Discussion of Polyethylene Glycol Mixtures and PEG + MWCNT Nanocolloids’ Behavior in Thermal Applications

Abstract

Nanocolloids are nanoparticles suspended in fluids with the aim of improving fluid capability at heat transfer, with a focus on thermal conductivity. The major advantage is the increase in thermal conductivity, with a certain influence on isobaric heat capacity and viscosity. Nevertheless, PEGs are able to create steady suspensions due to their chemical composition and are used in a number of applications. This paper discusses both the advantages and the drawbacks of a suspension of PEG 400 and MWCNT nanoparticles in terms of its relevance for heat transfer applications. Our investigation is built on a complex experimental procedure, as well as an analysis of the state of the art and a discussion of the experimental results in the context of the Prandtl number and thermal diffusivity. This analysis also includes different performance evaluation criteria that are extensively employed both in the heat transfer literature and in practice. The addition of MWCNTs to polyethylene glycol decreases the thermal transport, being influenced by both temperature and the addition of NPs. The results for MWCNT nanocolloids indicate an intensification of the pumping power of up to 29.7%. Also, an interesting option is the use of PEG mixtures as base fluids in order to combine their properties.

1. Introduction

Polyethylene glycol (PEG) can be employed for heat transfer owing to its good thermophysical properties; for example, it has increased latent heat capacity at melting, a property that can be attuned by changing the chemical molar mass, as was deployed by Minea [1]. On the other hand, PEG has been extensively considered for its well-established chemical and thermal stability, non-corrosive properties, lack of toxicity, and low price [1]. However, PEG’s main disadvantage is its reduced thermal conductivity (less than 0.4 W/mK); thus, an improvement in thermal conductivity can be achieved via the addition of materials with upsurged conductivity, such as nanoparticles (NPs). Considering this as a starting point, nanocolloids were developed to overcome the main drawback of polyethylene glycols in heat transfer applications. Another interesting aspect refers to the capacity of PEG to create stable suspensions due to its chemical composition. This aspect has been proven in the literature, where low quantities of PEG have been employed as surfactants in different processes (see Minea [1] for more details).

Moreover, to advance the convective heat transfer properties of the PEG-based fluid, a wide variety of nanoparticles can be added to the suspension, such as different Al, Mg, and Fe oxides, as well as carbon-based materials (e.g., MWCNTs, diamond, or graphene). But with all these benefits, no comprehensive research is available on the state of the art, even though several reviews of PEG-based nanofluids are available (see, for example, [2,3,4,5,6,7,8,9,10,11,12,13,14]). In general, heat transfer fluids with PEGs as the base liquid are obtained by adding NPs to a low-mass PEG. Nevertheless, the melting point of the PEG must also be taken into account, and a detailed analysis of these aspects is carried out by Minea [1] based on outcomes reported by a number of authors [2,3,4,5,6,7,8,9,10,11,12,13,14].

Previous studies revealed that the addition of NPs increases thermal conductivity with a reasonable increase in viscosity, a fact that is beneficial in heat transfer applications. A number of studies revealed an augmentation of thermal conductivity when nanoparticles were added to the base fluids. In terms of thermal conductivity variation with temperature, most of the researchers found a decrease (see, for example, [5,6]), while some found that temperature has no major influence on experimental values (see [8,9]).

Chereches et al. [3] considered the thermophysical properties of PEG 400 with the addition of alumina nanoparticles and found an increase in thermal conductivity, combined with an upsurge in viscosity. A similar trend was also noticed by Chereches et al. [7] for PEG + ZnO nanocolloids.

Recent studies by Marcos and Cabalero’s research group (see [6,8,10,15]) have investigated the properties of polyethylene glycol (PEG) fluids enhanced with various nanoparticles, including multi-walled carbon nanotubes (MWCNTs), graphene, and silver nanoparticles (NPs). The main focus of their research was to evaluate the changes in the fluids’ viscosity, thermal conductivity, and isobaric heat capacity, ultimately assessing their potential for heat transfer and storage.

Marcos et al. [8] found that adding functionalized graphene nanoplatelets to PEG 400 increased both its viscosity and thermal conductivity, along with a minor increase in the Stefan number.

In other experiments, Marcos et al. [6,8] observed that adding MWCNTs (up to 1% by weight) to PEG 400 significantly improved its thermal conductivity (by up to 12.7%) and diffusivity (by 13.5%). However, this came at the cost of a considerable increase in dynamic viscosity (by 29.6%).

Marcos et al. [10] also studied PEG 400 with silver nanoparticles in three different concentrations. They noted that the fluid maintained a Newtonian behavior, but its viscosity increased by up to 5.4% in the most concentrated suspension.

Cabaleiro et al. [15] investigated several carbon-based nanoparticles, including carbon black and different graphite/diamond nanomixtures. Their findings indicated that these additions resulted in a decrease in surface tension and a shift to non-Newtonian behavior, while thermal conductivity showed a slight increase.

Navidbakhsh and Majdan-Cegincara [16] explored the effects of iron (III) oxide (Fe₂O₃) nanoparticles on PEG 400 and its mixtures with higher-molar-mass PEGs (PEG 2000 and PEG 6000). A notable outcome of their work was the change in rheological behavior. The naturally Newtonian PEG 400 and the shear-thickening PEG mixtures became pseudoplastic (shear-thinning) upon the addition of the Fe₂O₃ nanoparticles.

This article concerns the complex analysis of a number of MWCNT + PEG nanocolloids, aiming to present a complete picture and to offer a solid conclusion on the heat transfer capacity of these nanocolloids. The properties were experimentally determined and discussed in detail in a recent article (see Chereches et al. [4]). A straightforward analysis in terms of the Prandtl number is performed, corroborated by several performance evaluation criteria, as well as of the pumping power variation if nanoparticles are added. All these aspects are extremely relevant for convective heat transfer, and the discussion in this paper involves both laminar and turbulent flow.

2. Materials and Methods

2.1. Materials

PEG is a polyether with many uses, both in industry and in medicine. PEG’s chemical structure is H−(O−CH2−CH2)n−OH, and it can be used in a variety of applications, such as in chemistry, heat exchange, medicine, etc.

Several studies and discussions on the thermal viscosity and isobaric heat capacity of PEG 400, PEG 200, mixtures thereof, and nanoparticle-enhanced liquids have been published by Chereches et al. (see [2,3,7]). Thus, in this article, we will consider several experiments performed to determine the influence of MWCNT NPs on thermal conductivity, specific heat, and viscosity [2,3,4,7], alongside an experiment on PEG 200 + PEG 400 mixtures, considered as potential base for innovative new nanocolloids.

MWCNT nanoparticles were acquired from Sigma Aldrich, Darmstadt, Germany (CAS number: 308068–56- 6) and have dimensions of 50–90 nm, a density of 2.1 g/cm³, and a BET of 28 m²/g.

The nanocolloids with MWCNTs were manufactured via the two-step method, which involves the mix of nanoparticles with the base fluid after suspensions calculations for weight concentration. The procedure follows the lab protocol and involves one hour of ultrasonic mixing in an ultrasonic homogenizer GETI GUC02A (Opava Czech Republic) with a power of 60 W and a frequency of 40 kHz. The stability of the suspensions, by means of pH tests, was determine with an Edge Multiparameter HI 2030 (Hanna Instruments, Cluj Napoca, Romania).

The viscosity was studied at ambient temperatures and between 283.15 and 333.15 K for the MWCNT mass loading of nanoparticles up to 0.10 wt %. Viscosity and rheological properties were determined with a Physica MCR 501 (Anton Paar, Graz, Austria) equipped with a Peltier system for temperature control and parallel plates with a diameter of 50 mm and a 0.5 mm gap (accuracy: 1.5%). For pure PEG 400, a Newtonian behavior, together with a viscosity increase of up to 32%, was perceived for all nanocolloids (with the increase in viscosity being relational to the mass loading of NPs). In the case of MWCNT nanocolloids, a non-Newtonian behavior was clearly perceived. If we look at the variation in viscosity with the increase in temperature for the investigated nanocolloids, the viscosity declines when heating.

The specific heat was checked with a Mettler Toledo differential scanning calorimeter, DSC 1, (Mettler Toledo, Columbus, OH, USA), with the temperature accuracy being 2 K. An increase in specific heat with NP loading was also found for all nanocolloids. In Chereches et al. [2,4], a variation in thermal conductivity upon heating up to 333.15 K for PEG 400 with MWCNTs is presented, demonstrating a lack of variation in the PEG 400 thermal conductivity, while the presence of NPs improves the thermal conductivity of the suspension. Thermal conductivity tests were performed on a C-Therm (C-Therm Technologies Ltd., Fredericton, NB, Canada) with an MTPS sensor. The tests were repeated 5 times at each temperature, while for temperature variation, a Vulcan furnace was considered.

All the data attained on the thermophysical features of the nanocolloids were judiciously analyzed in terms of their accuracy, and a comparison was performed with the current research available in the literature; however, the available information is rather limited owing to the uniqueness of these kinds of suspensions. More information, covering the experimental setup, equipment employed, and analyses performed, are included in [2,3,4].

The uncertainty of the experimental results for viscosity was 1.5% [2,3], the thermal conductivity measurement accuracy was ± 1%, the relative error for the entire experiment was determined to be 1.48% [2], and the accuracy of the isobaric specific heat was determined to be less than 5% [2,3].

2.2. Evaluation Method

In what follows, we will present the common equations used for the evaluation of the heat transfer, together with the dimensionless figures employed for heat transfer analysis.

The Prandtl number (Pr) provides information about which sort of heat transfer prevails (i.e., conduction or convection). If the Pr has a low value, the heat transfer is largely driven by conduction; consequently, molecular diffusion is the most relevant mechanism of heat transfer. Conversely, an elevated Pr signifies a considerably substantial thermal boundary layer. The Pr number is as follows:

$$\mathrm{Pr} = {\displaystyle \frac{{\mathrm{c}}_{\mathrm{p}}\mathsf{\eta }}{\mathrm{k}}}$$

(1)

where C_p, η, k are the specific heat, dynamic viscosity, and thermal conductivity, respectively (see also [17,18,19]).

In addition to Pr, thermal diffusivity is a well-established feature that offers pertinent evidence of the capacity of a fluid to carry heat. Thermal diffusivity is the ratio between the thermal conductivity and the density multiplied by the specific heat of the fluid, which is an intrinsic material characteristic since it depends exclusively on the thermophysical properties related to the fluid. In fact, for the material to effectively transmit the thermal wave, it is not enough for it to be highly conductive—that is, to be easily crossed by a thermal flow when heating is applied; the specific heat is also relevant in order to determine that the heat received at each elementary layer is not stored inside the layer itself. If the fluid has high thermal conductivity but also high density and specific heat in front of a thermal gradient, the flow rate will be high in the first layers of the material but it will not be able to pass through the following layers.

The best approach by which to evaluate convection is the Mouromtseff number (Mo), which can be evaluated for both laminar and turbulent flow, providing relevant information of the fluid’s behavior. The evaluation of the Mo number in laminar flow was discussed by Moldoveanu et al. [19], who noticed that the Mouromtseff number increases with the concentration of NPs for a number of nanofluids based on water and different oxides. The conclusion of their study was that all the nanocolloids can replace water in laminar convection in real-life applications.

The Mouromtseff number can be calculated as follows [20,21]:

$$\mathrm{M}\mathrm{o} = {\displaystyle \frac{{\mathsf{\rho }}^{\mathrm{a}}{\mathrm{k}}^{\mathrm{b}}{\mathrm{c}}_{\mathrm{p}}^{\mathrm{d}}}{{\mu }^{\mathrm{e}}}}$$

(2)

where ρ, k, C_p, µ are the density, thermal conductivity, specific heat, and dynamic viscosity of the fluid, respectively. In Equation (2) the exponents correspond to different practical situations, being dependent on the material, initial, or final conditions, etc. [22].

Moreover, the benefits of the nanocolloid in terms of its capacity to transfer heat can be evaluated if a comparison with the base fluid is achieved; thus using the ratio between the Mo for the base fluid and that of the nanocolloid, we can obtain extremely useful information [21]:

$$\mathrm{M}{\mathrm{o}}_{\mathrm{r}} = {\displaystyle \frac{\mathrm{M}{\mathrm{o}}_{\mathrm{n}\mathrm{f}}}{\mathrm{M}{\mathrm{o}}_{\mathrm{b}\mathrm{f}}}} = {\displaystyle \frac{{\mathrm{k}}_{\mathrm{n}\mathrm{f}}}{{\mathrm{k}}_{\mathrm{b}\mathrm{f}}}}$$

(3)

However, for turbulent flow, where heat transfer by convection is not based solely on conduction inside the liquid, the Mouromtseff number can be estimated by taking into account also the viscosity and the fluid density, as follows [21]:

$$\mathrm{M}\mathrm{o} = {\displaystyle \frac{{\mathsf{\rho }}^{0.8}{\mathrm{k}}^{0.67}{\mathrm{c}}_{\mathrm{p}}^{0.33}}{{\mathrm{\mu }}^{0.47}}}$$

(4)

In either case, if ${\displaystyle \frac{\mathrm{M}{\mathrm{o}}_{\mathrm{n}\mathrm{f}}}{\mathrm{M}{\mathrm{o}}_{\mathrm{b}\mathrm{f}}}}$ > 1, the nanocolloid can effectively replace the liquid in a heat exchange operation based on convective heat transfer.

Another pertinent method by which to evaluate the convection capacity of a new fluid compared to conventional heat transfer fluids is the estimation of the relative pumping power. Huminic and Huminic [23] conducted a study considering different FOMs (Figures Of Merit) and presented both the benefits and disadvantages of NFs based on ND (nano-diamond) + Ni, ND + Fe₃O₄, MWCNT + Fe₃O₄, and GO + Co₃O₄. The researchers established, using the equations of Mansour et al. [24], that in laminar flow, the relative heat transfer coefficient is weaker in comparison to the relative pumping power for the considered cases. In turbulent convection flow, the relative heat transfer coefficient is beyond the relative pumping power [23]. The equations of Mansour et al. [24] are as follows:

Laminar flow:

$${\mathrm{W}}_{\mathrm{r}} = {\displaystyle \frac{{\mathrm{W}}_{\mathrm{n}\mathrm{f}}}{{\mathrm{W}}_{\mathrm{b}\mathrm{f}}}} = {\displaystyle \frac{{\mathrm{\mu }}_{\mathrm{n}\mathrm{f}}}{{\mathrm{\mu }}_{\mathrm{b}\mathrm{f}}}}{\left({\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{b}\mathrm{f}}}{{\mathsf{\rho }}_{\mathrm{n}\mathrm{f}}}}\right)}^2$$

(5)

Turbulent flow:

$${\mathrm{W}}_{\mathrm{r}} = {\displaystyle \frac{{\mathrm{W}}_{\mathrm{n}\mathrm{f}}}{{\mathrm{W}}_{\mathrm{b}\mathrm{f}}}}={\left({\displaystyle \frac{{\mathrm{\mu }}_{\mathrm{n}\mathrm{f}}}{{\mathrm{\mu }}_{\mathrm{b}\mathrm{f}}}}\right)}^{0.25}{\left({\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{b}\mathrm{f}}}{{\mathsf{\rho }}_{\mathrm{n}\mathrm{f}}}}\right)}^2$$

(6)

In Equations (5) and (6), W is the pumping power of the fluid in the pipe; µ is the viscosity; and ρ is the density. r refers to “relative,” nf to the nanocolloid, and bf to the base fluid. In Equations (5) and (6), “relative” describes the ratio between the calculated characteristic of the base fluid and the nanocolloid.

Theoretically, with reference to the general equations of fluid mechanics, the pumping power can be found as follows [25]:

$$\mathrm{W} = \dot{\mathrm{v}}\mathsf{\Delta }\mathrm{P} = \mathrm{w}{\displaystyle \frac{\mathsf{\pi }{\mathrm{D}}^2}{4}}\left(\mathrm{f}{\displaystyle \frac{\mathrm{L}}{\mathrm{D}}}{\displaystyle \frac{\mathsf{\rho }{\mathrm{w}}^2}{2}}\right)$$

(7)

where $\dot{\mathrm{v}}$ is the volume flow rate; ΔP is the pressure difference; w it the velocity; f is the friction factor; L is the length; and D is the diameter.

On the other hand, Leinhard and Leinhard’s equations [26], which are valid for both flow regimes, are as follows:

Laminar flow:

$$\mathrm{f} = 64∕\mathrm{R}\mathrm{e}$$

(8)

Turbulent flow:

$$\mathrm{f} = {0.184}^{-0.2}$$

(9)

Considering Equations (2)–(9) for the same Re, we obtain the following:

$${\mathrm{W}}_{\mathrm{r}} = {\displaystyle \frac{{\mathrm{W}}_{\mathrm{n}\mathrm{f}}}{{\mathrm{W}}_{\mathrm{b}\mathrm{f}}}} = {\left({\displaystyle \frac{{\mathsf{\eta }}_{\mathrm{n}\mathrm{f}}}{{\mathsf{\eta }}_{\mathrm{b}\mathrm{f}}}}\right)}^3{\left({\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{b}\mathrm{f}}}{{\mathsf{\rho }}_{\mathrm{n}\mathrm{f}}}}\right)}^2$$

(10)

3. Results and Discussion

3.1. Heat Transfer Capability Evaluation

In Figure 1, the thermophysical properties of the base fluids are depicted, while in Figure 2, those of the nanocolloids are depicted. The suspension’s thermophysical properties (see Figure 2) reveal that the addition of extremely low-mass concentrations of MWCNTs does not significantly influence the specific heat or density, but it does have a more significant impact on viscosity and thermal conductivity. This phenomenon is normal when carbon-based materials are involved, especially due to their high density and upsurged thermal conductivity.

Most of the thermophysical properties of PEG 400-based nanocolloids were experimentally determined by Chereches et al. [2,3]. The density of the samples is considered using the equation of Pak and Cho [17]:

$${\mathsf{\rho }}_{\mathrm{n}\mathrm{f}} = \mathsf{\phi }{\mathsf{\rho }}_{\mathrm{p}} + \left(1 - \mathsf{\phi }\right){\mathsf{\rho }}_{\mathrm{f}}$$

(11)

3.1.1. Pr Number

A comparison of the Pr number for PEG 400 and various fluids can be seen in

Table 1. Pr number for various heat transfer fluids.

	Temperature, °C	Pr
PEG 200	25	625.77
PEG 400	30	862.16
Water	25	6.89
Ethanol	25	18.05
Glycerol	25	7612.74
Fluid, Dowtherm Q	20	54.19
Shell heat transfer oil	20	1003.00

, using references from Rapp [18] and producer specifics (e.g., Dowtherm and Shell oils).

As was earlier discussed, Pr is the ratio between momentum transport and total heat transport and is typically defined as the kinematic viscosity divided by the thermal diffusivity (α). The thermal diffusivity is as follows:

$$\mathsf{\alpha } = {\displaystyle \frac{\mathrm{k}}{\mathsf{\rho }{\mathrm{c}}_{\mathrm{p}}}}$$

(12)

In

Table 2. Percentage variation in the relative Pr number of the nanocolloids compared to PEG 400.

	Temperature, [K]
	293.15	303.15	313.15	323.15	333.15
PEG 400 + 0.025% MWCNTs	5.07	9.55	40.43	21.54	29.66
PEG 400 + 0.050% MWCNTs	19.00	24.80	30.23	38.18	47.88
PEG 400 + 0.075% MWCNTs	30.70	44.21	59.51	74.76	90.13
PEG 400 + 0.10% MWCNTs	41.40	59.20	75.49	90.76	109.33

, the relative Prandtl number (which is defined as the ratio of the Pr of the nanocolloid to the Pr of the base fluid) for the suspensions studied is presented.

From Table 2, one can see an upsurge in Pr when MWCNTs are suspended in PEG 400, a phenomenon that is attributable to the increase in viscosity, which means that thermal transport becomes more difficult. The increase extends to 41.4% at ambient temperature, but it extends to 109.33% at 333.15 K. Moreover, the MWCNT’s loading increases the Pr number, and this increase depends highly on the nanoparticles’ concentration. From Table 2 it can also be seen that the addition of a very small quantity of NPs leads to an increase in Pr of about 5%.

From Figure 3, we see the variation in the Pr number for the mixtures of PEG, where 1 represents 100% PEG 200. Analyzing the data, it can be seen that Pr increases with the addition of PEG 400 to the mixture, an upsurge that appears to be due to the high viscosity and low thermal conductivity of PEG 400.

3.1.2. Thermal Diffusivity

The thermal diffusivity experimental results for the investigated suspensions are presented in Figure 4. Thermal diffusivity defines the ability of a given material to exchange heat. Thus, from Figure 4, one can see that at room temperature, the thermal diffusivity of PEG 400 fluids with MWCNT nanoparticles is increasing. When these outcomes correlate with variations in the Pr number, we can see the major positive influence of the addition of NPs. Thus, the addition of NPs causes an upsurge in thermal diffusivity up to 11.2%, although Pr also increases with the increase in NP concentration, proving a relative development in heat transfer. Furthermore, in Figure 5, the thermal diffusivity for the PEG mixtures is plotted, showing a decrease in thermal diffusivity with an increase in the percentage of PEG 400 in the mixture. This phenomenon is ascribed mainly to PEG 200’s lower thermal conductivity when compared to the one of the higher-molar-mass PEGs (i.e., PEG 400).

3.1.3. Mo Number

The Mouromtseff number for convective heat transfer [21] is considered in this section, employing Equations (3) and (4) for the laminar and turbulent regimes, respectively. The Mo in the laminar regime indicates the variation in the thermal conductivity ratio, as one can see in Figure 6.

Figure 6 indicates that most of the nanocolloids have an Mo_r higher than 1, which means that the presence of NPs causes an upsurge in the laminar heat transfer, a phenomenon that is attributed to the increase in thermal conductivity. Experimental observation of thermal conductivity values for different NP loadings and temperatures confirms that the use of MWCNT nanoparticles causes an upsurge in Mo_r.

In turbulent flow (see Figure 7), where the viscosity takes the lead in terms of transport, another phenomenon occurs, and the addition of MWCNTs actually decreases Mo_r. This observation correlates with the Pr number investigation. The decrease is more pronounced once the NP loading in each of the suspensions upsurges.

3.2. Pumping Power Evaluation

The addition of NPs influences the pumping power of the liquid, and this phenomenon was also studied for the manufactured samples. The most appropriate approach, as was identified in the literature, is the use of Mansour et al.’s equations [24]—more precisely Equations (5) and (6), which are written differently for laminar and turbulent flow, as was explained earlier. The results are presented in Figure 8, and an increase in pumping power can be observed in almost all cases, even if this increase is minor in a few cases. Another observation is that the nanocolloids with MWCNTs have a higher pumping power in comparison to oxide nanocolloids; the highest increase in pumping power in the laminar regime is 29.7%, and in turbulent regime, it is 9.6%.

A different approach can be seen in Figure 8, where Equation (10) is employed in the analysis. Here, there is an increase in the pumping power of maximum (100%) for MWCNT-based nanocolloids, unrelated to the type of movement.

Moreover, the experimental results lead to the conclusion that the addition of very low quantities of MWCNTs in PEG 400 is feasible, leading to convective heat transfer augmentation, and it is thus a viable solution to improve the thermal regime of heat exchangers. This is due to the significant increase in the fluid’s viscosity when nanoparticles are added, which, in turn, necessitates more energy to pump the fluid through a system. This effect, which can be seen as a deterioration of the dynamic viscosity, directly impacts the pumping power required for the operation. On the other hand, the intrinsic properties of PEG 200 are better suited for heat transfer than those of PEG 400.

A quick technical–economic analysis reveals that the employment of low-molecular-weight PEGs as heat transfer fluids can serve as a good solution for medium-temperature heat transfer applications, especially due to their good thermal conductivity when compared with traditional fluids (i.e., thermal oils). However, the price of PEGs is about 20% higher than that of basic heat transfer oils (i.e., Shell oils). The addition of NPs can increase the overall price of the fluid; however, a small addition is not significant in terms of costs.

4. Conclusions

This paper offers a wide-ranging investigation, founded on experimental data, highlighting the effect of MWCNTs nanoparticles and addition to PEG 400. Moreover, several PEG mixtures were studied, and their intrinsic properties were assessed. This analysis took into account several criteria and performance evaluation indices, such as the Pr number, thermal diffusivity, pumping power, and Mo number, considering both the advantages and the disadvantages in terms of heat transfer enhancement. The main drawback noted in this analysis is that the addition of NPs causes an upsurge in pumping power, which is explained by increases in viscosity and density. This study approach is a novel one and relies on a well-developed primary examination of the PEG mixture and the behavior of the PEG 400 nanocolloid in both laminar and turbulent flow, involving well-known performance evaluation criteria.

The main conclusions of this analysis are as follows:

• The addition of MWCNTs to polyethylene glycol decreases nanocolloids thermal transport, being influenced by both the temperature and the NP loading.
• Most of the nanocolloids have a relative Mo > 1, indicating superior behavior in tube flow than the base fluid.
• The addition of nanoparticles to PEG 400 leads to an increase in pumping power, depending on the NP concentration. However, improved results are obtained for samples with low loads, where a relatively small influence is noticed.
• The results show that nanocolloids with multi-walled carbon nanotubes (MWCNTs) lead to an intensification of the pumping power. The highest upsurge in pumping power noted in the laminar regime is 29.7%, and in turbulent flow, it is 9.6%.
• An interesting option explored in this paper is the use of PEG mixtures as base fluids in order to combine their thermophysical properties.

However, the main limitations of introducing PEGs in practical applications are related to the lack of experimental results in close-to-real applications. Nevertheless, this study is a step forward in determining PEG’s heat exchange applications.

Finally, it can be concluded that the best practical solution may be the addition of low concentrations of nanoparticles in a mixture of PEG 400 and PEG 200, with the result being an intensification of convection heat transfer. This solution is a promising active technique for improving heat transfer.