# Numerical Study of a Heat Exchanger with a Rotating Tube Using Nanofluids under Transitional Flow

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}O

_{3}, Al

_{2}O

_{3}-Cu and Cu-water nanofluids were studied, with the Cu-water being the fluid with the best performance (19.33% improvement). Heat transfer was enhanced with inner tube rotation up to 500 rpm (41.2%). Nevertheless, pressure drop and friction values were increased due to both phenomena, leading to higher pumping power values for the operation of the heat exchanger. Hence, a balance between the performance and pumping power increase must be considered when modifications are made on a heat exchanger. The development of the numerical model might help in further optimizing, redesigning and scaling up heat exchangers.

## 1. Introduction

_{2}O

_{3}, TiO

_{2}and CuO being recurrent ones. Sonawane et al. [3] performed an experimental study of the heat transfer characteristics of an Al

_{2}O

_{3}-water nanofluid at a 2% and 3% volume concentration in a concentric tube heat exchanger, finding an increase in heat transfer with an increase in the concentration. Bahmani et al. [4] studied the heat transfer and turbulent flow characteristics of a similar nanofluid in parallel and counter-flow double tube heat exchanger by means of a numerical code, finding that the addition of nanoparticles to water enhanced the maximum thermal efficiency and average Nusselt number in 30% and 32.7%, respectively. Experimental studies from Rao et al. [5] showed that the forced convection of an Al

_{2}O

_{3}-water nanofluid at concentrations from 0.1 to 0.4% improved the heat transfer rate by 2.5% in a turbulent regime. Yang et al. [6] compared the performance of Al

_{2}O

_{3}and TiO

_{2}-water, finding that the Nusselt number of TiO

_{2}-water nanofluids was higher. Bajestan et al. [7] also found, experimentally and numerically, that the heat transfer characteristics of a TiO

_{2}-water nanofluid are higher than for raw water, with a maximum enhancement of 21%. CuO-water nanofluids have also shown an increase in the heat transfer coefficient up to 18–35% with respect to raw water in the work of Korpys et al. [8]. Cu- and CuO-water based nanofluids have been studied as well by Yang et al. [6] and Saeedan et al. [9]. However, it has been found that too high of concentrations of nanofluids seem to the worsen heat exchanger performance. Duangthongsuk and Wongwises [10] studied the behavior of a TiO

_{2}-water nanofluid with volume fractions from 0.2–2% in a horizontal double-tube counter-flow, finding that heat transfer coefficient was enhanced by 26% with respect to raw water in a 1% volume fraction, but it dropped by 14% with a 2% volume fraction. Other oxides have also shown good heat transfer properties: Kumar et al. [11] achieved increases of the Nusselt number up to 14.7% with Fe

_{3}O

_{4}, whereas Esfe et al. [12] reported a 21.8% increase with MgO. Likewise, other substances have been studied as fluid additives, such as carbon nanotubes. Halelfadl et al. [13] found an enhancement of 12% in heat transfer in a coaxial heat exchanger under a laminar regime. Multi-Walled Carbon Nanotubes (MWCNTs) were studied by Kumar and Chandrasekar [14], finding an increase in Nusselt numbers up to 30% for 0.6% concentration values. Nitrogen-doped graphene nanosheets have been also found to increase the heat transfer coefficient (Goodarzi et al. [15]). Heat transfer and friction factor values of a TiO

_{2}-Poly Vinyl Alcohol (PVA) nanofluid flowing in a plain tube with twisted tape were experimentally studied by Hazbehian et al. [16]. The general pattern is that nanofluids enhance the heat transfer rate and increase friction loss. Hybrid nanofluids are another option to consider. The most common are Al

_{2}O

_{3}-MgO, Cu-TiO

_{2}and Al

_{2}O

_{3}-Ag, reaching enhancements up to 49% in the Nusselt number (Madesh et al. [17]). Finally, another option to improve the performance of the working fluid is mixing two carriers, such as water and glycol, as performed by Reddy and Rao [18]. These authors found an increase of 10.73% in the heat transfer rate with a 60–40% distilled water–glycol mixture when adding 2% TiO

_{2}nanoparticles. The addition of stabilizers, such as cetyl trimethyl ammonium chloride (CTAC), to the mixture was also found to increase the heat exchanger performance by Korpys et al. [8], with the same effect observed by Homozi et al. [19] when adding sodium dodecyl sulfate to a hybrid Al

_{2}O

_{3}-Ag nanofluid.

_{2}O

_{3}-MgO hybrid nanofluid; Karimi et al. [28] used twisted tape inserts with different pitch ratio values and an Al

_{2}O

_{3}-water nanofluid, finding promising results. Darzi et al. [29] used a helical corrugated tube and Al

_{2}O

_{3}at a 4% concentration to increase heat transfer by a factor up to 3.31. Qi et al. [30] studied a TiO

_{2}-water nanofluid with smooth and corrugated tubes, finding an improvement in the heat transfer up to 14.8%, but at the cost of higher pressure drop values up to 6.5%. When inserting single- and double-strip helical screw tapes in a tube, Chaurasia and Sarviya [31] were able to increase the Nusselt number in 170 and 182%. Nakhchi and Esfahani [32] were also able to increase the Nusselt number and friction factor with perforated circular tubes with louvered strip vortex generators. A cone-shaped inserted double-tube heat exchanger with Al

_{2}O

_{3}and CuO-water nanofluids was studied by Karuppasamy et al. [33], finding that Al

_{2}O

_{3}had better performance than CuO. Nevertheless, Saedodin et al. [34] found that CuO had better performance when investigating SiO

_{2}-water, TiO

_{2}-water, Al

_{2}O

_{3}-water and CuO-water nanofluids in a circular tube with a turbulator. Mohamed et al. [35] compared Al

_{2}O

_{3}and Cu-water nanofluids, claiming that the Cu-water nanofluid showed the best performance.

_{2}O

_{3}-Cu-water hybrid nanofluid inside a vented cavity with a rotating cylinder. Although heat exchange was improved in all of these studies, the pressure drop (and hence the required pumping power) was increased.

_{2}-water nanofluid flowing through an annulus with different radii ratio values using the k-ε model to verify that heat transfer performance increased with the Reynolds number. The RNG k-ε model was used by Ard and Kiatkittipong [47] to study the effect of multiple twisted tapes with different arrangements and using a TiO

_{2}nanofluid, to find that the counter arrangement offered the best performance. This model was also used by Fattahi [48] to assess the heat transfer and pressure drop of a hybrid Al

_{2}O

_{3}-CuO-water nanofluid in a cylindrical pipe with twisted tape, modeling the fluid as a single phase. A maximum performance increase of 23% was found at a 2% concentration. YousefiMiab et al. [49] used the OpenFOAM solver to create gas pressure reducing stations utilizing an Al

_{2}O

_{3}nanofluid in shell and tube heat exchangers, discovering that increasing the shell side Peclet number and nanoparticle volume fraction increases the total heat transfer coefficient. Increasing the shell side Peclet number and the nanoparticle volume fraction also resulted in an increase in pressure loss, which was a disadvantage of the heater’s performance. Furthermore, Dbouk et al. [50] used CFD modeling to simulate a combined Poiseuille-Taylor-Couette flow in a multifunctional heat exchanger between two rotating concentric elliptically deformed annular tubes. It was discovered that the proposed Poiseuille–Taylor–Couette flow in this heat exchanger’s elliptically deformed concentric tubes can greatly improve heat and mass transfer at the Reynolds number. Upadhya et al. [51] studied the effect of using Casson, Micropolar and Hybrid magneto-nanofluids in a suspension of cross diffusion on entropy generation. They found that the hybrid nanofluid has a higher temperature profile than micropolar and Casson fluid. The micropolar fluid shows higher entropy generation compared to the Casson and hybrid nanofluid. Ghazanfari et al. [52] investigated the influence of nanofluids on twisted tube heat exchanger efficiency using CFD. They demonstrated that using nanofluids in twisted tubes enhanced heat transfer while increasing the pressure drop. Sundar and Mouli [53] analyzed the effectiveness and number of transfer units of Fe

_{3}O

_{4}-SiO

_{2}hybrid fluids through a plate heat exchanger. They concluded that increases in the volume concentration and Reynolds number lead to enhancements in the effectiveness and number of transfer units. Thirumalaisamy et al. [54] investigated the natural convective flow and thermal efficiency of an electroconductive ternary nanofluid-filled inclined partially heated rectangular porous cavity under the impacts of an inclined magnetic field. The results indicated that the average heat transfer rate is increased by 7.49% when augmenting nanofluids 33.3%.

_{2}O

_{3}, Cu and hybrid Cu-Al

_{2}O

_{3}water-based nanofluids. The effects of changing the tube rotational speed, as well as the nanoparticle concentration, on the effectiveness of the exchanger and the pressure drop that must be balanced by an increasing pumping power are also investigated and discussed. The development of the model might also be helpful for further optimizations, redesigning and scaling up similar heat exchangers.

## 2. Numerical Model

#### 2.1. Geometry

_{2}O

_{3}-water nanofluid, Cu-water nanofluid and Al

_{2}O

_{3}-Cu hybrid nanofluid. Figure 1 shows a view of the geometrical model.

#### 2.2. Boundary Conditions

_{cf}ranges between 2473 and 4947. This number was calculated based on the different cold fluid properties at different volume concentrations: 1, 2 and 3%. The Reynolds number of the hot fluid, hot water, flowing through the inner tube, Re

_{hf}, was fixed at 9780. Inlet temperature of nanofluids and hot water were fixed at 301 K and 333 K, respectively. The outer tube was assumed to be a stationary insulated wall. The speed of the rotating inner tube of the heat exchanger was fixed at the following values: 0, 100, 200, 300, 400 and 500 rpm, depending on each particular case. Non-slip wall conditions were applied to the surfaces of both tubes. A velocity-inlet condition was applied at the inlets of the inner tube and the annulus, with values specified depending on the flow rate. Finally, the pressure-outlet boundary condition was applied to both tube outlets. As it may be appreciated in Figure 1, the double-tube heat exchanger under study has a counter-flow configuration, with Reynolds numbers in the range of transitional flow.

#### 2.3. Governing Equations

_{i}is the Cartesian coordinate in the i-direction, u

_{i}is the mean component of velocity in the i-direction and $\rho $ is the fluid density.

#### 2.4. Thermophysical Properties of Fluids

#### 2.5. Numerical Method and Validation

^{−5}for continuity and momentum equations and 10

^{−6}for the energy equation. The simulation time took around 12 h for a fixed tube case and 72 h for a rotating tube case.

#### 2.6. Grid Independence Study

_{cf}= 2473 and an inner tube rotational speed of 0 rpm. A combination of a hexahedral and tetrahedral cell was used to generate the mesh, as shown in Figure 2. The relevant parameters to perform the grid independence study were considered to be the number of transfer units (NTU) and the pressure drop. Figure 3 shows the results of the grid independence study. It may be appreciated that the grid with 1,835,524 cells, with an error around 0.81% for the NTU, was accurate enough for the purposes of this study.

#### 2.7. Experimental Validation

## 3. Data Processing

_{LMTD}is the logarithmic mean temperature difference, calculated using Equation (23):

^{3}/s).

## 4. Results and Discussion

_{2}O

_{3}-water nanofluid, Cu-water nanofluid and Al

_{2}O

_{3}-Cu hybrid nanofluid through the double-tube heat exchanger at different volume concentration values (ϕ) of 1, 2 and 3% and different inner tube rotational speeds of 0, 100, 200, 300, 400 and 500 rpm. The cold fluid Reynolds number Re

_{cf}ranged between 2473 and 4947 and the hot fluid Reynolds number Re

_{hf}was fixed at 9780.

#### 4.1. Flow Analysis

_{cf}= 2473 for water at different inner tube rotational speed values. In Figure 5a, the flow pattern is mainly in the axial direction, with smooth velocity streamlines at 0 RPM. However, as the rotating speed increases (Figure 5b–d), the flow has both axial and rotational components. These flow patterns are thought to enhance convective heat transfer, due to the continuous disturbance of the boundary layer and generation of swirling. Greater angular velocities change the flow direction significantly, forcing the flow to encircle the tube and resulting in longer paths, as shown in Figure 5d at 500 RPM. This increase in rotational speed leads to more turbulence and warping of the flow around the tube, a fact known to enhance heat transfer.

#### 4.2. Number of Transfer Units (NTU)

_{2}O

_{3}-water nanofluid being the least effective for heat transfer. The increase in the nanoparticle concentration from 0 to 3% and the rotational speed from 0 to 500 rpm contribute to higher heat transmission values, increasing the efficiency of the heat exchanger for all nanoparticle types. The significant positive effect of the rotational speed on the convection heat transfer coefficient may be ascribed to the swirling flow that arises and is reinforced with increasing speeds. Additionally, comparing the results obtained with the different nanofluids and raw water, the benefits of incorporating nanoparticles are apparent, as the NTU increases substantially. Considering only the rotational effect, a mean increase in the NTU of around 0.146 when increasing the rotational speed from 0 to 500 rpm in pure water has been observed. When considering only the addition of nanoparticles, the mean increase in the NTU was found to be 0.078 for the addition of Cu nanoparticles at a 3% concentration. When both effects were combined, the mean increase in the NTU was found to be 0.300, hinting at possible constructive interference between the effects of the increase in rotational speed and the addition of nanoparticles to water.

_{2}O

_{3}-Cu hybrid nanofluid and the Al

_{2}O

_{3}-water nanofluid. For instance, at a 1% volume concentration and 500 rpm, the NTU was improved by around 46.9, 43.8 and 41.5%, respectively, for the Cu-water nanofluid, the Al

_{2}O

_{3}-Cu hybrid nanofluid and the Al

_{2}O

_{3}-water nanofluid compared to raw water at 0 rpm when Re

_{cf}= 2473. At Re

_{cf}= 4946, the same effect was observed, with NTU being enhanced by 46.1 (Cu), 42.6 (hybrid) and 36% (Al

_{2}O

_{3}), as shown in Figure 6a–d. Figure 6e–g show an NTU enhancement of 62.4 (Cu), 53.2 (hybrid) and 41.62% (Al

_{2}O

_{3}) at Re

_{cf}= 2473 at a 2% concentration and 500 rpm compared to raw water at 0 rpm. Similarly, at Re

_{cf}= 4946, the maximum NTU improvement was 55.1 (Cu), 43.5 (hybrid) and 40.6% (Al

_{2}O

_{3}). As depicted in Figure 6h–j, the increase in the nanoparticle concentration to 3% and the inner tube rotation to 500 rpm achieved a maximum NTU enhancement at Re

_{cf}= 4946 of 66.7 (Cu), 56.8 (hybrid) and 47.3% (Al

_{2}O

_{3}) with respect to raw water at 0 rpm. Hence, it seems that the Cu-water nanofluid was the most efficient one in terms of performance improvement. A particular detail may be commented about in Figure 6j, where it seems that Cu nanoparticles, at 500 rpm, might reach a maximum efficiency at a cold fluid Reynolds value below 5000, suggesting that further increases in its value could not result in a higher efficiency. This effect should be investigated in detail in future research.

#### 4.3. Effectiveness

_{cf}= 4946, the improvement was 5.2, 6.9 and 13.4%, respectively, compared with pure water. Maximum enhancement, nevertheless, arises from the combination of the nanofluid and inner tube rotation, reaching a 41.2% with a 3% concentration and 500 rpm. For the Al

_{2}O

_{3}-water nanofluid with 1, 2 and 3% concentration values at 0 rpm, as shown in Figure 7d–f, the enhancement was only 3.6, 4.5 and 8.7%, respectively. In this case, maximum enhancement occurred at a 3% concentration and 500 rpm and was equal to 30.6%. The improvement caused by the addition of the hybrid nanofluid with 1, 2 and 3% concentrations is shown in Figure 7g–i, where the enhancement at 0 rpm is equal to 3.9, 5.1 and 10.7%, respectively, when compared to raw water, reaching a maximum improvement at 500 rpm equal to 35.9%.

#### 4.4. Effect of Rotational Speed at Higher Reynolds Numbers

#### 4.5. Local Heat Transfer Coefficients

#### 4.6. Pressure Drop

_{cf}= 4946 and a 3% concentration at 500 rpm with respect to pure water at 0 rpm, as shown in Figure 9b. Figure 9d–f show the results for the Al

_{2}O

_{3}-water nanofluid under the same conditions, where the maximum pressure drop was 104.77%. Similarly, for the hybrid nanofluid, the pressure drop increased up to 124.6%, as shown in Figure 9g–i.

#### 4.7. Pumping Power

_{cf}= 4946 (Re

_{cf}/Re

_{hf}= 0.5058) for the three nanofluids studied. It may be appreciated that the increase in the nanoparticle concentration leads to an increase in the pumping energy, mainly as a result of the increased fluid density. Meanwhile, the increase in rotational speed leads to an increase in the pumping power. However, the values of pumping power, lying in the order of magnitude of 0.1 W, should not pose a high requirement in the pumps attached to the heat exchanger.

## 5. Conclusions

_{2}O

_{3}-water nanofluid showed better thermal performance values than raw water, with a maximum 12.4% improvement, but lower than the Al

_{2}O

_{3}-Cu hybrid nanofluid, with a maximum 15.34% improvement. The best performance was shown by the Cu-water nanofluid, improving the performance with respect to raw water up to 19.33%. When the rotational effect of the inner tube was added, the performance was increased by 47.3, 56.8 and 66.7% for the Al

_{2}O

_{3}, the hybrid and the Cu nanofluids at a 3% concentration, respectively, when rotating at 500 rpm. The effectiveness values were improved as well by 30.6, 35.9 and 41.2%, respectively. Nevertheless, the pressure drop along the heat exchanger was affected by these two actions, reaching maximum increase values of 104.77, 124.6 and 156.3%, respectively, compared to pure water with no rotation. This increase in the pressure drop and friction caused by the higher rotational speed and the density increase in the nanofluids, due to the higher concentration values, led to higher pumping power values required to operate the heat exchanger. Nevertheless, the maximum pumping power was found to be in the order of 0.1 W, so that should not pose great problems for normal pump operation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

_{s} | Heat transfer surface area: m^{2} |

c | Heat capacity rate, W/K |

cp | Specific heat capacity, J/kg K |

D | Diameter of outer tube, m |

d | Diameter of inside tube, m |

$G$ | Generation rate |

k | Thermal conductivity, W/m K |

L | Length of concentric tube, m |

ṁ | Mass flow rate, kg/s |

NTU | Number of Transfer Units |

ρ | Density, kg/m^{3} |

$\dot{Q}$ | Heat transfer rate, W |

Re | Reynolds number |

T | Temperature, K |

$\Delta {T}_{log}$ | Logarithmic mean temperature difference, K |

U | Overall heat transfer coefficient, W/m^{2} K |

u | Axial flow velocity, velocity component, m/s |

Z | Direction coordinates along the tube |

Greek symbols | |

$\alpha $ | Inverse effective turbulent Prandtl numbers |

ε | Effectiveness |

ϕ | Solid volume fraction |

μ | Dynamic viscosity, kg/m·s |

ρ | Density, kg/m^{3} |

Subscripts | |

avg | Average |

cf | Cold fluid |

eff | Effective |

f | Fluid |

h | Hydraulic, hybrid |

hf | Hot fluid |

i | Inlet, inner, direction |

max | Maximum |

min | Minimum |

nf | Nanofluid |

o | Outlet, outer |

p | Pressure |

s | Nanoparticle |

t | Turbulent |

## References

- Bezaatpour, M.; Goharkhah, M. Convective heat transfer enhancement in a double pipe mini heat Exchanger by magnetic field induced swirling flow. Appl. Therm. Eng.
**2020**, 167, 114801. [Google Scholar] [CrossRef] - Forooghi, P.; Flory, M.; Bertsche, D.; Wetzel, T.; Frohnapfel, B. Heat transfer enhancement on the liquid side of an industrially designed flat-tube heat exchanger with passive inserts—Numerical investigation. Appl. Therm. Eng.
**2017**, 123, 573–583. [Google Scholar] [CrossRef] - Sonawane, S.S.; Khedkar, R.S.; Wasewar, K.L. Study on concentric tube heat exchanger heat transfer performance using Al
_{2}O_{3}—Water based nanofluids. Int. Commun. Heat Mass Transf.**2013**, 49, 60–68. [Google Scholar] [CrossRef] - Bahmani, M.H.; Sheikhzadeh, G.; Zarringhalam, M.; Akbari, O.A.; Alrashed, A.A.A.A.; Shabani, G.; Goodarzi, M. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Adv. Powder Technol.
**2018**, 29, 273–282. [Google Scholar] [CrossRef] - Rao, M.S.E.; Sreeramulu, D.; Rao, C.J.; Ramana, M.V. Experimental Investigation on Forced Convective Heat Transfer Coefficient of a Nano fluid. Mater. Today Proc.
**2017**, 4, 8717–8723. [Google Scholar] [CrossRef] - Yang, C.; Li, W.; Nakayama, A. Convective heat transfer of nanofluids in a concentric annulus. Int. J. Therm. Sci.
**2013**, 71, 249–257. [Google Scholar] [CrossRef] - Bajestan, E.E.; Moghadam, M.C.; Niazmand, H.; Daungthongsuk, W.; Wongwises, S. Experimental and numerical investigation of nanofluids heat transfer characteristics for application in solar heat exchangers. Int. J. Heat Mass Transf.
**2016**, 92, 1041–1052. [Google Scholar] [CrossRef] - Korpyś, M.; Dzido, G.; Al-Rashed, M.H.; Wojcik, J. Experimental and numerical study on heat transfer intensification in turbulent flow of CuO–water nanofluids in horizontal coil. Chem. Eng. Process. Process Intensif.
**2020**, 153, 107983. [Google Scholar] [CrossRef] - Saeedan, M.; Nazar, A.R.S.; Abbasi, Y.; Karimi, R. CFD Investigation and neutral network modeling of heat transfer and pressure drop of nanofluids in double pipe helically baffled heat exchanger with a 3-D fined tube. Appl. Therm. Eng.
**2016**, 100, 721–729. [Google Scholar] [CrossRef] - Duangthongsuk, W.; Wongwises, S. An experimental study on the heat transfer performance and pressure drop of TiO
_{2}-water nanofluids flowing under a turbulent flow regime. Int. J. Heat Mass Transf.**2010**, 53, 334–344. [Google Scholar] [CrossRef] - Kumar, N.T.R.; Bhramara, P.; Addis, B.M.; Sundar, L.S.; Singh, M.K.; Sousa, A.C.M. Heat transfer, friction factor and effectiveness analysis of Fe3O4/water nanofluid flow in a double pipe heat exchanger with return bend. Int. Commun. Heat Mass Transf.
**2017**, 81, 155–163. [Google Scholar] [CrossRef] - Esfe, M.H.; Saedodin, S.; Mahmoodi, M. Experimental studies on the convective heat transfer performance and thermophysical properties of MgO–water nanofluid under turbulent flow. Exp. Therm. Fluid Sci.
**2014**, 52, 68–78. [Google Scholar] [CrossRef] - Halelfadl, S.; Estellé, P.; Maré, T. Heat transfer properties of aqueous carbon nanotubes nanofluids in coaxial heat exchanger under laminar regime. Exp. Therm. Fluid Sci.
**2014**, 55, 174–180. [Google Scholar] [CrossRef] - Kumar, P.C.M.; Chandrasekar, M. CFD analysis on heat and flow characteristics of double helically coiled tube heat exchanger handling MWCNT/water nanofluids. Heliyon
**2019**, 5, e02030. [Google Scholar] [CrossRef] [PubMed] - Goodarzi, M.; Kherbeet, A.S.; Afrand, M.; Sadeghinezhadd, E.; Mehrali, M.; Zahedi, P.; Wongwises, S.; Dahari, M. Investigation of heat transfer performance and friction factor of a counter-flow double-pipe heat exchanger using nitrogen-doped, graphene-based nanofluids. Int. Commun. Heat Mass Transf.
**2016**, 76, 16–23. [Google Scholar] [CrossRef] - Hazbehian, M.; Maddah, H.; Mohammadiun, H.; Alizadeh, M. Experimental investigation of heat transfer augmentation inside double pipe heat exchanger equipped with reduced width twisted tapes inserts using polymeric nanofluid. Heat Mass Transf.
**2016**, 52, 2515–2529. [Google Scholar] [CrossRef] - Madhesh, D.; Parameshwaran, R.; Kalaiselvam, S. Experimental investigation on convective heat transfer and rheological characteristics of Cu–TiO2 hybrid nanofluids. Exp. Therm. Fluid Sci.
**2014**, 52, 104–115. [Google Scholar] [CrossRef] - Reddy, M.C.S.; Rao, V.V. Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO
_{2}nanofluid in double pipe heat exchanger with and without helical coil inserts. Int. Commun. Heat Mass Transf.**2014**, 50, 68–76. [Google Scholar] [CrossRef] - Hormozi, F.; ZareNezhad, B.; Allahyar, H.R. An experimental investigation on the effects of surfactants on the thermal performance of hybrid nanofluids in helical coil heat exchangers. Int. Commun. Heat Mass Transf.
**2016**, 78, 271–276. [Google Scholar] [CrossRef] - El Maakoul, A.; El Metoui, M.; Abdellah, A.F.B.; Saadeddine, S.; Meziane, M. Numerical investigation of thermohydraulic performance of air to water double-pipe heat exchanger with helical fins. Appl. Therm. Eng.
**2017**, 127, 127–139. [Google Scholar] [CrossRef] - Nakhchi, M.E.; Hatami, M.; Rahmati, M. Experimental evaluation of performance intensification of double-pipe heat exchangers with rotary elliptical inserts. Chem. Eng. Process. Process Intensif.
**2021**, 169, 108615. [Google Scholar] [CrossRef] - Vaisi, A.; Moosavi, R.; Lashkari, M.; Soltani, M.M. Experimental investigation of perforated twisted tapes turbulator on thermal performance in double pipe heat exchangers. Chem. Eng. Process. Process Intensif.
**2020**, 154, 108028. [Google Scholar] [CrossRef] - Promvonge, P.; Promthaisong, P.; Skullong, S. Experimental and numerical heat transfer study of turbulent tube flow through discrete V-winglets. Int. J. Heat Mass Transf.
**2020**, 151, 119351. [Google Scholar] [CrossRef] - Murali, G.; Nagendra, B.; Jaya, J. CFD analysis on heat transfer and pressure drop characteristics of turbulent flow in a tube fitted with trapezoidal-cut twisted tape insert using Fe
_{3}O_{4}nano fluid. Mater. Today Proc.**2020**, 21, 313–319. [Google Scholar] [CrossRef] - Watel, B.; Harmand, S.; Desmet, B. Influence of fin spacing and rotational speed on the convective heat exchanges from a rotating finned tube. Int. J. Heat Fluid Flow
**2000**, 21, 221–227. [Google Scholar] [CrossRef] - Aliabadi, M.K.; Feizabadi, A. Performance intensification of tubular heat exchangers using compound twisted-tape and twisted-tube. Chem. Eng. Process. Process Intensif.
**2020**, 148, 107799. [Google Scholar] [CrossRef] - Singh, S.K.; Sarkar, J. Improving hydrothermal performance of hybrid nanofluid in double tube heat exchanger using tapered wire coil turbulator. Adv. Powder Technol.
**2020**, 31, 2092–2100. [Google Scholar] [CrossRef] - Karimi, A.; Al-Rashed, A.A.A.A.; Afrand, M.; Mahian, O.; Wongwises, S.; Shahsavar, A. The effects of tape insert material on the flow and heat transfer in a nanofluid-based double tube heat exchanger: Two-phase mixture model. Int. J. Mech. Sci.
**2019**, 156, 397–409. [Google Scholar] [CrossRef] - Darzi, A.A.R.; Farhadi, M.; Sedighi, K.; Aallahyari, S.; Delavar, M.A. Turbulent heat transfer of Al
_{2}O_{3}–water nanofluid inside helically corrugated tubes: Numerical study. Int. Commun. Heat Mass Transf.**2013**, 41, 68–75. [Google Scholar] [CrossRef] - Qi, C.; Luo, T.; Liu, M.; Fan, F.; Yan, Y. Experimental study on the flow and heat transfer characteristics of nanofluids in double-tube heat exchangers based on thermal efficiency assessment. Energy Convers. Manag.
**2019**, 197, 111877. [Google Scholar] [CrossRef] - Chaurasia, S.R.; Sarviya, R.M. Thermal performance analysis of CuO/water nanofluid flow in a pipe with single and double strip helical screw tape. Appl. Therm. Eng.
**2020**, 166, 114631. [Google Scholar] [CrossRef] - Nakhchi, M.E.; Esfahani, J.A. CFD approach for two-phase CuO nanofluid flow through heat exchangers enhanced by double perforated louvered strip insert. Powder Technol.
**2020**, 367, 877–888. [Google Scholar] [CrossRef] - Karuppasamy, M.; Saravanan, R.; Chandrasekaran, M.; Muthuraman, V. Numerical exploration of heat transfer in a heat exchanger tube with cone shape inserts and Al
_{2}O_{3}and CuO nanofluids. Mater. Today Proc.**2020**, 21, 940–947. [Google Scholar] [CrossRef] - Saedodin, S.; Zaboli, M.; Rostamian, S.H. Effect of twisted turbulator and various metal oxide nanofluids on the thermal performance of a straight tube: Numerical study based on experimental data. Chem. Eng. Process. Process Intensif.
**2020**, 158, 108106. [Google Scholar] [CrossRef] - Mohamed, M.A.; Trashorras, A.J.G.; Marigorta, E.B. Numerical Investigation of Heat Transfer with Nanofluids in Concentric Tube Heat Exchanger under Transitional Flow. Energy Perspect.
**2020**, 1, 34–56. Available online: http://globalpublisher.org/journals-1006/ (accessed on 17 January 2024). - Arzani, H.K.; Amiri, A.; Kazi, S.N.; Chew, B.T.; Badarudin, A. Experimental and numerical investigation of thermophysical properties, heat transfer and pressure drop of covalent and noncovalent functionalized graphene nanoplatelet-based water nanofluids in an annular heat exchanger. Int. Commun. Heat Mass Transf.
**2015**, 68, 267–275. [Google Scholar] [CrossRef] - Bahiraei, M.; Mazaheri, N.; Mohammadi, M.S.; Moayedi, H. Thermal performance of a new nanofluid containing biologically functionalized graphene nanoplatelets inside tubes equipped with rotating coaxial double-twisted tapes. Int. Commun. Heat Mass Transf.
**2019**, 108, 104305. [Google Scholar] [CrossRef] - Shi, Z.; Dong, T. Thermodynamic investigation and optimization of laminar forced convection in a rotating helical tube heat exchanger. Energy Convers. Manag.
**2014**, 86, 399–409. [Google Scholar] [CrossRef] - El-Maghlany, W.M.; Hanafy, A.A.; Hassan, A.A.; El-Magid, M.A. Experimental study of Cu–water nanofluid heat transfer and pressure drop in a horizontal double-tube heat exchanger. Exp. Therm. Fluid Sci.
**2016**, 78, 100–111. [Google Scholar] [CrossRef] - Moayedi, H. Investigation of heat transfer enhancement of Cu-water nanofluid by different configurations of double rotating cylinders in a vented cavity with different inlet and outlet ports. Int. Commun. Heat Mass Transf.
**2021**, 126, 105432. [Google Scholar] [CrossRef] - Abou-Ziyan, H.Z.; Helali, A.B.; Selim, M.Y.E. Enhancement of forced convection in wide cylindrical annular channel using rotating inner pipe with interrupted helical fins. Int. J. Heat Mass Transf.
**2016**, 95, 996–1007. [Google Scholar] [CrossRef] - Ali, M.A.M.; El-Maghlany, W.M.; Eldrainy, Y.A.; Attia, A. Heat transfer enhancement of double pipe heat exchanger using rotating of variable eccentricity inner pipe. Alex. Eng. J.
**2018**, 57, 3709–3725. [Google Scholar] [CrossRef] - Jasim, L.M.; Hamzah, H.; Canpolat, C.; Sahin, B. Mixed convection flow of hybrid nanofluid through a vented enclosure with an inner rotating cylinder. Int. Commun. Heat Mass Transf.
**2021**, 121, 105086. [Google Scholar] [CrossRef] - Gomaa, A.; Halim, M.A.; Elsaid, A.M. Experimental and numerical investigations of a triple concentric-tube heat exchanger. Appl. Therm. Eng.
**2016**, 99, 1303–1315. [Google Scholar] [CrossRef] - Abdollahzadeh, M.; Esmaeilpour, M.; Vizinho, R.; Younesi, A.; Pàscoa, J.C. Assessment of RANS turbulence models for numerical study of laminar-turbulent transition in convection heat transfer. Int. J. Heat Mass Transf.
**2017**, 115, 1288–1308. [Google Scholar] [CrossRef] - Siavashi, M.; Jamali, M. Heat transfer and entropy generation analysis of turbulent flow of TiO
_{2}-water nanofluid inside annuli with different radius ratios using two-phase mixture model. Appl. Therm. Eng.**2016**, 100, 1149–1160. [Google Scholar] [CrossRef] - Ard, S.E.; Kiatkittipong, K. Heat transfer enhancement by multiple twisted tape inserts and TiO
_{2}/water nanofluid. Appl. Therm. Eng.**2014**, 70, 896–924. [Google Scholar] [CrossRef] - Fattahi, A. Numerical simulation of a solar collector equipped with a twisted tape and containing a hybrid nanofluid. Sustain. Energy Technol. Assess.
**2021**, 45, 101200. [Google Scholar] [CrossRef] - YousefiMiab, E.; Islami, S.B.; Gharraei, R. Feasibility assessment of using nanofluids in shell and tube heat exchanger of gas pressure reducing stations through a new developed OpenFOAM solver. Int. J. Heat Fluid Flow
**2022**, 96, 108985. [Google Scholar] [CrossRef] - Dbouk, T.; Habchi, C.; Harion, J.L.; Drikakis, D. Heat transfer and mixing enhancement by Poiseuille-Taylor-Couette flow between two rotating elliptically-deformed annular tubes. Int. J. Heat Fluid Flow
**2022**, 96, 109011. [Google Scholar] [CrossRef] - Upadhya, S.M.; Raju, S.V.S.R.; Raju, C.S.K.; Shah, N.A.; Chung, J.D. Importance of entropy generation on Casson, Micropolar and Hybrid magneto-nanofluids in a suspension of cross diffusion. Chin. J. Phys.
**2022**, 77, 1080–1101. [Google Scholar] [CrossRef] - Ghazanfari, V.; Taheri, A.; Amini, Y.; Mansourzade, F. Enhancing heat transfer in a heat exchanger: CFD study of twisted tube and nanofluid (Al
_{2}O_{3}, Cu, CuO, and TiO_{2}) effects. Case Stud. Therm. Eng.**2024**, 53, 103864. [Google Scholar] [CrossRef] - Sundar, L.S.; Mouli, K.V.V.C. Effectiveness and number of transfer units of plate heat exchanger with Fe
_{3}O_{4}–SiO_{2}/Water hybrid nanofluids: Experimental and artificial neural network predictions. Case Stud. Therm. Eng.**2024**, 53, 103949. [Google Scholar] [CrossRef] - Thirumalaisamy, K.; Sivaraj, R.; Reddy, A.S. Fluid flow and heat transfer analysis of a ternary aqueous Fe
_{3}O_{4}+ MWCNT + Cu/H_{2}O magnetic nanofluid in an inclined rectangular porous cavity. J. Magn. Magn. Mater.**2024**, 589, 171503. [Google Scholar] [CrossRef] - Hatami, M.; Jing, D. Nanofluids Mathematical, Numerical, and Experimental Analysis; Academic Press: Cambridge, MA, USA, 2020; ISBN 978-0-08-102933-6. [Google Scholar]
- Siadaty, M.; Kazazi, M. Study of water based nanofluid flows in annular tubes using numerical simulation and sensitivity analysis. Heat Mass Transf.
**2018**, 54, 2995–3014. [Google Scholar] [CrossRef] - Babu, J.A.R.; Kumar, K.K.; Rao, S.S. State-of-art review on hybrid nanofluids. Renew. Sustain. Energy Rev.
**2017**, 77, 551–565. [Google Scholar] [CrossRef]

**Figure 4.**Experimental validation of (

**a**) NTU at RPM = 0, (

**b**) pressure drop at RPM = 0 and (

**c**) NTU at RPM = 500.

**Figure 5.**3D streamlines in the double tube with different rotational speeds at Re

_{cf}= 2470 (

**a**) 0 RPM, (

**b**) 100, (

**c**) 300 RPM and (

**d**) 500 RPM.

**Figure 7.**Effectiveness variation for different types of nanofluids at different concentrations (ϕ).

**Figure 9.**Pressure drop of the double-tube heat exchanger as a function of the volume concentration and rotational speeds for different nanofluids.

**Figure 10.**Pressure drop of cold fluid in the double-tube heat exchanger at Re

_{cf}= 4946 and 500 RPM along tube.

**Figure 11.**Pumping power required by the double-tube heat exchanger in terms of the volume concentration for various rotational speeds at Re

_{cf}= 4946 (

**a**) Cu, (

**b**) Al

_{2}O

_{3}, (

**c**) Al

_{2}O

_{3}-Cu.

**Figure 12.**Ratio of average heat transfer and pumping power (

**a**) Al

_{2}O

_{3}, (

**b**) Al

_{2}O

_{3}-Cu, (

**c**) Cu.

**Table 1.**Classification of main studies from the literature according to the heat exchanger morphology and nanofluid employed.

Author | Heat Exchanger Morphology | Working Fluid | Main Results |
---|---|---|---|

Bahmani et al. [4] | Concentric tube | Al_{2}O_{3}-water | Increasing the maximum thermal efficiency and the average Nusselt number by 30% and 32.7%, respectively. |

Saeedan et al. [9] | Double-pipe helically baffled | Cu, CuO and carbon nanotube | The heat transfer coefficient and pressure gradient were increased. |

Kumar and Chandrasekar [14] | Double helically coiled tube | MWCNT-water | The Nusselt number increased by 20, 24 and 30% for 0.2, 0.4 and 0.6% concentrations. |

Murali et al. [24] | Trapezoidal twisted tape | Fe_{3}O_{4} | The heat transfer rate increased by 78.6%. |

Watel et al. [25] | Rotating finned tube | Air | The convection of heat transfer was enhanced due to the rotation for each spacing fin. |

Singh and Sarkar [27] | Tapered wire coils in a double tube | Al_{2}O_{3}-MgO hybrid nanofluid | The Nusselt numbers inreased by 84, 71 and 47%. |

Qi et al. [30] | Corrugated double tube | TiO_{2}-water | Improving the heat transfer rate by a 14.8% at 0.5% volume concentration and a higher pressure drop that increased by 6.5%. |

Chaurasia and Sarviya [31] | Double and single strip helical screw | CuO-water | The Nusselt number was enhanced by 182 and 170% with the nanofluid for the double and single screw tapes. |

Saedodin et al. [34] | Twisted turbulator | SiO_{2}, Al_{2}O_{3}, CuO and TiO_{2} | The use of the turbulator increased the heat transfer rate and the CuO-water nanofluid had a higher heat transfer than the other nanofluids. |

Bahiraei et al. [37] | Rotating coaxial tube with double twisted tapes | Graphene nanoplatelet (GNP) | Rotation of the tube improved the heat transfer coefficient and increased the pressure drop. |

Shi and Dong [38] | Rotating helical tube | Water | A decrease in entropy generation due to heat transfer and an increase in entropy generation due to flow friction. |

El-Maghlany et al. [39] | Rotating inner tube | Cu-water | NTU was increased by 51.4% and the exchanger effectiveness by 30.7% |

Moayedi [40] | Double rotating cylinders in a vented cavity | Cu-water | Heat transfer was enhanced when the cylinders rotated and the mean Nusselt number, when cylinders rotated, was enhanced by 331.95%. |

Ziyan et al. [41] | Rotating inner pipe with helical fins | Air | The Nusselt number for both fins and the rotation were enhanced by about 7.5 times compared to those with the stationary plain pipe. |

Siavashi and Jamali [46] | Annulus with different radius ratios | TiO_{2}-water | The performance increased with an increase in the Reynolds number at a radius ratio 0.2, 0.4 and 0.6 compared to that of 0.8. |

Ard and Kiatkittipong [47] | Multiple twisted tapes | TiO_{2}-water | Twisted tapes in counter arrangement had a higher thermal performance than that in co-counter. |

Fattahi [48] | Cylindrical pipe | Al_{2}O_{3}-CuO-water hybrid | The Nusselt number at ϕ = 0.02 and ϕ = 0.04 was increased by 23% and 20%. |

**Table 2.**Thermophysical properties of pure water and nanoparticles at an ambient temperature and atmospheric pressure.

Physical Properties | ρ (kg/m^{3}) | c_{p} (J/kg·K) | k (W/m·K) | $\mathit{\mu}$ (Pa·s) |
---|---|---|---|---|

Pure water [55] | 997.1 | 4179 | 0.6 | 0.001 |

Al_{2}O_{3} [55] | 3970 | 765 | 36 | - |

Cu [55] | 8933 | 385 | 385 | - |

**Table 3.**Thermophysical properties of nanofluids for different concentrations calculated from Equations (10)–(18).

Nanofluid Properties | $\mathsf{\varphi}$ = 1% | $\mathsf{\varphi}$ = 2% | $\mathsf{\varphi}$ = 3% | ||||||
---|---|---|---|---|---|---|---|---|---|

Al_{2}O_{3} | Cu | Al_{2}O_{3}-Cu | Al_{2}O_{3} | Cu | Al_{2}O_{3}-Cu | Al_{2}O_{3} | Cu | Al_{2}O_{3}-Cu | |

ρ (kg/m^{3}) | 1026.829 | 1076.45 | 1051.644 | 1056.558 | 1155.8 | 1106.188 | 1086.287 | 1235.1 | 1160.732 |

C_{p} (J/kg·K) | 4047 | 3864.19 | 3953.42 | 3922.43 | 3592.6 | 3750.09 | 3804.69 | 3358.39 | 3565.896 |

k (W/m·K) | 0.61729 | 0.6181 | 0.6180 | 0.6349 | 0.63656 | 0.63641 | 0.65289 | 0.6554 | 0.6551 |

$\mu $ (Pa·s) | 0.001025 | 0.001025 | 0.00102562 | 0.001050 | 0.001050 | 0.00105248 | 0.001075 | 0.001075 | 0.00108058 |

**Table 4.**Heat exchanger effectiveness as a function of the Reynolds number and rotational speed. Results for water and Cu-water at ϕ = 3%.

Water | $\mathbf{\text{Cu-Water}}\mathbf{at}\mathsf{\varphi}$ = 3% | |||||
---|---|---|---|---|---|---|

Reynolds Number | ε (0 RPM) | ε (500 RPM) | Δε | ε (0 RPM) | ε (500 RPM) | Δε |

2473 | 0.247 | 0.317 | 0.070 | 0.275 | 0.371 | 0.096 |

3092 | 0.275 | 0.350 | 0.075 | 0.316 | 0.412 | 0.096 |

3712 | 0.306 | 0.373 | 0.067 | 0.346 | 0.449 | 0.103 |

4331 | 0.329 | 0.410 | 0.081 | 0.382 | 0.487 | 0.105 |

4946 | 0.353 | 0.436 | 0.083 | 0.401 | 0.499 | 0.098 |

10,500 | 0.370 | 0.439 | 0.069 | 0.425 | 0.517 | 0.092 |

14,000 | 0.426 | 0.499 | 0.073 | 0.461 | 0.537 | 0.076 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mohamed, M.A.E.-M.; Meana-Fernández, A.; González-Caballín, J.M.; Bowman, A.; Gutiérrez-Trashorras, A.J.
Numerical Study of a Heat Exchanger with a Rotating Tube Using Nanofluids under Transitional Flow. *Processes* **2024**, *12*, 222.
https://doi.org/10.3390/pr12010222

**AMA Style**

Mohamed MAE-M, Meana-Fernández A, González-Caballín JM, Bowman A, Gutiérrez-Trashorras AJ.
Numerical Study of a Heat Exchanger with a Rotating Tube Using Nanofluids under Transitional Flow. *Processes*. 2024; 12(1):222.
https://doi.org/10.3390/pr12010222

**Chicago/Turabian Style**

Mohamed, Mohamed A. El-Magid, Andrés Meana-Fernández, Juan M. González-Caballín, Anthony Bowman, and Antonio José Gutiérrez-Trashorras.
2024. "Numerical Study of a Heat Exchanger with a Rotating Tube Using Nanofluids under Transitional Flow" *Processes* 12, no. 1: 222.
https://doi.org/10.3390/pr12010222