Thermal performance of a new nanofluid containing biologically functionalized graphene nanoplatelets inside tubes equipped with rotating coaxial double-twisted tapes

International Communications in Heat and Mass Transfer 108 (2019) 104305

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Thermal performance of a new nanofluid containing biologically functionalized graphene nanoplatelets inside tubes equipped with rotating coaxial double-twisted tapes Mehdi Bahiraeia, Nima Mazaherib, Mehran Sheykh Mohammadic, Hossein Moayedid,e,

T

⁎

a

Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran c Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran d Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam e Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam b

A R T I C LE I N FO

A B S T R A C T

Keywords: Biologically produced nanofluid Rotating coaxial double-twisted tapes Heat transfer enhancement Swirl flow Energy efficiency Graphene nanoplatelets

This research attempts to investigate the benefits of utilizing two heat transfer enhancement methods simultaneously. These techniques include employing biological graphene-based nanofluid and using rotating coaxial double-twisted tapes (RCDTT) to enhance heat transfer inside tubes. Using the nanofluid is desirable such that at twisted ratio of 2.5 and rotational speed of 0 rpm, the heat transfer coefficient improves about 16.3% by increase of the concentration from 0 to 0.1%. Furthermore, higher rotational speed is suggested such that its increase from 0 to 900 rpm, at twisted ratio of 3.5 and concentration of 0%, causes a 77% increment in the heat transfer coefficient. Lower twisted ratios are also more effective for enhancing heat transfer rate. The rotational speed increment has the great impact on the pressure drop, such that a 34% increment in the pressure drop occurs with increasing the rotational speed from 300 rpm to 900 rpm at weight fraction of 0.075% and twisted ratio of 3.5. Owing to the more intense disturbances generated by greater rotational speeds, the particle residence time becomes greater leading to pumping power increment. The figure of merit for all the cases is higher than 1, which is an excellent outcome from energy efficiency viewpoint.

1. Introduction Today, rapid development of industrial heat transfer devices and consequently energy consumption intensification have led to design more efficient thermal systems, which can effectively reduce the value of wasted energy and lead to saving the energy. Recently, heat transfer enhancement methods (HTEMs) have been beneficial ways in order to enhance the overall efficiency of heat transfer devices and reduce their energy consumptions [1]. Use of these techniques in many industrial arenas and engineering situations such as heat exchangers, heat recovery in power planets, solar collectors, and so forth is a suitable route to increase the overall performances of such thermofluidic systems [2]. These techniques commonly consist of two main groups including passive and active. The passive approaches are based on changing configurations of devices and adding some extra instruments such as ribs, twisted tapes, wire coils etc. They improve flow mixing and result in the superior heat transfer rates without using any external power. Whereas, the active techniques require an extra power source to ⁎

increase flow mixing by mechanical aids such as utilizing suction and injection of working fluid, jet impingement, electrostatic field, fluid vibration, and so on [3–6]. In the last decade, several efforts have been made in order to apply the HTEMs in various thermal systems for different applications. Many researchers have conducted experimental and numerical investigations on these methods with the purpose of realizing the effects of them on different thermofluidic devices. One of the most effective passive methods is to use the swirl flow generators with the aim of improving flow mixing and reach greater heat transfer amounts. Among various swirl flow generators, twisted tapes are more promising owing to their low cost and simplicity [7]. Twisted tapes are made in various configurations and all of them are able to increase heat transfer efficiency by means of generating intense swirl flow and preventing thermal boundary layer development. An empirical study was performed by Ponnada et al. [8] on heat transfer efficiency of various kinds of the twisted tape. The authors compared thermal characteristics of the water within the circular tube fitted with three types of twisted tape including

Corresponding author at: Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail address: [email protected] (H. Moayedi).

https://doi.org/10.1016/j.icheatmasstransfer.2019.104305

0735-1933/ © 2019 Elsevier Ltd. All rights reserved.

International Communications in Heat and Mass Transfer 108 (2019) 104305

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improvement of a titania–water nanofluid in presence of rotating twisted tapes was empirically evaluated by Qi et al. [33]. They demonstrated that the combination of nanofluid and rotating twisted tapes leads to significant thermal performance with a 101.6% improvement. As is known, the key benefit of nanofluids is their greater thermal conductivity compared with traditional working fluids. The higher thermal conductivity of nanofluids emanates from the presence of nanoparticles which have great thermal conductivity. Therefore, employing the nanoparticles with higher thermal conductivity can significantly reduce thermal resistance and eventually, superior thermal efficiency is obtained. Among the various kinds of nanoparticles examined in the last two decades, graphene nanoplatelets have excellent thermal properties which make them great choice for use in nanofluids. So far, several investigations have been carried out on using graphenebased nanofluids with the goal of heat transfer enhancement in various heat transfer devices [34–39]. Sarafraz et al. [40] performed an experimental study on the thermal and frictional characteristics of a nanofluid containing the graphene nanoplatelets through a microchannel at various Reynolds numbers and heat loads. The findings indicated that the nanofluid increased the Nusselt number and heat transfer coefficient by about 80%. Furthermore, a minor increment in the friction coefficient and the pressure loss occurred that was attributed to the intensification of the frictional forces. Bahiraei et al. [41] investigated the thermal performance of a hybrid nanofluid having graphene nanoplatelets coated with platinum within the pipes equipped with single and double twisted tapes. They found that utilizing the nanofluid at higher concentrations leads to superior heat exchange amount accompanied with pumping power intensification. The authors also stated that the double twisted tape demonstrated greater performance compared to the single one. Heat transfer features of a hybrid nanofluid having graphene nanosheets and Fe3O4 nanoparticles through a straight tube were investigated by Askari et al. [42]. Their experimental results indicated that this kind of nanofluid in a straight pipe can improve the convection heat transfer coefficient around 14.5% at concentration of 1%. The heat transfer performance of a shell-tube heat exchanger working with graphene-based nanofluid was examined through experiments by Ghozatloo et al. [43]. It was found that utilizing the nanofluid leads to the thermal conductivity increment in comparison with the pure liquid. In addition, the nanofluid with concentration of 0.1% wt. caused an around 35.6% increment in the heat transfer coefficient. As can be noticed, the available literature about utilizing both swirl flow generators and graphene based nanofluids simultaneously is sparse. Additionally, the studies on effects of employing rotating twisted tapes are also insignificant. Hence, the main purpose of this research is to evaluate the heat transfer and flow attributes of a novel environmentally friendly nanofluid containing graphene nanosheets through tube enhanced with coaxial double twisted tapes (RCDTT), which rotate inside the tube at different angular velocities. Based on the best knowledge of the authors, no investigations have been performed in this regard so far, and one of the main contributions of this work is to employ twisted tapes having rotational speed.

perforated twisted tape having alternate axis, perforated twisted tape and conventional twisted tape with different twisted ratios. It was observed that the heat exchange amount in the tubes equipped with the perforated twisted tape having alternate axis, perforated twisted tape and common twisted tape increased about 48%, 44% and 33%, respectively. Samruaisin et al. [9] researched the thermal and frictional features of a pipe enhanced with regularly spaced quadruple twisted tape. It was found that the full length quadruple twisted tape illustrated higher heat exchange amount in comparison with the spaced quadruple twisted tape, whereas led to greater pressure drop. The findings indicated that the full length twisted tape causes more intense cross flow than spaced one, and this results in greater heat exchange amount. The hydrothermal attributes of the heat exchanger pipe equipped with multiple twisted tapes were studied empirically and computationally by Piriyarungrod et al. [10]. The obtained results demonstrated that utilizing the multiple twisted tape results in greater heat exchange amount than the single twisted tape. Nakhchi and Esfahani [11] performed a numerical research in order to study the effects of twisted tape with various cut shapes inside a circular pipe. The outcomes revealed that utilizing the cut shaped twisted tapes can considerably improve the flow mixing and enhance the heat exchange as well as friction factor. They also reported that the impact of cut shaped twisted tapes on heat exchange and pressure loss is basically dependent on the cut ratio. Saysroy and Eiamsa-ard [12] studied the hydrothermal features of a tube equipped with multichannel twisted tapes. Their study was conducted for water at both turbulent and laminar flow conditions. The authors reported that the multichannel twisted tape creates the multi swirling flows and intensifies the mixing of flow, which enhances the heat transfer performance in comparison with the empty tube. The flow and heat transfer characteristics of a new type of twisted tape, namely coaxial cross twisted tape, were investigated by Liu et al. [13]. They illustrated that this type of twisted tape is able to improve the heat transfer significantly by means of generating strong swirl flows and reduce the boundary layer thickness. They reported that the Nusselt number of the pipe equipped with coaxial twisted tape enhanced about 151–192% in comparison with the convectional twisted tape. Another way to improve the efficiency of thermal devices is to change working fluid with a fluid having higher thermal conductivity. Nanofluids, which recently receive great attention from researchers can make this goal [14–18]. Because of poor thermal conductivity of the traditional working fluids, employing appropriate nanofluids can beneficially improve the heat transfer characteristics due to great thermal conductivity which significantly decreases the thermal resistance. In the last few years, number of investigations in this regard has grown, and several scholars have conducted numerical and experimental investigations in order to figure out the merit of utilizing nanofluids in different thermal equipment [19–29]. Some of these contributions have concentrated on application of nanofluids in channels equipped with twisted tapes. Eiamsa-ard and Wongcharee [30] experimentally studied the heat transfer improvement of silver–water nanofluid in a microfine pipe in presence of non-uniform twisted tapes. The authors concluded that both of the heat exchange amount and pumping power increase with the addition of more nanoparticles to pure fluid as well as reducing the twisted ratio of the twisted tapes. Syam Sundar et al. [31] experimentally researched thermal performance of alumina–water nanofluid through the solar flat plate collector equipped with twisted tapes. They reported a 21% increment in the heat exchange amount by utilizing nanofluid with concentration of 0.3% at Reynolds number of 13,000, and also about 50% improvement was observed for the twisted tape with twisted ratio of 5. The thermofluidic features of a Cu–water nanofluid inside the plain pipe enhanced with twisted tapes were studied through experiments by Khoshvaght-Aliabadi and Eskandari [32]. It was observed that the heat exchange rate enhances by use of twisted tapes, while further improves using both twisted tapes and nanofluid such that the overall enhancement ratio improved 87% in presence of twisted tape and nanofluid at concentration of 0.3%. Heat transfer

2. Definition of geometry and nanofluid In this paper, the rotating coaxial double twisted tapes (RCDTT) with different twisted ratios (λ = 2.5, 3 and 3.5) and rotational speeds (ω = 0, 300, 600 and 900 rpm) are employed inside the circular tubes in the case of using a biologically produced graphene-based nanofluid. The coaxial double twisted tape consists of the two conventional twisted tapes which are perpendicular to each other. Fig. 1a illustrates the isometric view of the pipe equipped with the coaxial double twisted tape, whereas Fig. 1b shows the geometric parameters of the configuration under study. It should be noted that the parameter λ represents the twisted ratio and is defined as the ratio of tape pitch (p) to tape width (w). Moreover, the value of the tape thickness (δ) is considered 2

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Fig. 1. Configuration under study: a) isometric view, b) geometric variables.

including steady flow and heat transfer, homogeneous fluid, incompressible flow and neglecting natural convection and thermal radiation. Furthermore, the single phase method is applied for simulating the nanofluid flow in this study since this approach decreases the computations time with a reasonable accuracy [45]. Considering these considerations, the governing equations can be regarded as follows [46]: Mass equation:

0.8 mm. To reduce the thermal resistance of the coolant to achieve higher heat transfer rate, a biologically produced nanofluid containing graphene nanoplatelets (GNPs) is utilized in which the GNPs are functionalized using clove buds. Sadri et al. [44] synthesized the nanofluid via this approach and reported its great stability. In order to better realize this preparation method, a brief explanation of the preparing technique applied by Sadri et al. [44] is presented here. With the goal of improving the stability of GNPs inside the polar solvents, Sadri et al. [44] presented a biological method which is based on dried clove buds. Initially, the clove extract was prepared and then, the functionalization process was conducted. The preparation of the clove extract was started by adding 15 g of cloves into distilled water at temperature of 80 °C. The preparation scheme of clove extract is presented in Fig. 2a. In the next step, the solution was homogenized, and the functionalization process was carried out in which 5 g of GNPs were added into 1000 ml of clove extract and were blended for 15 min. After that, 25 ml of hydrogen peroxide was added into the solution and the main parts of the cloves such as the β-caryophyllene, eugenol, and eugenyl acetate were grafted into the GNPs. Fig. 2b illustrates the first reactions of the free radical grafting, while Fig. 2c depicts the formation of the clove functionalized graphene nanoplatelets (CGNPs) via the free radical grafting. The achieved mixture was ultrasonicated about 10 min and then heated. In the following, the solution was centrifuged at 14,000 rpm and then was dried. Finally, the obtained sample (i.e., clove treated GNPs powder) was dispersed into distilled water at various concentrations. The morphology of the CGNPs is presented in Fig. 3a by the transmission electron microscopy (TEM) image. The edge defects and wrinkles of the CGNPs are evident from this figure. Moreover, it was demonstrated that this technique provides high stability for the nanofluid, which is shown in Fig. 3b for different concentrations. It was reported that the maximum sedimentation value is around 10.4% at concentration of 0.075%.

∂ui =0 ∂x i

(1)

Momentum equation:

∂ (ρnf ui uj ) ∂x i

=−

∂P ∂ ⎧ + μ ∂x i ∂x j ⎨ nf ⎩

⎛ ∂ui + ∂uj ⎞ ⎫ + ∂ (−ρ u ′ u′ ) ⎜ ⎟ nf i j ∂x i ⎠ ⎬ ∂x j ⎝ ∂x j ⎭

(2)

Energy equation:

∂ (ui T ) ∂ ⎧ ∂T ⎫ = (Γ + Γt ) ∂x i ∂x j ⎨ ∂ xj ⎬ ⎩ ⎭

(3)

In the abovementioned equations, the symbols P, u and T respectively indicate the pressure, velocity and temperature. Moreover, μ and ρ demonstrate viscosity and density, respectively. It should be noted that the subscript nf denotes the nanofluid. Besides, Γt and Γ respectively are the turbulent thermal diffusivity and molecular thermal diffusivity, and can be calculated as below [47]:

Γt =

Γ=

3. Governing equations

μt , nf ρnf Prt

(4)

μnf ρnf Pr

(5)

where Pr is the Prandtl number. Modeling of turbulent flow in this research is performed via the RNG k–epsilon model which is the appropriate model to consider the effects of swirl flows and rotational flows with reasonable computations time. The model equations including the Turbulent Kinetic Energy (TKE) equation and turbulent energy dissipation equation are presented in the following [47]: Turbulent kinetic energy equation (k):

The 3D models of tubes equipped with rotating coaxial double twisted tapes are initialized and analyzed via the finite volume method. The numerical simulations are performed with the aim of solving the governing equations and characterizing the heat transfer and flow attributes of the nanofluid in such a configuration. It should be noted that some assumptions are considered through the present analysis 3

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Fig. 2. (a) Preparation of clove extract, (b) first reactions of free radical grafting, (c) formation of clove functionalized GNPs via free radical grafting [44]. Reprinted with permission from Elsevier.

∂ (ρnf kui ) ∂x i

=

∂ ⎛ ∂k ⎞ ⎜αk μeff ⎟ + G k− ρε ∂x i ⎝ ∂x j ⎠

∂ (ρnf εui ) ∂x i

(6)

Turbulent energy dissipation equation (ε):

=

∂ ⎛ ∂ε ⎞ ε ε2 (Gk ) − C2ε ρnf − Rε ⎜α ε μeff ⎟ + C1ε ∂x j ⎝ ∂x j ⎠ k k

(7)

In the aforesaid relations, the generation rate of TKE is indicated by Gk that is dependent on velocity gradients, and can be determined as follows: 4

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quantities are presented in below:

C1ε = 1.42, C2ε = 1.68, Cμ = 0.0845, αk = 1.39, αε = 1.39 To enhance the precision of the current turbulent model, the enhanced wall treatment technique is employed for near wall modeling. Actually, this approach is a combination of enhanced wall function and two-layer model, which can provide higher accuracy near the wall. In this study, the thermal and frictional phenomena are evaluated via using following non-dimensional parameters: Nusselt number:

Nu =

hD β

(11)

Prandtl number:

ν Γ

Pr =

(12)

Reynolds number:

ρuDeff

Re =

μ

(13)

In these relations, Deff is the tube effective diameter, h is convective heat transfer coefficient, β is thermal conductivity, and ν is the kinematic viscosity. Friction factor [48]:

f=

2ΔP Deff ρu2 L

(14)

where L is tube length. The Figure of Merit (FoM) parameter is employed with the aim of evaluating the efficiency of utilizing the rotating twisted tapes compared to the static twisted tapes. In this paper, this parameter is defined as below [49]:

( (

NuRotating

FoM = Fig. 3. (a) The TEM image of CGNPs, (b) stability of the CGNP–water nanofluid for different concentrations [44]. Reprinted with permission from Elsevier.

Gk = −ρui′ u′j

(8)

Moreover, μeff and μt respectively denote the effective viscosity and turbulent viscosity, which can be determined by the following expressions [47]:

μeff = μnf + μt , nf μt = ρCμ

NuStatic

)

1/3

fStatic

)

(15)

Actually, this parameter considers the ratio of heat transfer improvement over friction factor intensification at an invariant pumping power, which can demonstrate a good viewpoint of energy efficiency. Moreover, the required pumping power is calculated from the following expression [50]:

∂uj ∂x i

fRotating

Ẇ = V̇ ΔP

(16)

in which V̇ is the volumetric flow rate.

(9)

3.1. Nanofluid properties

k2 ε

(10)

In each mathematical modeling, the accuracy of prediction is of major importance [51–55]. Thermophysical properties of the environmentally friendly GNP–water nanofluid are obtained from the experimental results of Sadri et al. [44]. In fact, the reported data from the experiments are modeled through the mathematical functions,

where Cμ is a constant. It should be mentioned that the inverse effective turbulent Prandtl number for ε and k is respectively denoted by αε and αk. The constants which are used in the model equations as well as their

Table 1 The mathematical models of the thermophysical properties for the GNP–water nanofluid. φ (%)

Density (kg/m3)

Specific heat (J/kgK)

Thermal conductivity (W/mK)

Viscosity (kg/ms)

0

− 0.299T + 1085.9 (Error = 0.02%)

0.390785T + 4024.3 (Error = 0.006%)

0.001720T + 0.088392 (Error = 0.16%)

57088068189526.9 × T −6.78787530 (Error = 0.82%)

0.025

− 0.302T + 1086.9 (Error = 0.02%)

0.303262T + 4031.8 (Error = 0.01%)

0.002490T − 0.117917 (Error = 0.1%)

3182747598404320 × T −7.48673854 (Error = 1.17%)

0.075

− 0.3T + 1086.5 (Error = 0.02%)

0.549938T + 3929.3 (Error = 0.007%)

0.003835T − 0.480637 (Error = 0.4%)

224642464502279 × T −7.02097292 (Error = 1.07%)

0.1

− 0.3T + 1086.6 (Error = 0.021%)

0.390920T + 3961.2 (Error = 0.01%)

0.004643T − 0.693898 (Error = 0.17%)

259261195184927 × T −7.04218680 (Error = 0.8%)

5

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which are listed in Table 1. These models are used in the analyses with the goal of solving the governing equations. Moreover, the mean deviation between the values predicted by the functions and those obtained from the experiments is presented below each function in Table 1. 3.2. Boundary conditions The nanofluid enters via the inlet of tubes enhanced with RCDTT with uniform temperature as well as uniform velocity. The inlet temperature of nanofluid is considered 300 K and the inlet velocity is measured via the Reynolds number. The boundary condition at the tube outlet is considered zero relative pressure. Besides, the no-slip condition and constant heat flux is applied on the tube wall. The entire conditions for all the boundaries are presented as mathematical form in the following: At the tube entrance: uz =

Re μnf ρnf Deff

, ux = uy = 0, T = 300K.

At the tube outlet: Poutlet = Patmosphere. ∂T At the tube wall: ux = uy = uz = 0, − β ⎡ ∂r ⎤ = q″. ⎣ ⎦ For the coaxial double-twisted tape: angular velocity = ω0. 4. Numerical method and validation This study assesses the hydrothermal characteristics of the tubes equipped with RCDTT by solving the governing partial differential equations using the numerical method which is based on the control volume method. The pressure-based solver is selected and pressure–velocity coupling is conducted via the SIMPLE technique. Furthermore, all equations are solved by employing second-order method. It is noteworthy that the solutions are assumed to be converged when the residuals reach 10−6 for all variables. 4.1. Grid check Fig. 4. Grid tests results: a) pressure drop, b) wall temperature.

Different grids are evaluated to eliminate the effects of mesh size sensitivity and obtain an optimum cell number. The test model consists of the pipe equipped with RCDTT with twisted ratio of 2.5 and rotational speed of 0 rpm. The base fluid is selected for performing the grid check, and constant heat flux is employed on the tube wall. Two parameters including the pressure loss and wall temperature are considered as the grid test criteria. Fig. 4 displays the grid independency results. As is clear, the difference between mesh including 2.2 × 106 cells and that having 2 × 106 cells is minor. Hence, the grid having 2 million cells is chosen as optimum mesh for conducting main analyses.

Table 2 Comparison between Nusselt number obtained from Eiamsa-ard et al. [56] and those achieved via current study.

4.2. Validation To ensure the validity of the present computational approach, the obtained results are compared with those reported through the experimental work performed by Eiamsa-ard et al. [56]. In this validation, the Nusselt number of a pipe equipped with single twisted tape at twisted ratio of 3 is compared with the experimental results. Table 2 lists the Nusselt number for different Reynolds numbers in the cases of both present results and those reported by Eiamsa-ard et al. [56]. It is found that the maximum deviation is less than 6%. Hence, the present numerical method has a reasonable precision and the numerical outcomes are reliable.

Re

Eiamsa-ard et al.

Present study

Error [%]

3788 5037 6332 7627 8830 10,125 11,328 12,623 13,871 15,167 16,462 17,711 18,960 20,209

59.97 68.96 77.31 85.65 92.70 102.99 111.34 120.97 129.32 137.02 146.01 154.35 165.93 172.98

61.53 72.70 80.47 90.30 96.70 107.67 115.98 126.26 134.48 143.70 153.73 162.50 172.69 181.35

2.60 5.42 4.09 5.44 4.31 4.55 4.17 4.37 4.00 4.88 5.29 5.28 4.07 4.84

numerical simulations are performed for various twisted ratios, namely 2.5, 3 and 3.5. It should be mentioned that the numerical analyses are carried out at constant Reynolds number of 5000, and invariant heat flux of 200,000 W/m2 is employed on the tube wall. The results consist of local and global assessments which can provide a comprehensive view of hydrothermal attributes. Fig. 5 shows the local convection heat transfer coefficient along the pipe enhanced with RCDTT for different twisted ratios, concentrations and rotational speeds. Clearly, the variation of the heat transfer coefficient along the tube is irregular for all cases because of changes in the flow pattern and variation of the turbulence level along the tube. In

5. Results and discussion This study concentrates on the heat transfer and fluid flow attributes of an environmentally friendly nanofluid having graphene nanosheets through a pipe fitted with rotating coaxial double twisted tape at various nanoparticle weight concentrations of 0, 0.025, 0.075 and 0.1%. Moreover, the rotational speed changes from 0 to 900 rpm, and the 6

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Fig. 5. Local convection heat transfer coefficient along the pipe equipped with RCDTT for different twisted ratios, rotational speeds and concentrations.

Fig. 7. Temperature contours at various cross sections as well as velocity vectors at weight fraction of 0.025% and twisted ratio of 3 for: a) ω = 0 rpm, b) ω = 900 rpm.

magnified on Fig. 7). On the other hand, increasing the rotational speed causes higher turbulence kinetic energy because of mean velocity gradient increment. This can effectively enhance the heat transfer coefficient and decrease the boundary layer thickness. Fig. 8 shows the contours of turbulence kinetic energy at z = 280 mm, concentration of 0% and twisted ratio of 2.5 for various angular velocities. As is clear, the turbulence kinetic energy level in the condition of grater rotational speed is considerably

Fig. 6. Nusselt number at weight fraction of 0% and twisted ratio of 3.5 for: a) ω = 0 rpm, b) ω = 900 rpm.

fact, the flow mixing intensity varies by change in longitudinal direction such that the convective heat transfer coefficient increases along the tube (except tube entrance). Moreover, greater rotational speed results in greater heat transfer coefficient, which can be attributed to the generation of more significant swirl flow and superior flow mixing. Fig. 6 depicts the Nusselt number at weight fraction of 0% and twisted ratio of 3.5 for different rotational speeds. As is obvious, the trend of Nusselt number is not uniform along the tube and has an intermittent trend. This occurs due to stronger impingement of the flow to the wall in the twisted tape corners. Furthermore, the impact of rotational speed on the Nusselt number is severe such that by the increment of the rotational speed, the Nusselt number is greatly enhanced. As seen, by rising the rotational speed, the convective heat transfer coefficient significantly enhances. Fig. 7 illustrates the temperature contours for five different cross sections of the pipe enhanced with the RCDTT at weight fraction of 0.025% and twisted ratio of 3 for different rotational speeds. Moreover, the velocity vectors at z = 150 mm are highlighted in this figure. As can be understood, the higher rotational speed causes more intense flow mixing and stronger swirl flow, which prevent the thermal boundary layer growth. Consequently, lower wall temperature and more uniform temperature distribution are obtained, which result in the greater convection heat transfer coefficient. As highlighted in this figure, more intense disruption of the thermal boundary layer is seen for the higher rotational speed such that in this case, the thermal boundary layer does not grow even near the tube outlet, whereas in the condition of smaller angular velocity, the thermal boundary layer grows near the tube inlet (this phenomenon has been

Fig. 8. Contours of turbulence kinetic energy at cross section of z = 280 mm, weight fraction of 0% and twisted ratio of 2.5 for: a) ω = 300 rpm, b) ω = 900 rpm. 7

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Fig. 9. Temperature profiles at z = 260 mm and twisted ratio of 3.5 for various weight fractions.

greater especially near the wall, which causes the higher convective heat transfer coefficient. Another key point from Fig. 5 is the impact of the weight fraction on the convection heat transfer coefficient. As can be seen from this figure, higher concentration leads to greater convective heat transfer coefficient which is owing to larger thermal conductivity of the nanofluid that reduces the thermal resistance significantly. Fig. 9 presents the temperature distributions at z = 260 mm, twisted ratio of 3.5 and ω = 0 rpm for various concentrations. As can be seen, in the case of higher concentration, the temperature distribution is more uniform and the wall temperature is smaller, which reveals higher cooling performance. In addition, the magnitude of Average Absolute Deviation (A.A.D) for both the temperature profiles is reported in Fig. 9. In fact, when the A.A.D possesses lower value, the temperature profile will be more uniform. In the case of Fig. 9, the A.A.D is found 5.3 at concentration of 0.1%, while that related to the base fluid is 6, which confirms the more uniform temperature distribution at the higher concentration. The influence of the twisted ratio on the convective heat transfer coefficient is also evident from Fig. 5. Regarding this figure, the convective heat transfer coefficient increases with the twisted ratio reduction. This occurs owing to greater flow disturbances caused by lower twisted ratios. To better understand the differences between different twisted ratios, Fig. 10 illustrates the temperature contours and velocity vectors at cross section of z = 150 mm for concentration of

Fig. 11. Average convection heat transfer coefficient as a function of the weight fraction for all the conditions under investigation.

0.075% and ω = 0 rpm at various twisted ratios. Clearly, the superior flow impingement to the wall occurs in the condition of lower twisted ratio, and the wall temperature is smaller as well. More intense impingement of the flow to the wall can disturb the thermal boundary layer and decrease the temperature gradients. As a consequence, the wall temperature reduces, which leads to higher convective heat transfer coefficient. Fig. 11 illustrates the average convection heat transfer coefficient in terms of the concentration for all the cases under study. Evidently, the convective heat transfer coefficient has increasing trend versus the weight fraction for all the conditions. This is an excellent result because demonstrates the merit of utilizing the nanofluid, which causes the improvement of the convection heat transfer. For example, at twisted ratio of 2.5 and ω = 0 rpm, the convection heat transfer coefficient improves about 16.3% with the increment of the weight fraction from 0 to 0.1%. As per Fig. 11, the angular velocity has a significant impact on the average convection heat transfer coefficient such that a 77% enhancement in this parameter is obtained with increasing the angular velocity from 0 to 900 rpm at twisted ratio of 3.5 and φ = 0%. This result reveals the great influence of the rotational speed on the convection heat transfer, which emanates from the more intense swirl flows and more profound boundary layer perturbation at the greater rotational speeds. In the other words, higher convective heat transfer coefficient demonstrates the better cooling performance, which leads to smaller wall temperature. Figs. 12 and 13 respectively illustrate the velocity vectors and temperature contours at φ = 0% and twisted ratio of 3.5 for different rotational speeds. As is obvious from these two figures, the cross flows in the condition of larger angular velocity are stronger, which lead to lower wall temperature and enhance the heat transfer capability of the working liquid. In fact, as the rotational speed increases, more axial flow is converted into swirl flow and thus, the hot flow near the wall visits core region while the cold flow inside the central region visits the hot wall and therefore, the higher cooling performance is obtained. In order to better clarify the rotational speed impact on the wall temperature, the isotemperature surfaces of the flow at φ = 0.025% and twisted ratio of 3 for different rotational speeds are displayed in Fig. 14. Indeed, these surfaces illustrate the areas of the nanofluid flow with temperature equal to 306 K. As is clear, in the condition of lower angular velocity, the area having temperature of 306 K remains up to a larger distance from the tube inlet because the flow mixing is poorer and thus, the heat reaches from the tube wall to the central region with a higher delay. However, for higher rotational speed, the nanofluid flow can receive heat more efficiently and the area with temperature of

Fig. 10. The temperature contours and velocity vectors at cross section of z = 150 mm, rotational speed of 0 rpm and weight fraction of 0.075% for: a) λ = 3.5, b) λ = 2.5. 8

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With respect to Fig. 11, the effect of the twisted ratio on the convection heat transfer coefficient becomes insignificant at the greater angular velocities. This can be attributed to the presence of the excessive turbulence at the greater angular velocity, which reduces the impact of the twisted ratio. Although employing the RCDTT having high rotational speeds and utilizing the nanofluid with high concentrations increase the convention heat transfer, this improvement is accompanied with the pressure drop increment which is a crucial disadvantage. The pressure drop is an important parameter because determines the power required for transferring the fluid. Table 3 presents the pressure loss for all the conditions under investigation. As can be noticed, adding more nanoparticles into the base fluid considerably augments the pressure drop. For example, at twisted ratio of 3 and rotational speed of 300 rpm, the pressure drop increases around 13% by increase of the concentration from 0 to 0.1%. The reason is the viscosity increment of the nanofluid at larger concentrations, which can adversely affect the wall shear stress and cause more pressure drop. Based on Table 3, the influence of the twisted ratio on the pressure drop is evident. As is clear, the pressure loss is augmented by decrease of the twisted ratio. It can be attributed to the greater velocity gradients at lower twisted ratios, which consequently lead to increment of wall shear stress. Fig. 15 displays the contours of the wall shear stress at concentration of 0.025% and ω = 0 rpm for various twisted ratios. Regarding this figure, the wall shear stress augments at the lower twisted ratio, which can intensify the pressure drop. As can be understood from Table 3, the impact of the rotational speed on the pressure loss increment is severe such that about 34% increment in the pressure drop occurs with increasing the rotational speed from 300 rpm to 900 rpm at φ = 0.075% and twisted ratio of 3.5. This is owing to longer path of the fluid particles in the case of larger angular velocity. As the angular velocity intensifies, the path of the particles becomes longer and this phenomenon causes higher residence time for the particles. In fact, greater angular velocity forces the particles to flow in more circular patterns and the path changes become more intense. Fig. 16 illustrates the flow pathlines at φ = 0% and twisted ratio of 3.5 for different rotational speeds. As is obvious, greater angular velocity significantly changes the flow direction and forces the flow to turn around the tube, which results in longer path of the flow. Fig. 17 illustrates the particle residence time at concentration of 0% and twisted ratio of 3.5 for various angular velocities. For drawing this figure, the analysis is conducted by injecting 100 particles inside the flow domain at the tube inlet. These particles are injected at the central line in x direction. With respect to this figure, higher rotational speed leads to residence time increment and the more non-uniform residence time distribution. This demonstrates that the higher rotational speed changes the path of the particles significantly, and increases the pressure drop as well. Considering the viewpoint of energy efficiency, an important parameter which must be evaluated in order to design more effective heat transfer equipment is pumping power which is completely related to pressure drop. Fig. 18 shows the pumping power for different cases under study. It is perceived that the increases of the concentration and angular velocity augment the pumping power, while reducing the twisted ratio leads to greater pumping power. As mentioned before, increasing the concentration augments the nanofluid viscosity and results in greater pressure drop which causes higher pumping power. For example, about 20% increment in the pumping power is obtained with the increase of the weight fraction from 0 to 0.1% at twisted ratio of 3.5 and rotational speed of 600. Meanwhile, the pumping power increment in the cases of both twisted ratio decrement and rotational speed increment is due to the higher pressure drop caused by more intense velocity gradients which was discussed before. As can be stated, employing RCDTT with low twisted ratio and high angular velocity and also increasing the nanofluid concentration result

Fig. 12. Velocity vectors at φ = 0% and twisted ratio of 3.5 for: a) ω = 0 rpm, b) ω = 900 rpm.

Fig. 13. Temperature contours at φ = 0% and twisted ratio of 3.5 for: a) ω = 0 rpm, b) ω = 900 rpm.

Fig. 14. Iso-temperature surfaces at φ = 0.025% and twisted ratio of 3 for: a) ω = 300 rpm, b) ω = 900 rpm.

306 K disappears faster. It is noteworthy that when the heat reaches the central region faster, the wall experiences a more significant temperature reduction. 9

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Table 3 Pressure loss [Pa] for all the conditions under investigation. φ [%]

0 0.025 0.075 0.1

ω=0

ω = 300 rpm

ω = 600 rpm

ω = 900 rpm

λ = 2.5

λ=3

λ = 3.5

λ = 2.5

λ=3

λ = 3.5

λ = 2.5

λ=3

λ = 3.5

λ = 2.5

λ=3

λ = 3.5

377.6 402.6 409.1 428.2

296.0 315.3 320.7 335.8

248.9 264.8 269.6 282.3

394.3 418.4 425.7 444.7

317.2 335.9 342.0 357.1

273.3 288.5 294.0 306.8

434.2 459.5 467.4 487.8

360.9 380.5 387.5 403.9

317.7 336.2 342.5 356.7

477.2 502.6 511.1 532.2

407.0 428.6 436.2 453.2

368.9 386.7 393.6 409.5

Fig. 15. Wall shear stress at concentration of 0.025% and ω = 0 rpm for: a) λ = 3.5, b) λ = 2.5.

Fig. 18. Required pumping power for different twisted ratios, concentrations and rotational speeds.

Fig. 16. Pathlines at φ = 0% and twisted ratio of 3.5 for: ω = 0 rpm, b) ω = 300 rpm. Fig. 19. FoM parameter for all cases under study.

in great convective heat transfer coefficient and improve the cooling efficacy while cause pumping power intensification. Considering the viewpoint of energy efficiency, great pumping power is an adverse parameter whereas heat transfer enhancement is a desired outcome. In order to achieve the optimal condition and realize the overall effect of the rotational speed, concentration and twisted ratio, the FoM parameter is presented in Fig. 19. Clearly, the magnitude of the FoM is larger than 1 for all the conditions, which shows the merit of employing both the nanofluid and rotating twisted tape. Moreover, increasing the rotational speed significantly augments the value of the FoM, which means that with increase of the rotational speed, the pumping power increment is insignificant in comparison with the heat transfer enhancement. This phenomenon manifests the great advantageous of utilizing RCDTT in the tubes. Moreover, the maximum value of FoM is 1.59, which occurs at rotational speed of 900 rpm, φ = 0.025% and

Fig. 17. Particle residence time at concentration of 0% and twisted ratio of 3.5 for various angular velocities.

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twisted ratio of 3.5. The minimum value of FoM is 1.02, which occurs at rotational speed of 300 rpm, φ = 0.075% and twisted ratio of 3. From the obtained results, it becomes evident that simultaneous deployment of the RCDTT and nanofluid contributes to significant enhancement in the convection heat transfer due to superior flow mixing and lower thermal resistance concurrently. It is found that utilizing lower twisted ratio, higher concentration and greater angular velocity lead to higher heat transfer coefficient, while increase the needed pumping power as well. Finally, for reaching the best condition based on the energy efficiency, employing the case with low concentration, high rotational speed and great twisted ratio is recommended.

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6. Conclusion 3D numerical analyses of the nanofluid containing the biologically functionalized GNPs inside the tubes equipped with the rotating coaxial double twisted tapes have been carried out. The obtained hydrothermal characteristics demonstrate great merit of employing the nanofluid as well as utilizing the RCDTT. The main and important outcomes attained in this investigation are presented in the following: - Utilizing this type of nanofluid rather than the pure liquid is recommended owing to significant improvement in the heat exchange amount accompanied with small pumping power intensification. - At twisted ratio of 2.5 and ω = 0 rpm, the convective heat transfer coefficient improves about 16.3% by the increase of the concentration from 0 to 0.1%. - Due to low concentration of the nanofluid, the pressure drop increment is insignificant, such that at twisted ratio of 3 and rotational speed of 300 rpm, the pressure drop intensifies around 13% by the increase of the concentration from 0 to 0.1%. - The higher viscosity of the nanofluid in comparison with its base liquid causes pumping power increment, for example, an about 20% increment in the pumping power occurs with the increase in the weight fraction from 0 to 0.1% at twisted ratio of 3.5 and rotational speed of 600. - Employing the twisted tapes with high rotational speeds is suggested because of creating the powerful swirl flows, more significant impingement of flow to the wall and extreme disturbance of the thermal boundary layer, which lead to superior heat exchange amount and higher values of the FoM. - By increasing the rotational speed from 0 to 900 rpm at twisted ratio of 3.5 and φ = 0%, an almost 77% improvement in the convective heat transfer coefficient is attained. - Because of more intense disturbances caused by greater rotational speeds, the fluid particles encounter the longer path, and the particle residence time becomes greater leading to pumping power increment. - The rotational speed increment has the great impact on the pressure drop, such that an about 34% increment in the pressure drop occurs with increasing the rotational speed from 300 rpm to 900 rpm at φ = 0.075% and twisted ratio of 3.5. - Using twisted tapes with lower twisted ratio results in greater heat exchange amount, whereas considerably augments the pressure drop because of higher velocity gradients. - The enhancement in heat transfer coefficient with the decrease of the twisted ratio becomes lower at larger angular velocities. - The trend of local heat transfer coefficient along the tubes is irregular because of the non-uniform turbulence level along the tube. - Employing smaller twisted ratios and larger rotational speeds leads to superior turbulence kinetic energy. References [1] M. Sheikholeslami, M.G. Bandpy, D.D. Ganji, Review of heat transfer enhancement methods: focus on passive methods using swirl flow devices, Renew. Sust. Energ.

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