDHWout [°C]	Ns	Exergy
0	3	91.3	45.1	4714	411	2.06	0.87	44.3	0.0036	0.74
0	12	91.3	45.1	4714	337	0.51	0.57	34.8	0.0007	0.61
0.5	3	88.5	41.5	4168	384	1.91	0.85	42.9	0.0038	0.72
0.5	12	88.5	41.5	4168	315	0.48	0.55	34.0	0.0007	0.59
1.0	3	85.9	39.3	4003	360	1.80	0.84	41.8	0.0040	0.71
1.0	12	85.9	39.3	4003	296	0.46	0.54	33.5	0.0007	0.58
2.0	3	82.3	36.7	3681	327	1.64	0.82	40.3	0.0043	0.69
2.0	12	82.3	36.7	3681	272	0.43	0.52	32.5	0.0008	0.56

and

Table 6. Energy efficiency of the analyzed solar installation based on nanofluid with stabilizer.

Concentration [%]	DHW Flow [L/min]	Re	Nu	h [W/m2K]	U [W/m2K]	NTU	Efficiency, ε	TDHWout [°C]	Ns	Exergy
0.5	3	87.7	41.8	4175	384	1.92	0.85	42.8	0.0038	0.72
0.5	12	87.7	41.8	4175	315	0.48	0.55	33.9	0.0007	0.59
1.0	3	84.8	39.7	4215	360	1.80	0.84	41.7	0.0040	0.71
1.0	12	84.8	39.7	4215	296	0.46	0.54	33.4	0.0007	0.58
2.0	3	78.5	38.0	4120	327	1.64	0.82	40.2	0.0043	0.69
2.0	12	78.5	38.0	4120	272	0.43	0.52	32.5	0.0008	0.56

summarize and compare the energy efficiency results for these two flow rates in the DHW installation.

The incorporation of Tween 80 at a concentration of 0.2 wt% led to a moderate decrease in viscosity and an insignificant enhancement in thermal and exergy efficiencies. This limited efficacy may be attributed to the concentration employed and the inherent characteristics of Tween 80. Alternative surfactants or increased concentrations could potentially augment dispersion stability and more effectively decrease viscosity, thereby enhancing heat transfer performance. Subsequent research should investigate a broader spectrum of surfactants and dosages to ascertain optimal formulations that maximize the advantages of nanofluids while minimizing unfavorable effects such as increased viscosity or foaming.

At a low DHW flow rate of 3 L/min, the heat exchanger achieves high thermal effectiveness for all fluids. The base fluid exhibits the highest thermal effectiveness (~0.87), followed closely by Al₂O₃ nanofluid both without (~0.85) and with Tween 80 (~0.85). The lower flow rate results in a smaller heat capacity rate of the DHW stream, which increases the number of transfer units (NTU), enhancing heat transfer efficiency and allowing DHW outlet temperatures around 43–44 °C. The dependence of the convective and global heat transfer coefficients on the flow is given in Figure 3.

Increasing the DHW flow rate to 12 L/min leads to a noticeable reduction in thermal effectiveness for all fluids. The effectiveness drops to approximately 0.57 for the base fluid and about 0.55 for both nanofluids. This decline is due to the higher mass flow rate of the DHW, increasing its heat capacity rate and thus lowering the NTU and heat exchanger effectiveness. Correspondingly, DHW outlet temperatures decrease to the range of 33–35 °C.

Exergy efficiency follows the trend of thermal effectiveness but shows a less severe decline with increasing flow rate. At 3 L/min, the base fluid achieves the highest exergy efficiency (~0.74), while both nanofluids reach about 0.72. At 12 L/min, efficiencies decrease to ~0.61 for the base fluid and ~0.59 for the nanofluids. The slight advantage of the base fluid is associated with its lower viscosity, resulting in higher Reynolds numbers and more favorable convective heat transfer.

The inclusion of Tween 80 in the Al₂O₃ nanofluid slightly reduces the fluid’s viscosity compared to the nanofluid without Tween, marginally improving Reynolds numbers and convective heat transfer coefficients. However, the impact on overall thermal and exergy performance remains limited under the tested conditions, with both nanofluids performing similarly.

In conclusion, the DHW flow rate significantly impacts the thermal and exergy performance of the heat exchanger, with higher flow rates reducing both efficiencies due to increased heat capacity rates of the DHW stream. The base fluid consistently outperforms the Al₂O₃ nanofluids with and without Tween 80, primarily due to lower viscosity and higher Reynolds numbers. Although Tween 80 helps reduce viscosity, its effect on performance is modest. Optimization of nanofluid properties and operating conditions is required to harness their potential benefits in solar thermal systems.

3.2. Effect on Heat Transfer and Efficiency

The heat transfer performance and overall efficiency of the plate heat exchanger (PHE) were evaluated for the base fluid (water + 60% EG) and Al₂O₃ nanofluids (both with and without Tween 80 additive) under varying domestic hot water (DHW) flow rates.

The base fluid exhibited the highest Reynolds numbers due to its relatively low viscosity, resulting in enhanced convective heat transfer coefficients (h) compared to Al₂O₃ nanofluids. Nanofluids, especially those without Tween, showed slightly reduced Reynolds numbers due to higher viscosities, which led to moderately lower h values. The addition of Tween 80 decreased the viscosity of the nanofluids slightly, improving the Reynolds number and hence the convective heat transfer coefficient, though the improvement was marginal.

Thermal effectiveness (ε) closely followed the trend of heat transfer coefficients. The base fluid demonstrated the highest effectiveness, reaching values up to 0.87 at lower DHW flow rates. Al₂O₃ nanofluids showed slightly lower effectiveness, with marginal improvement when Tween 80 was added (see Figure 4). However, the differences in effectiveness across all fluids remained within a narrow range, indicating that the nanofluids did not drastically outperform the base fluid under the studied conditions.

Optimization of nanofluid properties and operating conditions is required. Despite the higher thermal conductivity of nanofluids, their increased viscosity resulted in decreased flow turbulence and, consequently, reduced heat transfer coefficients. This viscosity effect dampened the potential gains from improved thermal conductivity. The inclusion of Tween 80 partially mitigated this issue by reducing viscosity, slightly enhancing heat transfer performance without significantly affecting thermal effectiveness.

The exergy efficiency mirrored the behavior of thermal effectiveness, with the base fluid maintaining a slight advantage. While nanofluids offer improved thermal conductivity, the associated pressure drops and increased entropy generation (reflected in Ns) can reduce the net efficiency of the system. Tween 80 impact on lowering viscosity contributed to a modest efficiency increase, suggesting potential for optimizing nanofluid formulations to maximize practical benefits.

In conclusion, this study confirms that the choice of working fluid critically affects heat transfer and efficiency in solar thermal systems. The base fluid (water + 60% EG) currently offers superior performance primarily due to its lower viscosity and higher Reynolds numbers, which promote more effective convective heat transfer. Nanofluids with Al₂O₃, while promising due to enhanced thermal conductivity, require viscosity management—such as via additives like Tween 80—to approach or surpass base fluid performance. Further research into nanofluid rheology and system design optimization is necessary to fully leverage the advantages of nanofluids in thermal applications.

3.3. Entropy Generation and Exergy Efficiency

This study compares the impact of domestic hot water (DHW) flow rate and working fluid type on the exergy efficiency and entropy generation within the heat exchanger.

Exergy efficiency reflects how effectively the system converts available energy into useful work, beyond mere heat transfer. It is noticed that the base fluid (water + 60% EG) exhibited the highest exergy efficiency, approximately 74% at low flow (3 L/min), dropping to about 61% at high flow (12 L/min). The Al₂O₃ nanofluids, both with and without Tween 80, showed slightly lower exergy efficiencies—around 69–72% at low flow and 56–59% at high flow. The decrease in exergy efficiency with increasing flow rate is related to the reduced temperature difference, which limits the quality of the energy utilized.

Entropy generation, N_s, quantifies the irreversibility of thermodynamic processes in the system—higher values indicate greater energy losses and reduced efficiency. For both fluid types, increasing DHW flow resulted in decreased entropy generation due to shorter contact time and smaller temperature differences between fluids (see Figure 5). Nanofluids exhibited somewhat higher entropy generation than the base fluid, primarily due to their higher viscosity and consequently lower Reynolds numbers. The addition of Tween 80 slightly reduced entropy generation in the nanofluid, suggesting lower irreversibility, likely due to improved flow conditions.

To summarize, the base fluid consistently demonstrates higher exergy efficiency and lower entropy generation, leading to more efficient and less loss-prone heat exchange under typical operating conditions. The Al₂O₃ nanofluids, with and without Tween 80, show similar performance, with potential for improved utilization through further optimization of viscosity and flow parameters. Increasing DHW flow rate lowers exergy efficiency and alters entropy generation characteristics, an important consideration for system design.

An increase in the DHW flow from 3 to 12 L/min causes a decrease in both the efficiency and exergy effectiveness, which is a natural effect of the increased heat flux and the shortened exchange time.

3.4. Comparative Interpretation of Heat Transfer and Exergy Performance

The numerical results obtained in this study for Al₂O₃-based nanofluids, both with and without Tween 80 additive, were compared against recent findings reported by [31,32,33,34] to validate the model and assess the practical relevance of the findings.

At a domestic hot water (DHW) flow rate of 3 L/min, the Reynolds numbers calculated in this work ranged between 78 and 88, which is slightly lower than the Reynolds number range of approximately 100 to 300 reported by [51]. This variation can be attributed to differences in exchanger geometry, fluid formulations, and operating conditions.

The convective heat transfer coefficients (h) for Al₂O₃ nanofluids in this study were between 4100 and 4200 W/m²K, aligning well with the 4000–7000 W/m²K range documented by [10,51,52]. The base fluid (Water + 60% EG) demonstrated a higher h (~4700 W/m²K), consistent with its lower viscosity and consequently higher flow turbulence.

Global heat transfer coefficients U calculated here varied from 315 to 411 W/m²K, comparable to the 350–600 W/m²K range in the literature. Differences likely stem from smaller heat exchanger surface area and material properties affecting thermal resistance.

Thermal effectiveness ε for nanofluids spanned 0.82 to 0.85 at low flow and decreased to 0.52–0.55 at high flow, consistent with reported values between 0.75 and 0.95 [10,51]. The base fluid consistently showed superior effectiveness (~0.87 at 3 L/min).

Exergy efficiency (η_ex) ranged from 0.69 to 0.72 at low flow and 0.56 to 0.59 at high flow for nanofluids, which corresponds well to the 0.6–0.8 range reported by [51,53]. The base fluid exhibited slightly higher values (~0.74 and ~0.61, respectively), reflecting better flow characteristics.

While [10,51,52,53,54] do not explicitly report entropy generation numbers, their discussion indicates that entropy generation increases with Reynolds number due to viscous effects, a trend confirmed by our results where nanofluids exhibit slightly higher entropy generation than the base fluid.

In summary, the present numerical findings are consistent with the established literature, validating the applied methodology and supporting the feasibility of Al₂O₃ nanofluids in solar thermal applications. The minor performance differences emphasize the need for optimization of nanofluid rheology and heat exchanger design.

3.5. Sensitivity Anlysis Result

In accordance with the assumptions of the sensitivity analysis given in Section 2.5, the results of the sensitivity indices (relative change in effect per unit relative change in parameter) are presented in

Table 7. Sensitivity indicators—relative change in exergy and energy efficiency per unit relative change in the chosen parameter.

Parameter	Efficiency Sensitivity	Exergy Sensitivity
Thermal conductivity (W/m·K)	+1.80	+1.35
Viscosity (mPa·s)	−3.15	−2.70
Distance between plates (mm)	−0.12	−0.10
Corrugation angle (°)	+0.10	+0.08
Nanofluid flow (L/min)	+0.08	+0.06
Ambient temperature (°C)	−0.05	−0.04

and Figure 6a–f.

Sensitivity analysis performed for six key parameters revealed a clear dominance of nanofluid viscosity, μ, in shaping both heat transfer efficiency, ε, and exergy efficiency. A 10% increase in viscosity resulted in a decrease in efficiency of approximately 3.1% and in exergy efficiency of 2.7%. This means that viscosity accounts for approximately 50–60% of the total variability of the results compared to the other parameters studied.

The second most important parameter is thermal conductivity, k, showing a 10% increase, which results in an improvement in heat transfer efficiency by approximately 1.8% and exergy efficiency by 1.35%. This accounts for approximately 25–30% of the changes in the studied results. Increasing the thermal conductivity of the nanofluid is therefore a significant factor in improving the system’s efficiency.

Geometric parameters such as the corrugation angle, β, and the plate spacing, b, have a moderate but noticeable effect on the results. The corrugation angle positively affects efficiency and exergy, but its effect is relatively small—a change in the 20–40° range translates to about a 0.1% change in efficiency, which is less than 5% of the total variability. The plate spacing has a negative effect on the system parameters, with a 10% increase in spacing resulting in about a 0.1–0.12% decrease in efficiency, which is also less significant compared to viscosity and thermal conductivity.

Ambient temperature, T_a, and nanofluid flow,$\dot{V,}$ have the least impact on the analyzed parameters. Changing ambient temperature within the 0–40 °C range causes only a minimal decrease in efficiency (approximately 0.05%), which is less than 3% of the viscosity effect. Nanofluid flow within the 2–4 L/min range improves efficiency and exergy by approximately 0.06–0.08%, which is also a very limited effect.

3.6. Results of an Environmental Analysis of a Solar Installation with Nanofluids

The supplementary energy needed to heat the water calculated from Formula (9):

-

for the base fluid: ${\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}={\displaystyle \frac{3000}{0.87}}\approx 3448\hspace{0.17em}\mathrm{kWh}$;

-

for the nanofluid: ${\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}={\displaystyle \frac{3000}{0.85}}\approx 3529\hspace{0.17em}\mathrm{k}\mathrm{W}\mathrm{h}$.

The additional supplementary energy required when using the nanofluid is obtained from Formula (10):

$$\Delta \mathrm{E}={\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}-{\mathrm{E}}_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p},\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}=-81\hspace{0.17em}\mathrm{kWh},$$

which means an increased energy consumption of 81 kWh/year compared to the base fluid.

The reduction/increase in CO₂ emissions is calculated from Formula (11):

$$\Delta \mathrm{C}{\mathrm{O}}_2=\Delta \mathrm{E}\times \mathrm{E}\mathrm{F}=-81\times 0.2=-16.2\hspace{0.17em}\mathrm{kg} {\mathrm{CO}}_2.$$

The negative value indicates an increase in emissions of approximately 16 kg CO₂ annually.

The condition for carbon footprint improvement by the nanofluid assumes a higher system efficiency than that of the base fluid, which would bring ecological benefits, i.e., ${\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}>{\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}=0.87$.

The impact of nanofluid efficiency on CO₂ emission reduction in the installation, expressed as a percentage reduction in emissions, is obtained from Formula (12):

-

at ${\epsilon }_{nano}=0.90$ the CO₂ reduction is approximately 3.3%;

-

at ${\epsilon }_{nano}=0.92$ the CO₂ reduction is approximately 5.5%;

-

at ${\epsilon }_{nano}=0.95$ the CO₂ reduction is approximately 8.4%.

Concluding the environmental analysis, the current nanofluid with an efficiency of 0.85 does not provide ecological benefits but rather increases the carbon footprint of the installation. For the nanofluid to be beneficial, its heat exchange efficiency must exceed a minimum of 0.87 (the efficiency of the base fluid). With a slight increase in efficiency to about 0.92, an approximately 5% reduction in CO₂ emissions can be achieved, which is a significant ecological benefit.

Using Formula (13), Figure 7 was prepared, enabling a practical assessment of CO₂ emission reduction depending on the efficiency of a nanofluid-based installation used as the working fluid—in this case, for domestic hot water (DHW) preparation.

The red vertical line in Figure 6 represents the efficiency of the base fluid (0.87). The area above this line corresponds to the gain in CO₂ emission reduction when the nanofluid has a higher efficiency. For nanofluid efficiencies above 0.87, a positive emission reduction occurs. At ${\mathrm{\epsilon }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}={\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}=0.87$, the CO₂ emission reduction is 0%, meaning no benefit. Nanofluid efficiencies above 0.87 yield positive emission reductions; for example, ${ \epsilon }_{nano}=0.90$ corresponds to about a 3.3% CO₂ reduction, ${ \epsilon }_{nano}=0.92$ to 5.5%, and ${ \epsilon }_{nano}=0.95$ to roughly 8.4%.

Comparing the obtained results with the literature data [10,51,52,53,54], it can be concluded that a nanofluid with 0.90 efficiency saves about 115 kWh of energy annually compared to the base fluid, which confirms the present analysis. However, the literature data indicate potential for ecological improvement at higher heat exchange efficiencies, translating to a CO₂ emission reduction of approximately 23 kg per year.

Using comparative data from [10,51,52,53,54] and assuming the nanofluid heat exchanger efficiency averages around ${\epsilon }_{nano}=0.90$ (values reported between 0.85 and 0.95 in the literature), and the base fluid efficiency ${\mathrm{\epsilon }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}=0.87$, the CO₂ emission reduction will be $\Delta \mathrm{C}{\mathrm{O}}_2=23\hspace{0.17em}\mathrm{kg} {\mathrm{CO}}_2/$ year.

Therefore, the installation analyzed in this work with nanofluid efficiency of 0.85 produces a slightly higher carbon footprint than the installation with the base fluid. For nanofluids from the literature [51] achieving about 0.90 efficiency, a real reduction in CO₂ emissions of approximately 6–7% compared to the base system is possible. This highlights that improving nanofluid heat exchange efficiency—through viscosity optimization, concentration adjustment, or heat exchanger geometry—is crucial.

Below, a general correlation formula is presented which, based on the thermophysical properties and efficiencies of both the base fluid and nanofluid, allows estimation of the percentage reduction in the carbon footprint of the installation. The correlation includes viscosity and thermal conductivity due to their impact on flow and turbulence.

$${\mathrm{CO}}_{2 \mathrm{Reduction} }\left(\%\right)\approx \left(1-{\displaystyle \frac{{\epsilon }_{base}}{{\epsilon }_{nano}}}\right)\times 100\times \left(1-\alpha {\displaystyle \frac{{\mu }_{nano}}{{\mu }_{base}}}+\beta {\displaystyle \frac{k_{nano}}{k_{base}}}\right)$$

(14)

where ${\mathrm{\mu }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}, {\mathrm{k}}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}$ are the viscosity and thermal conductivity of the nanofluid, respectively, and ${\mathrm{\mu }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}, {\mathrm{k}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$ are the viscosity and thermal conductivity of the base fluid. The coefficients $\mathrm{\alpha }, \mathrm{\beta }$ are fitted parameters, for example, $\mathrm{\alpha }\approx 0.5, \mathrm{\beta }\approx 0.3$. The factor $\left(1-{\displaystyle \frac{{\mathrm{ϵ}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}{{\mathrm{ϵ}}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}}\right)$ directly accounts for the difference in efficiency (the main source of energy savings), while $\left(1-\mathrm{\alpha }{\displaystyle \frac{{\mathrm{\mu }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}+\mathrm{\beta }{\displaystyle \frac{{\mathrm{k}}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{k}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}\right)$ considers the impact of changes in viscosity and thermal conductivity on the heat transfer effectiveness and hydraulic resistance.

If the nanofluid has significantly higher viscosity than the base fluid (${\mathrm{\mu }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}/{\mathrm{\mu }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}>1$), the CO₂ reduction will be diminished (a negative effect). However, if the nanofluid’s thermal conductivity is substantially higher than that of the base fluid, the CO₂ reduction effect will be enhanced. The most significant factor, however, is the difference in efficiencies.

Next, using data from the present optimization and the literature [10,51,52,53,54], the quadratic regression model was used to fit the coefficients $\mathrm{\alpha }, \mathrm{\beta }$ as follows:

$$y=\left(1-{\displaystyle \frac{{\epsilon }_{base}}{{\epsilon }_{nano}}}\right)\times 100\times \left(1-\alpha x_1+\beta { x}_2\right).$$

(15)

where $x_1={\displaystyle \frac{{\mathrm{\mu }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}$, and ${ x}_2={\displaystyle \frac{{\mathrm{k}}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{k}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}$.

After fitting the viscosity and conductivity data, we obtained the following:

$$y={\mathrm{CO}}_{2 \mathrm{Reduction} }\left(\%\right)\approx \left(1-{\displaystyle \frac{{\epsilon }_{base}}{{\epsilon }_{nano}}}\right)\times 100\times \left(1-\mathrm{\alpha }(\mathrm{\mu },\mathrm{k}){\displaystyle \frac{{\mathrm{\mu }}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}+\mathrm{\beta }(\mathrm{\mu },\mathrm{k}){\displaystyle \frac{{\mathrm{k}}_{\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}}}{{\mathrm{k}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}\right).$$

(16)

The total effect can be written as follows:

$${\mathrm{CO}}_{2 \mathrm{Reduction} }\left(\%\right)\approx \left(1-{\displaystyle \frac{{\epsilon }_{base}}{{\epsilon }_{nano}}}\right)\times 100\times \left(1-E(\mu , k)\right),$$

(17)

where $E\left(x_1,x_2\right)=a_0+a_1{x}_1+a_2{x}_2+{a_3{x}_1}^2+{a_4{x}_2}^2+a_5{x}_1{x}_2;a_0=1376.92,a_1=-17.19,a_2=-2553.65,a_3=-1195.25,a_4=2575.33,a_5=-180.62.$

In order to validate the adopted model, the coefficient of determination was determined, which is close to one and equal to R² = 0.99. Figure 8 shows the predicted vs. actual values, where the scattered points are close to the red line, which means that the model correctly predicts the actual values of CO₂ emission reduction.

In turn, the residuals shown in Figure 9 are randomly scattered around zero with no visible patterns, which indicates that the model has no systematic errors and the regression assumptions are met.

The presented model is justified by existing data from the literature that suggest a preliminary statement of its accuracy. Nevertheless, the validation method has some limitations due to the variability in experimental conditions and measurement uncertainties across diverse sources. The lack of recently acquired experimental data tailored specifically to this research constrains the extensive quantification of model uncertainties, particularly concerning exergy and carbon footprint predictions. Future inquiry will aim to execute dedicated tests to deliver a high-quality validation data set. Moreover, juxtaposing the model’s outputs with a more vast array of literature values, encompassing variability and confidence intervals, serves to contextualize the model’s predictive capacity and its obligation.

4. Conclusions

Although the nanofluids based on Al₂O₃ lightly reduced thermal efficiency and, under baseline cases, boosted annual CO₂ emissions, the results emphasize a pathway for improvement. Properly tuning the composition of nanofluid, usage of the surfactants, and system optimization (e.g., maximizing ε > 0.90) may unlock their potential to enhance energy and environmental performance. Therefore, nanofluids should be seen as a promising but conditional solution, whose effectiveness depends strongly on precise application design.

The addition of Tween 80 surfactant (0.2 wt%) proved to be crucial for improving the flow regime: a reduction in viscosity by about 10–15% resulted in an increase in the Reynolds number and heat transfer coefficient, although the effect on the efficiency ε and exergy η_ex remained marginal. This confirms that subtle changes in composition can have a significant impact on the flow character, even if they do not dramatize the final energy parameters. Additionally, some nanofluids achieving thermal efficiency ε > 0.90, which translates into even more significant ecological (lower carbon footprint) and economic (lower operating costs) benefits, as well as higher efficiency of solar systems compared to the results presented in this paper.

The intensity of the DHW flow plays an important role: a higher intensity (12 L/min) reduces the NTU value, which results in a decrease in both ε and η_ex, while a lower intensity (3 L/min) emphasizes the advantage of the nanofluid over the base fluid in low-flow conditions. This is why it is recommended to adapt the solar–DHW installation designs to the specifics of operation in order to use the optimal range of intensities.

The numerical model based on the energy balance equations and dynamic update of the thermophysical properties of nanofluids, solved with the ode45 solver, showed high agreement with the literature data. This confirms that the approach based on NTU–ε with the consideration of the variability of properties is an effective tool for predicting the behavior of solar systems with nanofluids.

Environmental analysis revealed that at ε < 0.87 nanofluids can increase annual CO₂ emissions by up to ≈16 kg, while achieving ε ≈ 0.92 allows for emission reduction by about 5%. This conclusion shows that the increase in thermal conductivity alone does not guarantee eco-engineering benefits—it is crucial to achieve an appropriate compromise between efficiency and minimizing the carbon footprint.

To fully exploit the potential of nanofluids, future research should focus on optimization of nanoparticle concentration and type of surfactants (different types and concentrations to obtain higher ε with minimal exergy losses), experiments with other exchanger geometries (e.g., channels with variable cross-section, microgrooves), analysis of transitional and turbulent flows to verify the behavior of nanofluids outside the laminar–steady state regime.

In light of the obtained results, it is also recommended to conduct long-term operational tests, taking into account the stability of nanoparticle suspensions and their effect on corrosion and deposition of pollutants, which will allow us to assess the real costs of maintaining the installation.

In summary, Al₂O₃ nanofluids with Tween 80 have the potential to support efficient and ecological solar systems, but their practical application requires a holistic computational, experimental, and environmental approach to maximize energy benefits while limiting negative thermodynamic effects and emissions.