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Backward-facing step heat transfer of the turbulent regime for functionalized graphene nanoplatelets based water–ethylene glycol nanofluids
International Journal of Heat and Mass Transfer 97 (2016) 538–546
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Backward-facing step heat transfer of the turbulent regime for functionalized graphene nanoplatelets based water–ethylene glycol nanofluids Ahmad Amiri a,⇑, Hamed Khajeh Arzani b,⇑, S.N. Kazi b,⇑, B.T. Chew b, A. Badarudin b a b
Chemical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran Department of Mechanical Engineering, University of Malaya, Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Article history: Received 24 November 2015 Received in revised form 6 February 2016 Accepted 16 February 2016
Keywords: Backward-facing step Heat transfer Turbulent Ethylene glycol Functionalization Graphene nanoplatelets
a b s t r a c t Herein, an experimental study on thermo-physical properties of ethylene glycol-functionalized graphene nanoplatelets/water–ethylene glycol nanofluids (EGGNP-WEG) and a numerical study on the convective heat transfer over a backward-facing step are performed. Accordingly, EGGNP was first synthesized covalently to achieve a stable colloidal solution in water–ethylene glycol mixture. Some characterizations were applied to analyze the surface functionality and morphology of EGGNP-flakes. To study the convective heat transfer coefficient in turbulent regime, a numerical study is performed at different weight fractions of EGGNP. According to the results, a higher weight concentration of EGGNP in basefluid indicates a greater extent of convective heat transfer coefficient and thermal conductivity, implying higher heat transfer rate over a backward-facing step. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The thermo-physical phenomena of separation and reattachment e.g. backward-facing step, involving heat transfer, are frequently encountered in many engineering problems like electrical rotating machines. Thus, investigation of the convection heat transfer over a backward facing step is one of the interest topics in many research studies. Heat transfer applications of backward facing step appear in different industrial equipment such as combustors, aircraft, gas turbine engines, and buildings. It is obvious that the separation and reattachment of the flow can change the flow structure and has a direct influence on the heat transfer mechanism as well as thermal performance of equipment [1]. Thus, numerous studies have been investigated to determine the real mechanism of flow separation and reattachment, the best geometry for heat transfer applications, and best type of working fluids in the past decades [2,3]. Although, the flow over a backward-facing step with heat transfer was investigated by some scientists [4,5], a majority of studies considered the isothermal flow, commonly in two dimensional geometry.
⇑ Corresponding authors. E-mail addresses: [email protected] (A. Amiri), [email protected], [email protected] (H.K. Arzani), [email protected] (S.N. Kazi). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.02.042 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
A study on the two non-Newtonian liquids was performed in a sudden expansion in the presence of viscoelastic polyacrylamide (PAA) solutions and a purely viscous shear-thinning liquid [6]. According to their results, the reattachment length of nonNewtonian fluid was shorter than that of Newtonian counterparts and surely water. Abu-Nada [7] performed a numerical study on the entropy over a backward facing step for different expansion ratios. Different expansion ratios of 1/4, 1/3, 1/2, 2/3, and 3/4 were selected and the results presented an increase in the Reynolds number with the value of total entropy generation number, which was for the high range of Reynolds number. A numerical study on the laminar regime in a rectangular duct including backwardfacing step was performed by Nie and Armaly [8]. They suggested the appearance of the maximum reattachment length at the sidewall. Also, they concluded that as the step height enhances, the amount of Nusselt number increases. Biswas et al. [9] investigated the laminar fluid flow behavior over a three dimensional backward-facing step with various expansion ratios. They concluded that the formation of wall jets at the side wall within the separating shear layer, formed by the spanwise of the velocity moves towards the symmetry channel plane. An experimental study have been done by Armaly et al. [10] for measuring the velocity over a backward-facing step by using two-component laser Doppler velocimeter in laminar regime. In another similar study, Hsieh et al. [11] studied the flow over a backward-facing
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step by the Direct Simulation Monte Carlo method (DSMC). According to their results, the side walls can significantly affect the flow structure and thermal characteristics in the 3-D structure. Bao and Lin [12] also utilized the DSMC approach for investigation of the thermal performance over the microscale backward-facing step in the transition regime. They reported that the streamwise velocity is positive at the Knudsen number of 0.136, indicating the lack of the reversed flow after the step. Also, they concluded that there is a non-linear connection between the mass flow rate and pressure drop ratio in traditional flow. As mentioned above, a majority of studies focused on having novelty in changing design such as expansion ratio, in particular in the laminar regime, and neglected thermo-physical properties of working fluid. Thus, as another novelty for improving heat transfer rate over a backward-facing step is the utilization of nanofluids. A combination of nanofluids with thermal conductivity and backward-facing step can result in an effective approach for enhancing the heat transfer rate. In addition, previous studies [13–16] showed that nanofluids made of the mixture of basefluids and nanoparticles with good thermal conductivity could enhance the thermal performance of the different heat transfer equipment. The main reason for increasing the thermal conductivity of basefluid loaded with nanostructures is attributed to the Brownian motion of the nanostructures suspended in the working fluid [17– 23]. Also, the formation of surface nanolayers can be another reason for enhancing the thermal conductivity [17]. The first study on the heat transfer rate of nanofluid in a backward-facing step was performed by Abu-Nada [1]. To reach the purpose, five nanofluids of CuO-, Al2O3-, Ag-, Cu- and TiO2-based water nanofluids were synthesized and convective heat transfer coefficient was investigated. He concluded that there is a direct connection between the Nusselt number and the volume fraction of nanoparticles in basefluids. As an important result, they demonstrated that Nusselt number is significantly dependent of the thermo-physical properties of the nanoparticles inside the recirculation zone. Mohammed et al. [24,25] investigated the influence of different nanofluids (8 nanofluids) on the mixed convective heat transfer over the vertical and horizontal backward-facing step. Their results showed that the nanofluids with secondary recirculation regions have lower Nusselt number and the diamond-based water nanofluid illustrated the maximum Nusselt number in the presence of primary recirculation region. Al-Aswadi et al. [26] showed that nanofluids with low dense nanoparticles demonstrate higher velocity than those with high dense nanoparticles. Kherbeet et al. [27] investigated the heat transfer behaviors of four types of nanofluids (Al2O3-, CuO-, SiO2- and ZnO-based water nanofluid) in the laminar regime over a microscale backward-facing step. The results showed the lack of recirculation region behind the step for all prepared samples at different concentrations. In addition, the results suggested that SiO2-based water nanofluid has the highest Nusselt number as compared with other nanofluids. In addition, the results showed that the amount of Nusselt number enhances with the increment of the volume fraction of the nanoparticles in the base fluid. Kherbeet et al. [28] performed a numerical study on the laminar mixed convection flow of nanofluids over a horizontal microscale forward-facing step (MFFS) using a finite volume method. Different nanofluids including SiO2-, Al2O3-, CuO-, and ZnO-based ethylene glycol nanofluids at various volume fractions investigated in terms of heat transfer parameters and the results demonstrated that the SiO2-based ethylene glycol nanofluid had the maximum Nusselt number. They also reported that the Nusselt number increases with decreasing nanoparticle density and diameter as well as increasing volume fraction of nanoparticles. It is obvious from the above literature review that the terms of thermal conductivity of nanoparticles was neglected. In addition, most of the previous studies on the backward-facing step involved
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metal- or metal oxide-based water or ethylene glycol as the basefluid and there is no study concentrated on nanofluids including carbon nanostructures. It is known that the thermal conductivity of most carbon particles such as carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) are much higher than that of metal or metal oxide nanoparticles. This implies that the carbon-base nanoparticle have higher potential for enhancing the thermal conductivity of base fluids [29]. Despite some promising thermal properties of graphene nanopleteles in the field of nanofluids, the strong van der Waals interactions have limited their thermal applications. Non-covalent and covalent functionalizations are the effective approaches to improve the dispersibility of GNPs. Also, there is not any study in water–ethylene glycol media over backward-facing step. Herein, three phases of study have been performed to investigate the heat transfer behavior of EG-treated GNP based water– EG coolants over a backward facing step. First, a promising and potentially industrially scalable functionalization approach is employed to prepare ethylene glycol-functionalized graphene nanoplatelets (EGGNP) and EGGNP based water–EG coolant (EGGNP-WEG). First phase followed by analyzing EG-treated GNP samples in terms of functionality and morphology. Second phase of study comprises of the experimental-evaluation of the thermo-physical, rheological and colloidal properties of EGGNPWEG. As the three phase of study, a numerical analysis on the heat transfer over a backward-facing step is performed in the presence of EGGNP-WEG at different weight concentrations. The main objective was to investigate the heat transfer enhancement and pressure drop in the presence of EGGNP in basefluid. The latter is obtained by the calculation of the performance index. 2. Material and methods 2.1. Preparation of EGGNP-WEG coolants To prepare EGGNP-WEG, anhydrous Aluminum Chloride (AlCl3) with purity of 99.999% was prepared from Sigma–Aldrich. All of the other chemicals were also bought from Sigma–Aldrich in analytical grade. Pristine Graphene Nanoplatelets (GNPs) with purity > 90 wt%, and Number of layer < 30 were purchased from Nanostructured & Amorphous Materials, Inc. The pristine GNP (0.5 g) and AlCl3 (9.27 g) were typically placed in a planetary ball-mill container and agitated with speed of 500 rpm for 1 h. The obtained mixture was poured into a vessel filled with 80 ml of anhydrous EG and then sonicated for 15 min with a probe-sonicator to reach a homogeneous back suspension. The concentrated hydrochloric acid (1 ml) was poured into the vessel over sonication time. After sonication, the suspension was transferred into a microwave (Milestone MicroSYNTH programmable microwave system) and heated for 15 min at 150 °C. The resultant mixture was filtered with a PTFE membrane and subsequently washed with abundant DI water to remove any unreacted materials. Filtration cake was then dried for 48 h at 50 °C and labeled as EGGNP. While the pristine GNP is not soluble in most organic solvents, the EGGNP was significantly soluble in both water and EG. The easily-miscible EG functionalities can explain a significant increase in dispersibility of the functionalized GNP with EG in both media of water and EG. To synthesize EGGNP-WEG coolants at different weight concentrations, the known amount of EGGNP was poured into a vessel filled with a mixture of water and EG with a volumetric ratio of 40:60 and sonicated with a probe-sonicator for 10 min. 2.2. Experimental equipment The prepared EGGNP was analyzed in terms of structure, morphology and thermo-physical properties. Fourier transform
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infrared spectroscopy, FTIR, (Bruker IFS 66/S), Raman spectroscopy (Renishaw confocal spectrometer at 514 nm), thermo-gravimetric analysis, TGA, (TGA-50 Shimadzu), and high-resolution transmission electron microscopy, TEM, (HT7700) were employed to analyze the main structure and morphology of the sample. Regarding thermo-physical properties, a differential scanning calorimeter (Perkin Elmer Diamond DSC) was applied for measuring the specific heat capacities of EGGNP-WEG. The thermal conductivity of EGGNP-WEG samples were obtained by a KD2 Pro-thermal analyzer (Decagon Devices, USA). Also, the rheological property of samples was measured by a Brook field rheometer (DVIII Ultra Rheometer), comprising a RTD temperature probe for monitoring the samples.
rk ¼ 1:00; re ¼ 1:30; C 1e ¼ 1:44; C 2e ¼ 1:92
C l ¼ 0:09;
ð7Þ To assess the effectiveness of EGGNP, a performance index (e) is selected as an appropriate parameter to clarify the range of temperature and velocity that can be used by the synthesized coolant:
e¼
hnf =hbf Rh ¼ DPnf DPbf RDP
ð8Þ
Rh is the ratio of the heat transfer enhancement of the new coolant (GNP-WEG) to the base-fluid and RDP is the ratio of pressure drop of synthesized coolant to the basefluid. 3.2. Physical model and assumptions
3. Numerical implementation The numerical method available in the commercial CFD package of ANSYS-Fluent, V15 has been used here. Fluent uses a finite volume approach to convert the governing partial differential equations into a system of discrete algebraic equations. As the discretization methods, a second-order upwind scheme is selected for the momentum, turbulent kinetic energy and turbulent dissipation rate equations whereas the first order upwind for energy equation is selected. For two-phase calculations, the phase momentum equations with the shared pressure are solved in a coupled and segregated fashion. The phase coupled SIMPLE (PC-SIMPLE) algorithm is employed for the pressure–velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm to multiphase flows. The scaled residuals for the velocity components and energy are set equal to 108 and 109, respectively. 3.1. Governing equations Considering the turbulent forced convection in a steady flow of an incompressible and Newtonian fluid, the governing equations can be written as follows [30]: (a) Continuity equation
r ðqeff VÞ ¼ 0
The geometry and flow domain are schematically illustrated in Fig. 1. The geometrical dimensions were 12.7 (mm) inlet diameter, 200 (mm) upstream length, 25.4 (mm) outlet diameter and 1000 (mm) downstream length with an expansion ratio of 2. At the inlet, temperature was set up to 303 K and the downstream wall was exposed to the constant heat flux of 10,000 (W/m2) while all other walls were insulated. The base fluid (ethylene glycol) and the nanoparticles are assumed to have a thermal equilibrium and no slip condition occurs. The fluid flow is considered to be Newtonian and incompressible. The thermo-physical properties of the mixture of EG-water and EGGNP-WEG coolants at different weight concentrations were obtained from experimental tests. 3.3. Grid study The meshing tool available in ANSYS was used to construct the computational mesh. A structured mesh based on a rectangular grid was used throughout the domain. Several grid distributions had been tested and the results were compared to ensure that the calculated results were grid independent. Fig. 2 shows the comparison of surface Nusselt numbers for Reynolds number of 5000 and pure water as a working fluid at three different grid
ð1Þ
y
(b) Momentum equations
12.7mm
¼ rP þ l r2 V q r ðv 0 v 0 Þ r ðqeff V VÞ eff eff (c) Conservation of energy
¼ r ðkeff þ kt ÞrT r ðqeff C p;eff V TÞ
ð2Þ
25.4mm 200mm
ð3Þ
X
1000mm
Fig. 1. 2D geometrical configuration of backward-facing step.
r ðqeff kVÞ ¼ r r ðqeff eVÞ ¼ r
lt rðkÞ þ Gk qeff e rk
lt e re þ C 1e Gk C 2e qeff e re k
Gk ¼ lt rV þ ðrVÞT ;
ð4Þ
lt ¼ qeff C l
k
80.00
142129
70.00
195994
60.00
249859
50.00 40.00 30.00 20.00 10.00
ð5Þ
0.00 0.2
2
e
90.00
Nu
P and T are the time In the above equations, the symbols V, averaged flow variables, while the symbol v0 represents the fluctuations in velocity. The term in the momentum equations qeff r ðv 0 v 0 Þ represents the turbulent shear stress. The terms of keff and kt represent the effective molecular conductivity and the turbulent thermal conductivity, respectively. To model flow in the turbulent regime, the standard k–e model can be employed based on the Launder and Spalding study [31], which is as follow:
ð6Þ
0.4
0.6 Pipe Length (m)
0.8
1
Fig. 2. Local Nusselt numbers for Re = 5000 and pure water at three different grid distributions.
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Fig. 3. Mesh configuration of backward facing step.
distributions. It has shown that obtained results are independent of the number of grid points. To reduce computational time and effort, the total grid points and the elements have employed throughout the tube are 142,129 and 140,800, respectively. A non-uniform grid was utilized in the meshing phase. Noteworthy, the grids are smaller where close to the separated region (backward phase of flow happen) for obtaining better results (see Fig. 3). 4. Result and discussion 4.1. Functionalization analysis To investigate functional groups, two characterization techniques of TGA and FTIR were applied. Furthermore, the
morphology of EGGNP was investigated by TEM. Fig. 4a and b illustrate the TGA traces and FTIR spectra of both pristine and treated GNP, respectively. First, TGA trace of the EGGNP shows an evidence about functionalization by using thermal analysis of sample. While there is not any weight loss less than 500 °C in TGA trace of pristine sample, a sharp weight loss at temperature range of 140– 500 °C is obvious in the EGGNP trace, which is attributed to the decomposition of ethylene glycol groups. Also, the obtained results indicate that the functionalization of GNP with EG is successful. As another evidence, FTIR spectrum of EGGNP demonstrates some infrared absorption intensities as the cues of EG molecules. Two broad peaks at 3486 and 1141 cm1 are attributed to the OAH and CAO stretching vibrations, respectively. These peaks could be due to the reaction of one of the hydroxyl groups of EG with GNP and/or the attached hydroxyl groups on the GNP. The
Fig. 4. (a) Thermogravimetric analysis traces (b) FTIR spectra of the pristine and EGGNP, (c) & (d) TEM images of the EGGNP.
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peak at 1592 cm1 is related to the C@C graphitic stretching mode of GNP, which is infrared-activated by functionalization. The stretching and in-plane bending vibrations of the CAH bond show a couple of peaks at the ranges of 2850–3000 cm1 and a peak at 1403 cm1, respectively. The lack of these peaks in pristine sample confirmed our claim regarding functionalization. Overall, based on the results of FTIR and TGA, the alkyl and hydroxyl groups are successfully attached to the GNP material through an electrophilic addition reaction under microwave irradiation [32]. EG as a functional group, not only provide suitable colloidal stability, but also synthesized suspension has no corrosive function. Fig. 4 panels (c) and (d) illustrate the TEM images of the EGGNP. Although the TEM images are not able to determine functional groups, the noticeable alterations in morphology or surface deterioration are visible in the TEM images. It can be seen some lines in the TEM images, which are attributed to the wrinkles on the EGGNP surface due to the inherent instability of 2D structures. The wrinkles (waviness) can be obtained during the sonication and microwave procedures [13]. 4.2. Thermo-physical properties Dynamic viscosities of water–EG and EGGNP-WEG mixtures were experimentally obtained at high shear rate of 140 s1 for different temperatures, which are illustrated in Fig. 5a. It can be seen that the viscosity of EGGNP increases with increasing in the concentration of EGGNP. Also, a decrease in viscosity with increasing temperature is another obvious trend in the figure, which is obtained from weakening of the intermolecular forces of the fluid itself [33]. Interestingly, the amount of enhancement in the viscosity of prepared nanofluids with increase weight concentration is almost insignificant as compared with the water–EG mixture. Also,
the viscosity of DI water and EG mixture and EGGNP-WEG coolants as a function of the shear rate for different weight concentrations are represented in Fig. S1 (supplementary information) at 25 °C. The effective viscosities of basefluid and nanofluids were measured in the shear rate range of 20–160 s1. It can be seen that viscosity of the water and ethylene glycol mixture is independent of the shear strain rate, indicating Newtonian behavior. Also, after the EGGNP loading in basefluid, all samples showed the Newtonian behavior as well. The densities of EGGNP-WEG and water–EG mixtures are illustrated for different temperatures and weight concentrations in Fig. 5b. Obviously, as the temperature increases, the density of EGGNP-WEG as well as the base-fluid decreases. In addition, the density of EGGNP-WEG increases with increasing the weight concentration of nanosheets. It can be due to higher density of GNP nanosheets than that of both water and EG. Also, an insignificant decrease is obvious by increasing the temperature. As an example the density of the EGGNP-WEG at maximum concentration of 0.2 wt% decreases by 2.8% as compared with basefluid at 65 °C. The thermal conductivity plot of EGGNP-WEG for the temperature of 25 °C to 65 °C and the weight concentrations of 0.01%, 0.05%, 0.1% and 0.2% shows in Fig. 5c. First, the thermal conductivity of EGGNP-WEG is higher than that of water–EG mixture at different temperatures and weight concentrations. Similar to the conventional working fluids, the thermal conductivity of EGGNPWEG increases with increasing the temperature, however this rising trend is more significant in the presence of EGGNP. The main mechanism for thermal conductivity enhancement with increase of EGGNP concentration is attributed to the Brownian motion of the nanosheets in the basefluid [17]. As one of the thermo-physical properties, the specific heat capacity plot of EGGNP-WEG as functions of temperature and
Fig. 5. (a) Dynamic viscosity at shear rate of 140 s1, (b) density, (c) thermal conductivity and (d) specific heat capacity of the water–EG mixture and EGGNP-WEG for different concentrations and temperatures.
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Fig. 6. Streamline of velocity with weight fraction of 0.2% (a) Re = 5000, (b) Re = 10,000, (c) Re = 15,000, isothermal streamline with weight fraction of 0.2% (d) Re = 5000, (e) Re = 10,000, (f) Re = 15,000.
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weight concentration of EGGNP is illustrated in Fig. 5d. The results suggest that an increase in the weight concentration of EGGNP leads to a drop in the specific heat capacity. Also, the specific heat capacity of all samples increases gradually with the temperature. It is noteworthy that the drop in the specific heat capacity of samples in the presence of EGGNP is due to the lower specific heat capacity of EGGNP than that of the base-fluid. 4.3. Numerical study The numerical study on the forced convection heat transfer for the turbulent regime over a backward-facing step has been performed in the presence of EGGNP-WEG coolants for various Reynolds numbers and weight concentrations. There are 15 cases of simulation, where weight concentrations of 0%, 0.01%, 0.05%, 0.1%, and 0.2% and the Reynolds numbers of 5000, 10,000 and 15,000 have been selected. The streamlines in the turbulent regime for the weight concentration of 0.2% and Reynolds number of 5000, 10,000 and 15,000 are presented in Fig. 6a, b and c respectively.
Streamline plots present the flow patterns for backward-facing step for the expansion ratio of 1:2. In addition, as the Reynolds number increases, the flow at the edge of the step separates and a recirculation zone is observed behind the step [34]. As another important phenomenon, the size of recirculation zone increases with an increase in the Reynolds number. From the streamline plots, it is seen that the recirculation region expands in terms of length with the increase of Reynolds number. Thus, the largest recirculation region in our results is obtained for Re of 15,000, which can be resulted in higher heat transfer rate improvement due to the recirculation formation [34]. For more clarification, isothermal streamlines are presented in Fig. 6d, e and f for three Reynolds numbers of 5000, 10,000 and 15,000, respectively. Fig. 7(a–c) and (d–f) are respectively presented the forced convective heat transfer coefficient (hx) and the local Nusselt numbers (Nux) of EGGNP-WEG as well as basefluid as a function of the Reynolds number and weight concentration. First, all of the forced convective heat transfer coefficient plots show the same characteristic
Fig. 7. Distribution of convective heat transfer coefficient for different weight concentrations at (a) Re = 5000, (b) Re = 10,000, and (c) Re = 15,000 and local Nusselt number at (d) Re = 5000, (e) Re = 10,000, and (f) Re = 15,000.
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behavior. Based on the results, both Nux and hx values are small in the recirculation zone, significantly increase through the recirculation zone to reach a maximum in the reattachment region and followed by decreasing into the recovery region to a stable value, which is in agreement with Nie and Armaly [8], Lancial et al. [34], Cheng et al. [35] and Heshmati et al. [36]. It can be observed that the Nusselt number and convective heat transfer coefficient are higher for the cases with higher Re number, with maximum Nu of 342.61 for Re of 15,000 and weight concentration of 0.2%. Consequently, the higher Re number, the higher Nu is and the higher the position of the happened maximum Nusselt number is. It can be seen that the maximum Nusselt number and heat transfer points move depending on the Reynolds number. Also, all of the plots regarding the Nusselt number profile and heat transfer coefficient at constant Re number present the same maximum points, indicating Xmax is independent of weight concentration of nanofluids, which is confirmed by [36]. The value of Xmax is 0.24.5, 0.25.5, and 0.26 m for Re numbers of 5000, 10,000, and 15,000, respectively. Further downstream, where the variation of Nu tends to be constant, the flow become fully-developed. All samples showed similar results in terms of weight concentration, meaning the higher weight concentration, the higher heat transfer coefficient and Nusselt number are. As it is seen in Fig. 7, the maximum enhancement in the forced convective heat transfer coefficient for EGGNP-WEG is 50% at Xmax. The reason for larger enhancement of the convective heat transfer with increasing concentration was suggested by Aravind et al. [17] using a simple analogy that the connective heat transfer can be introduced with k/r, where r and k are the thickness of thermal boundary layer and thermal conductivity of sample, respectively. Thus, the convective heat transfer coefficient increases with increasing k and/or decreasing r. According to [17,37], carbon nanostructures such as carbon nanotubes and graphene decrease the thermal boundary layer thickness. On the other hand, they increase the thermal conductivity of working fluids such as water and EG, as is obvious in our experimental results, indicating a significant increase in the convective heat transfer coefficient. Also, the higher Nusselt number for the EGGNP-WEG coolants in comparison with basefluid is attributed to the improved thermal conductivity, which leads to the lower temperature difference between the tube wall and bulk fluid. The friction factor for the upper and lower walls at different weight concentrations of EGGNP is shown in Fig. 8a at constant inlet flow temperature of 35 °C. It is also clear from Fig. 8a, as there are two peaks for skin friction coefficient for all cases. It is seen that the numerical friction shows some fluctuations, which is attributed to the circulation zone and followed by showing similar friction factor in the fully-developed regime. In addition, although the difference is not significant, the friction factor increases as the concentration of EGGNP increases, which is in agreement with many experimental results in different regimes of flow, meaning basefluid has the lowest friction factor. The second peak can be attributed to the secondary recirculation region. Fig. 8b is shown the ratio of skin friction factor of nanofluid to basefluid at different weight concentrations. It can be seen as the weight concentration increases, the ratio of the ratio of skin friction factor of nanofluid to basefluid increases. Fig. 8c presents the performance index of EGGNP-WEG for different weight concentration and Reynolds numbers. The performance index (e) is the ratio of the heat transfer rate to the pressure drop. Some studies (e.g., [38]) illustrates that the addition of nanoparticles increases the heat transfer rate enhancement and the pressure drop together, which is desirable and undesirable, respectively. Noticeably, the performance index results of all samples in Xmax for all Reynolds number is greater than 1, indicating the effectiveness of the prepared coolant over
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Fig. 8. (a) Prediction of skin friction factor, (b) the ratio of skin friction factor of EGGNP to basefluid, and (c) the performance index of the synthesized coolant versus weight concentrations of EGGNP for various Reynolds numbers.
a backward facing step. This figure also shows that mance index curves for different Reynolds number peaks for a weight concentration of 0.05%, and that by a decrease of the performance index for further the weight concentration of EGGNP.
the perforreach their is followed increase in
5. Conclusion This study analyses the recirculation phenomena in a turbulent flow downstream over a backward facing step. A new type of coolant including functionalized GNP with EG and synthesized and were tested to study the influences of graphene nanostructure and fluid flow on heat transfer, by changing the Reynolds number and weight fraction of flakes.
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Both thermo-physical data obtained experimentally and numerical simulation showed that the value and the position of maximum Nu only depends on Re in the turbulent regime, and is independent of weight fraction of nanoparticles. The skin friction coefficient results are also independent of weight fraction of EGGNP in coolant. The obtained results were resulted in: By considering both Nusselt number enhancement and pressure drop, the backward facing step shows the highest performance index in weight concentration of 0.05%. Concentration of nanoparticles has no effect on the position of the maximum heat transfer position and the reattachment position. Increasing weight concentration of EGGNP in basefluids can result in higher values of the fully developed Nusselt number and convective heat transfer coefficient. The higher Re number, the higher position of maximum Nu is and the higher the position of the fully developed Nusselt number is.
Acknowledgements The authors gratefully acknowledge High Impact Research Grant UM.C/625/1/HIR/MOHE/ENG/45 and UMRG Grant RP012B13AET, Faculty of Engineering, University of Malaya, Malaysia for support to conduct this research work. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.02.042. References [1] E. Abu-Nada, Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step, Int. J. Heat Fluid Flow 29 (1) (2008) 242–249. [2] J.-T. Lin, B. Armalyy, T. Chen, Mixed convection heat transfer in inclined backward-facing step flows, Int. J. Heat Mass Transf. 34 (6) (1991) 1568–1571. [3] H. Abu-Mulaweh, B.F. Armaly, T. Chen, Measurements in buoyancy-assisting laminar boundary layer flow over a vertical backward-facing step—uniform wall heat flux case, Exp. Thermal Fluid Sci. 7 (1) (1993) 39–48. [4] G.C. Vradis, M. Volkan Otugen, J.G. Sanchez, Heat Transfer Over a BackwardFacing Step: Solutions to a Benchmark Problem, vol. 222, ASMEPUBLICATIONS-HTD, 1993. 27–27. [5] G.C. Vradis, L. Vannostrand, Laminar coupled flow downstream of an asymmetric sudden expansion, J. Thermophys. Heat Transfer 6 (2) (1992) 288–295. [6] B. Pak, Y.I. Cho, S.U. Choi, Separation and reattachment of non-Newtonian fluid flows in a sudden expansion pipe, J. Nonnewton. Fluid Mech. 37 (2) (1990) 175–199. [7] E. Abu-Nada, Entropy generation due to heat and fluid flow in backward facing step flow with various expansion ratios, Int. J. Exergy 3 (4) (2006) 419–435. [8] J. Nie, B.F. Armaly, Three-dimensional convective flow adjacent to backwardfacing step-effects of step height, Int. J. Heat Mass Transf. 45 (12) (2002) 2431– 2438. [9] G. Biswas, M. Breuer, F. Durst, Backward-facing step flows for various expansion ratios at low and moderate Reynolds numbers, J. Fluids Eng. 126 (3) (2004) 362–374. [10] B.F. Armaly, A. Li, J. Nie, Measurements in three-dimensional laminar separated flow, Int. J. Heat Mass Transf. 46 (19) (2003) 3573–3582. [11] T.-Y. Hsieh, Z.-C. Hong, Y.-C. Pan, Flow characteristics of three-dimensional microscale backward-facing step flows, Numer. Heat Transf., Part A Appl. 57 (5) (2010) 331–345.
[12] F.-B. Bao, J.-Z. Lin, Continuum simulation of the microscale backward-facing step flow in a transition regime, Numer. Heat Transf., Part A Appl. 59 (8) (2011) 616–632. [13] A. Amiri et al., Performance dependence of thermosyphon on the functionalization approaches: an experimental study on thermo-physical properties of graphene nanoplatelet-based water nanofluids, Energy Convers. Manage. 92 (2015) 322–330. [14] A. Navaei et al., Heat transfer enhancement of turbulent nanofluid flow over various types of internally corrugated channels, Power Tech. 286 (2015) 332– 341. [15] A. Amiri et al., One-pot, efficient functionalization of multi-walled carbon nanotubes with diamines by microwave method, Appl. Surf. Sci. 257 (23) (2011) 10261–10266. [16] A. Amiri et al., Laminar convective heat transfer of hexylamine-treated MWCNTs-based turbine oil nanofluid, Energy Convers. Manage. 105 (2015) 355–367. [17] S.J. Aravind et al., Investigation of structural stability, dispersion, viscosity, and conductive heat transfer properties of functionalized carbon nanotube based nanofluids, J. Phys. Chem. C 115 (34) (2011) 16737–16744. [18] H. Yarmand et al., Experimental investigation of thermo-physical properties, convective heat transfer and pressure drop of functionalized graphene nanoplatelets aqueous nanofluid in a square heated pipe, Energy Convers. Manage. 114 (2016) 38–49. [19] H. Yarmand et al., Nanofluid based on activated hybrid of biomass carbon/graphene oxide: Synthesis, thermo-physical and electrical properties, Int. Commun. Heat Mass 72 (2016) 10–15. [20] M. Shanbedi et al., Thermal performance prediction of two-phase closed thermosyphon using adaptive neuro-fuzzy inference system, Heat Transfer Eng. 36 (3) (2015) 315–324. [21] H.K. Arzani et al., 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 68 (2015) 267–275. [22] W.S. Sarsam et al., A review of studies on using nanofluids in flat-plate solar collectors, Sol. Energy 122 (2015) 1245–1265. [23] M. Xing, J. Yu, R. Wang, Thermo-physical properties of water-based singlewalled carbon nanotube nanofluid as advanced coolant, Appl. Therm. Eng. 87 (2015) 344–351. [24] H. Mohammed et al., Influence of nanofluids on mixed convective heat transfer over a horizontal backward-facing step, Heat Transf. Asian Res. 40 (4) (2011) 287–307. [25] H. Mohammed et al., Mixed convective flows over backward facing step in a vertical duct using various nanofluids-buoyancy-assisting case, Thermophys. Aeromech. 42 (1) (2012) 1–30. [26] A. Al-Aswadi et al., Laminar forced convection flow over a backward facing step using nanofluids, Int. Commun. Heat Mass Transfer 37 (8) (2010) 950– 957. [27] A.S. Kherbeet, H.A. Mohammed, B. Salman, The effect of nanofluids flow on mixed convection heat transfer over microscale backward-facing step, Int. J. Heat Mass Transf. 55 (21) (2012) 5870–5881. [28] A.S. Kherbeet et al., Combined convection nanofluid flow and heat transfer over microscale forward-facing step, Int. J. Nanopart. 7 (1) (2014) 1–25. [29] A. Amiri et al., Synthesis of polyethylene glycol-functionalized multi-walled carbon nanotubes with a microwave-assisted approach for improved heat dissipation, RSC Adv. 5 (45) (2015) 35425–35434. [30] T.M. Shih, Numerical Heat Transfer, CRC Press, 1984. [31] B.E. Launder, D. Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng. 3 (2) (1974) 269–289. [32] A. Amiri et al., Microwave-assisted synthesis of highly-crumpled, few-layered graphene and nitrogen-doped graphene for use as high-performance electrodes in capacitive deionization, Sci. Rep. 5 (2015) 17503. [33] G.H. Ko et al., An experimental study on the pressure drop of nanofluids containing carbon nanotubes in a horizontal tube, Int. J. Heat Mass Transf. 50 (23) (2007) 4749–4753. [34] N. Lancial et al., Effects of a turbulent wall jet on heat transfer over a nonconfined backward-facing step, Int. J. Heat Fluid Flow 44 (2013) 336–347. [35] J.-C. Cheng, Y.-L. Tsay, Effects of solid and slotted baffles on the convection characteristics of backward-facing step flow in a channel, Heat Mass Transf. 42 (9) (2006) 843–852. [36] A. Heshmati, H. Mohammed, A. Darus, Mixed convection heat transfer of nanofluids over backward facing step having a slotted baffle, Appl. Math. Comput. 240 (2014) 368–386. [37] A. Amiri et al., Toward improved engine performance with crumpled nitrogendoped graphene based water–ethylene glycol coolant, Chem. Eng. J. 289 (2016) 583–595. [38] K.H. Solangi et al., Experimental investigation of heat transfer performance and frictional loss of functionalized GNP-based water coolant in a closed conduit flow, RSC Adv. 6 (2016) 4552–4563.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Backward-facing step heat transfer of the turbulent regime for functionalized graphene nanoplatelets based water–ethylene glycol nanofluids Ahmad Amiri a,⇑, Hamed Khajeh Arzani b,⇑, S.N. Kazi b,⇑, B.T. Chew b, A. Badarudin b a b
Chemical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran Department of Mechanical Engineering, University of Malaya, Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Article history: Received 24 November 2015 Received in revised form 6 February 2016 Accepted 16 February 2016
Keywords: Backward-facing step Heat transfer Turbulent Ethylene glycol Functionalization Graphene nanoplatelets
a b s t r a c t Herein, an experimental study on thermo-physical properties of ethylene glycol-functionalized graphene nanoplatelets/water–ethylene glycol nanofluids (EGGNP-WEG) and a numerical study on the convective heat transfer over a backward-facing step are performed. Accordingly, EGGNP was first synthesized covalently to achieve a stable colloidal solution in water–ethylene glycol mixture. Some characterizations were applied to analyze the surface functionality and morphology of EGGNP-flakes. To study the convective heat transfer coefficient in turbulent regime, a numerical study is performed at different weight fractions of EGGNP. According to the results, a higher weight concentration of EGGNP in basefluid indicates a greater extent of convective heat transfer coefficient and thermal conductivity, implying higher heat transfer rate over a backward-facing step. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The thermo-physical phenomena of separation and reattachment e.g. backward-facing step, involving heat transfer, are frequently encountered in many engineering problems like electrical rotating machines. Thus, investigation of the convection heat transfer over a backward facing step is one of the interest topics in many research studies. Heat transfer applications of backward facing step appear in different industrial equipment such as combustors, aircraft, gas turbine engines, and buildings. It is obvious that the separation and reattachment of the flow can change the flow structure and has a direct influence on the heat transfer mechanism as well as thermal performance of equipment [1]. Thus, numerous studies have been investigated to determine the real mechanism of flow separation and reattachment, the best geometry for heat transfer applications, and best type of working fluids in the past decades [2,3]. Although, the flow over a backward-facing step with heat transfer was investigated by some scientists [4,5], a majority of studies considered the isothermal flow, commonly in two dimensional geometry.
⇑ Corresponding authors. E-mail addresses: [email protected] (A. Amiri), [email protected], [email protected] (H.K. Arzani), [email protected] (S.N. Kazi). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.02.042 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
A study on the two non-Newtonian liquids was performed in a sudden expansion in the presence of viscoelastic polyacrylamide (PAA) solutions and a purely viscous shear-thinning liquid [6]. According to their results, the reattachment length of nonNewtonian fluid was shorter than that of Newtonian counterparts and surely water. Abu-Nada [7] performed a numerical study on the entropy over a backward facing step for different expansion ratios. Different expansion ratios of 1/4, 1/3, 1/2, 2/3, and 3/4 were selected and the results presented an increase in the Reynolds number with the value of total entropy generation number, which was for the high range of Reynolds number. A numerical study on the laminar regime in a rectangular duct including backwardfacing step was performed by Nie and Armaly [8]. They suggested the appearance of the maximum reattachment length at the sidewall. Also, they concluded that as the step height enhances, the amount of Nusselt number increases. Biswas et al. [9] investigated the laminar fluid flow behavior over a three dimensional backward-facing step with various expansion ratios. They concluded that the formation of wall jets at the side wall within the separating shear layer, formed by the spanwise of the velocity moves towards the symmetry channel plane. An experimental study have been done by Armaly et al. [10] for measuring the velocity over a backward-facing step by using two-component laser Doppler velocimeter in laminar regime. In another similar study, Hsieh et al. [11] studied the flow over a backward-facing
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step by the Direct Simulation Monte Carlo method (DSMC). According to their results, the side walls can significantly affect the flow structure and thermal characteristics in the 3-D structure. Bao and Lin [12] also utilized the DSMC approach for investigation of the thermal performance over the microscale backward-facing step in the transition regime. They reported that the streamwise velocity is positive at the Knudsen number of 0.136, indicating the lack of the reversed flow after the step. Also, they concluded that there is a non-linear connection between the mass flow rate and pressure drop ratio in traditional flow. As mentioned above, a majority of studies focused on having novelty in changing design such as expansion ratio, in particular in the laminar regime, and neglected thermo-physical properties of working fluid. Thus, as another novelty for improving heat transfer rate over a backward-facing step is the utilization of nanofluids. A combination of nanofluids with thermal conductivity and backward-facing step can result in an effective approach for enhancing the heat transfer rate. In addition, previous studies [13–16] showed that nanofluids made of the mixture of basefluids and nanoparticles with good thermal conductivity could enhance the thermal performance of the different heat transfer equipment. The main reason for increasing the thermal conductivity of basefluid loaded with nanostructures is attributed to the Brownian motion of the nanostructures suspended in the working fluid [17– 23]. Also, the formation of surface nanolayers can be another reason for enhancing the thermal conductivity [17]. The first study on the heat transfer rate of nanofluid in a backward-facing step was performed by Abu-Nada [1]. To reach the purpose, five nanofluids of CuO-, Al2O3-, Ag-, Cu- and TiO2-based water nanofluids were synthesized and convective heat transfer coefficient was investigated. He concluded that there is a direct connection between the Nusselt number and the volume fraction of nanoparticles in basefluids. As an important result, they demonstrated that Nusselt number is significantly dependent of the thermo-physical properties of the nanoparticles inside the recirculation zone. Mohammed et al. [24,25] investigated the influence of different nanofluids (8 nanofluids) on the mixed convective heat transfer over the vertical and horizontal backward-facing step. Their results showed that the nanofluids with secondary recirculation regions have lower Nusselt number and the diamond-based water nanofluid illustrated the maximum Nusselt number in the presence of primary recirculation region. Al-Aswadi et al. [26] showed that nanofluids with low dense nanoparticles demonstrate higher velocity than those with high dense nanoparticles. Kherbeet et al. [27] investigated the heat transfer behaviors of four types of nanofluids (Al2O3-, CuO-, SiO2- and ZnO-based water nanofluid) in the laminar regime over a microscale backward-facing step. The results showed the lack of recirculation region behind the step for all prepared samples at different concentrations. In addition, the results suggested that SiO2-based water nanofluid has the highest Nusselt number as compared with other nanofluids. In addition, the results showed that the amount of Nusselt number enhances with the increment of the volume fraction of the nanoparticles in the base fluid. Kherbeet et al. [28] performed a numerical study on the laminar mixed convection flow of nanofluids over a horizontal microscale forward-facing step (MFFS) using a finite volume method. Different nanofluids including SiO2-, Al2O3-, CuO-, and ZnO-based ethylene glycol nanofluids at various volume fractions investigated in terms of heat transfer parameters and the results demonstrated that the SiO2-based ethylene glycol nanofluid had the maximum Nusselt number. They also reported that the Nusselt number increases with decreasing nanoparticle density and diameter as well as increasing volume fraction of nanoparticles. It is obvious from the above literature review that the terms of thermal conductivity of nanoparticles was neglected. In addition, most of the previous studies on the backward-facing step involved
539
metal- or metal oxide-based water or ethylene glycol as the basefluid and there is no study concentrated on nanofluids including carbon nanostructures. It is known that the thermal conductivity of most carbon particles such as carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) are much higher than that of metal or metal oxide nanoparticles. This implies that the carbon-base nanoparticle have higher potential for enhancing the thermal conductivity of base fluids [29]. Despite some promising thermal properties of graphene nanopleteles in the field of nanofluids, the strong van der Waals interactions have limited their thermal applications. Non-covalent and covalent functionalizations are the effective approaches to improve the dispersibility of GNPs. Also, there is not any study in water–ethylene glycol media over backward-facing step. Herein, three phases of study have been performed to investigate the heat transfer behavior of EG-treated GNP based water– EG coolants over a backward facing step. First, a promising and potentially industrially scalable functionalization approach is employed to prepare ethylene glycol-functionalized graphene nanoplatelets (EGGNP) and EGGNP based water–EG coolant (EGGNP-WEG). First phase followed by analyzing EG-treated GNP samples in terms of functionality and morphology. Second phase of study comprises of the experimental-evaluation of the thermo-physical, rheological and colloidal properties of EGGNPWEG. As the three phase of study, a numerical analysis on the heat transfer over a backward-facing step is performed in the presence of EGGNP-WEG at different weight concentrations. The main objective was to investigate the heat transfer enhancement and pressure drop in the presence of EGGNP in basefluid. The latter is obtained by the calculation of the performance index. 2. Material and methods 2.1. Preparation of EGGNP-WEG coolants To prepare EGGNP-WEG, anhydrous Aluminum Chloride (AlCl3) with purity of 99.999% was prepared from Sigma–Aldrich. All of the other chemicals were also bought from Sigma–Aldrich in analytical grade. Pristine Graphene Nanoplatelets (GNPs) with purity > 90 wt%, and Number of layer < 30 were purchased from Nanostructured & Amorphous Materials, Inc. The pristine GNP (0.5 g) and AlCl3 (9.27 g) were typically placed in a planetary ball-mill container and agitated with speed of 500 rpm for 1 h. The obtained mixture was poured into a vessel filled with 80 ml of anhydrous EG and then sonicated for 15 min with a probe-sonicator to reach a homogeneous back suspension. The concentrated hydrochloric acid (1 ml) was poured into the vessel over sonication time. After sonication, the suspension was transferred into a microwave (Milestone MicroSYNTH programmable microwave system) and heated for 15 min at 150 °C. The resultant mixture was filtered with a PTFE membrane and subsequently washed with abundant DI water to remove any unreacted materials. Filtration cake was then dried for 48 h at 50 °C and labeled as EGGNP. While the pristine GNP is not soluble in most organic solvents, the EGGNP was significantly soluble in both water and EG. The easily-miscible EG functionalities can explain a significant increase in dispersibility of the functionalized GNP with EG in both media of water and EG. To synthesize EGGNP-WEG coolants at different weight concentrations, the known amount of EGGNP was poured into a vessel filled with a mixture of water and EG with a volumetric ratio of 40:60 and sonicated with a probe-sonicator for 10 min. 2.2. Experimental equipment The prepared EGGNP was analyzed in terms of structure, morphology and thermo-physical properties. Fourier transform
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infrared spectroscopy, FTIR, (Bruker IFS 66/S), Raman spectroscopy (Renishaw confocal spectrometer at 514 nm), thermo-gravimetric analysis, TGA, (TGA-50 Shimadzu), and high-resolution transmission electron microscopy, TEM, (HT7700) were employed to analyze the main structure and morphology of the sample. Regarding thermo-physical properties, a differential scanning calorimeter (Perkin Elmer Diamond DSC) was applied for measuring the specific heat capacities of EGGNP-WEG. The thermal conductivity of EGGNP-WEG samples were obtained by a KD2 Pro-thermal analyzer (Decagon Devices, USA). Also, the rheological property of samples was measured by a Brook field rheometer (DVIII Ultra Rheometer), comprising a RTD temperature probe for monitoring the samples.
rk ¼ 1:00; re ¼ 1:30; C 1e ¼ 1:44; C 2e ¼ 1:92
C l ¼ 0:09;
ð7Þ To assess the effectiveness of EGGNP, a performance index (e) is selected as an appropriate parameter to clarify the range of temperature and velocity that can be used by the synthesized coolant:
e¼
hnf =hbf Rh ¼ DPnf DPbf RDP
ð8Þ
Rh is the ratio of the heat transfer enhancement of the new coolant (GNP-WEG) to the base-fluid and RDP is the ratio of pressure drop of synthesized coolant to the basefluid. 3.2. Physical model and assumptions
3. Numerical implementation The numerical method available in the commercial CFD package of ANSYS-Fluent, V15 has been used here. Fluent uses a finite volume approach to convert the governing partial differential equations into a system of discrete algebraic equations. As the discretization methods, a second-order upwind scheme is selected for the momentum, turbulent kinetic energy and turbulent dissipation rate equations whereas the first order upwind for energy equation is selected. For two-phase calculations, the phase momentum equations with the shared pressure are solved in a coupled and segregated fashion. The phase coupled SIMPLE (PC-SIMPLE) algorithm is employed for the pressure–velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm to multiphase flows. The scaled residuals for the velocity components and energy are set equal to 108 and 109, respectively. 3.1. Governing equations Considering the turbulent forced convection in a steady flow of an incompressible and Newtonian fluid, the governing equations can be written as follows [30]: (a) Continuity equation
r ðqeff VÞ ¼ 0
The geometry and flow domain are schematically illustrated in Fig. 1. The geometrical dimensions were 12.7 (mm) inlet diameter, 200 (mm) upstream length, 25.4 (mm) outlet diameter and 1000 (mm) downstream length with an expansion ratio of 2. At the inlet, temperature was set up to 303 K and the downstream wall was exposed to the constant heat flux of 10,000 (W/m2) while all other walls were insulated. The base fluid (ethylene glycol) and the nanoparticles are assumed to have a thermal equilibrium and no slip condition occurs. The fluid flow is considered to be Newtonian and incompressible. The thermo-physical properties of the mixture of EG-water and EGGNP-WEG coolants at different weight concentrations were obtained from experimental tests. 3.3. Grid study The meshing tool available in ANSYS was used to construct the computational mesh. A structured mesh based on a rectangular grid was used throughout the domain. Several grid distributions had been tested and the results were compared to ensure that the calculated results were grid independent. Fig. 2 shows the comparison of surface Nusselt numbers for Reynolds number of 5000 and pure water as a working fluid at three different grid
ð1Þ
y
(b) Momentum equations
12.7mm
¼ rP þ l r2 V q r ðv 0 v 0 Þ r ðqeff V VÞ eff eff (c) Conservation of energy
¼ r ðkeff þ kt ÞrT r ðqeff C p;eff V TÞ
ð2Þ
25.4mm 200mm
ð3Þ
X
1000mm
Fig. 1. 2D geometrical configuration of backward-facing step.
r ðqeff kVÞ ¼ r r ðqeff eVÞ ¼ r
lt rðkÞ þ Gk qeff e rk
lt e re þ C 1e Gk C 2e qeff e re k
Gk ¼ lt rV þ ðrVÞT ;
ð4Þ
lt ¼ qeff C l
k
80.00
142129
70.00
195994
60.00
249859
50.00 40.00 30.00 20.00 10.00
ð5Þ
0.00 0.2
2
e
90.00
Nu
P and T are the time In the above equations, the symbols V, averaged flow variables, while the symbol v0 represents the fluctuations in velocity. The term in the momentum equations qeff r ðv 0 v 0 Þ represents the turbulent shear stress. The terms of keff and kt represent the effective molecular conductivity and the turbulent thermal conductivity, respectively. To model flow in the turbulent regime, the standard k–e model can be employed based on the Launder and Spalding study [31], which is as follow:
ð6Þ
0.4
0.6 Pipe Length (m)
0.8
1
Fig. 2. Local Nusselt numbers for Re = 5000 and pure water at three different grid distributions.
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Fig. 3. Mesh configuration of backward facing step.
distributions. It has shown that obtained results are independent of the number of grid points. To reduce computational time and effort, the total grid points and the elements have employed throughout the tube are 142,129 and 140,800, respectively. A non-uniform grid was utilized in the meshing phase. Noteworthy, the grids are smaller where close to the separated region (backward phase of flow happen) for obtaining better results (see Fig. 3). 4. Result and discussion 4.1. Functionalization analysis To investigate functional groups, two characterization techniques of TGA and FTIR were applied. Furthermore, the
morphology of EGGNP was investigated by TEM. Fig. 4a and b illustrate the TGA traces and FTIR spectra of both pristine and treated GNP, respectively. First, TGA trace of the EGGNP shows an evidence about functionalization by using thermal analysis of sample. While there is not any weight loss less than 500 °C in TGA trace of pristine sample, a sharp weight loss at temperature range of 140– 500 °C is obvious in the EGGNP trace, which is attributed to the decomposition of ethylene glycol groups. Also, the obtained results indicate that the functionalization of GNP with EG is successful. As another evidence, FTIR spectrum of EGGNP demonstrates some infrared absorption intensities as the cues of EG molecules. Two broad peaks at 3486 and 1141 cm1 are attributed to the OAH and CAO stretching vibrations, respectively. These peaks could be due to the reaction of one of the hydroxyl groups of EG with GNP and/or the attached hydroxyl groups on the GNP. The
Fig. 4. (a) Thermogravimetric analysis traces (b) FTIR spectra of the pristine and EGGNP, (c) & (d) TEM images of the EGGNP.
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peak at 1592 cm1 is related to the C@C graphitic stretching mode of GNP, which is infrared-activated by functionalization. The stretching and in-plane bending vibrations of the CAH bond show a couple of peaks at the ranges of 2850–3000 cm1 and a peak at 1403 cm1, respectively. The lack of these peaks in pristine sample confirmed our claim regarding functionalization. Overall, based on the results of FTIR and TGA, the alkyl and hydroxyl groups are successfully attached to the GNP material through an electrophilic addition reaction under microwave irradiation [32]. EG as a functional group, not only provide suitable colloidal stability, but also synthesized suspension has no corrosive function. Fig. 4 panels (c) and (d) illustrate the TEM images of the EGGNP. Although the TEM images are not able to determine functional groups, the noticeable alterations in morphology or surface deterioration are visible in the TEM images. It can be seen some lines in the TEM images, which are attributed to the wrinkles on the EGGNP surface due to the inherent instability of 2D structures. The wrinkles (waviness) can be obtained during the sonication and microwave procedures [13]. 4.2. Thermo-physical properties Dynamic viscosities of water–EG and EGGNP-WEG mixtures were experimentally obtained at high shear rate of 140 s1 for different temperatures, which are illustrated in Fig. 5a. It can be seen that the viscosity of EGGNP increases with increasing in the concentration of EGGNP. Also, a decrease in viscosity with increasing temperature is another obvious trend in the figure, which is obtained from weakening of the intermolecular forces of the fluid itself [33]. Interestingly, the amount of enhancement in the viscosity of prepared nanofluids with increase weight concentration is almost insignificant as compared with the water–EG mixture. Also,
the viscosity of DI water and EG mixture and EGGNP-WEG coolants as a function of the shear rate for different weight concentrations are represented in Fig. S1 (supplementary information) at 25 °C. The effective viscosities of basefluid and nanofluids were measured in the shear rate range of 20–160 s1. It can be seen that viscosity of the water and ethylene glycol mixture is independent of the shear strain rate, indicating Newtonian behavior. Also, after the EGGNP loading in basefluid, all samples showed the Newtonian behavior as well. The densities of EGGNP-WEG and water–EG mixtures are illustrated for different temperatures and weight concentrations in Fig. 5b. Obviously, as the temperature increases, the density of EGGNP-WEG as well as the base-fluid decreases. In addition, the density of EGGNP-WEG increases with increasing the weight concentration of nanosheets. It can be due to higher density of GNP nanosheets than that of both water and EG. Also, an insignificant decrease is obvious by increasing the temperature. As an example the density of the EGGNP-WEG at maximum concentration of 0.2 wt% decreases by 2.8% as compared with basefluid at 65 °C. The thermal conductivity plot of EGGNP-WEG for the temperature of 25 °C to 65 °C and the weight concentrations of 0.01%, 0.05%, 0.1% and 0.2% shows in Fig. 5c. First, the thermal conductivity of EGGNP-WEG is higher than that of water–EG mixture at different temperatures and weight concentrations. Similar to the conventional working fluids, the thermal conductivity of EGGNPWEG increases with increasing the temperature, however this rising trend is more significant in the presence of EGGNP. The main mechanism for thermal conductivity enhancement with increase of EGGNP concentration is attributed to the Brownian motion of the nanosheets in the basefluid [17]. As one of the thermo-physical properties, the specific heat capacity plot of EGGNP-WEG as functions of temperature and
Fig. 5. (a) Dynamic viscosity at shear rate of 140 s1, (b) density, (c) thermal conductivity and (d) specific heat capacity of the water–EG mixture and EGGNP-WEG for different concentrations and temperatures.
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Fig. 6. Streamline of velocity with weight fraction of 0.2% (a) Re = 5000, (b) Re = 10,000, (c) Re = 15,000, isothermal streamline with weight fraction of 0.2% (d) Re = 5000, (e) Re = 10,000, (f) Re = 15,000.
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weight concentration of EGGNP is illustrated in Fig. 5d. The results suggest that an increase in the weight concentration of EGGNP leads to a drop in the specific heat capacity. Also, the specific heat capacity of all samples increases gradually with the temperature. It is noteworthy that the drop in the specific heat capacity of samples in the presence of EGGNP is due to the lower specific heat capacity of EGGNP than that of the base-fluid. 4.3. Numerical study The numerical study on the forced convection heat transfer for the turbulent regime over a backward-facing step has been performed in the presence of EGGNP-WEG coolants for various Reynolds numbers and weight concentrations. There are 15 cases of simulation, where weight concentrations of 0%, 0.01%, 0.05%, 0.1%, and 0.2% and the Reynolds numbers of 5000, 10,000 and 15,000 have been selected. The streamlines in the turbulent regime for the weight concentration of 0.2% and Reynolds number of 5000, 10,000 and 15,000 are presented in Fig. 6a, b and c respectively.
Streamline plots present the flow patterns for backward-facing step for the expansion ratio of 1:2. In addition, as the Reynolds number increases, the flow at the edge of the step separates and a recirculation zone is observed behind the step [34]. As another important phenomenon, the size of recirculation zone increases with an increase in the Reynolds number. From the streamline plots, it is seen that the recirculation region expands in terms of length with the increase of Reynolds number. Thus, the largest recirculation region in our results is obtained for Re of 15,000, which can be resulted in higher heat transfer rate improvement due to the recirculation formation [34]. For more clarification, isothermal streamlines are presented in Fig. 6d, e and f for three Reynolds numbers of 5000, 10,000 and 15,000, respectively. Fig. 7(a–c) and (d–f) are respectively presented the forced convective heat transfer coefficient (hx) and the local Nusselt numbers (Nux) of EGGNP-WEG as well as basefluid as a function of the Reynolds number and weight concentration. First, all of the forced convective heat transfer coefficient plots show the same characteristic
Fig. 7. Distribution of convective heat transfer coefficient for different weight concentrations at (a) Re = 5000, (b) Re = 10,000, and (c) Re = 15,000 and local Nusselt number at (d) Re = 5000, (e) Re = 10,000, and (f) Re = 15,000.
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behavior. Based on the results, both Nux and hx values are small in the recirculation zone, significantly increase through the recirculation zone to reach a maximum in the reattachment region and followed by decreasing into the recovery region to a stable value, which is in agreement with Nie and Armaly [8], Lancial et al. [34], Cheng et al. [35] and Heshmati et al. [36]. It can be observed that the Nusselt number and convective heat transfer coefficient are higher for the cases with higher Re number, with maximum Nu of 342.61 for Re of 15,000 and weight concentration of 0.2%. Consequently, the higher Re number, the higher Nu is and the higher the position of the happened maximum Nusselt number is. It can be seen that the maximum Nusselt number and heat transfer points move depending on the Reynolds number. Also, all of the plots regarding the Nusselt number profile and heat transfer coefficient at constant Re number present the same maximum points, indicating Xmax is independent of weight concentration of nanofluids, which is confirmed by [36]. The value of Xmax is 0.24.5, 0.25.5, and 0.26 m for Re numbers of 5000, 10,000, and 15,000, respectively. Further downstream, where the variation of Nu tends to be constant, the flow become fully-developed. All samples showed similar results in terms of weight concentration, meaning the higher weight concentration, the higher heat transfer coefficient and Nusselt number are. As it is seen in Fig. 7, the maximum enhancement in the forced convective heat transfer coefficient for EGGNP-WEG is 50% at Xmax. The reason for larger enhancement of the convective heat transfer with increasing concentration was suggested by Aravind et al. [17] using a simple analogy that the connective heat transfer can be introduced with k/r, where r and k are the thickness of thermal boundary layer and thermal conductivity of sample, respectively. Thus, the convective heat transfer coefficient increases with increasing k and/or decreasing r. According to [17,37], carbon nanostructures such as carbon nanotubes and graphene decrease the thermal boundary layer thickness. On the other hand, they increase the thermal conductivity of working fluids such as water and EG, as is obvious in our experimental results, indicating a significant increase in the convective heat transfer coefficient. Also, the higher Nusselt number for the EGGNP-WEG coolants in comparison with basefluid is attributed to the improved thermal conductivity, which leads to the lower temperature difference between the tube wall and bulk fluid. The friction factor for the upper and lower walls at different weight concentrations of EGGNP is shown in Fig. 8a at constant inlet flow temperature of 35 °C. It is also clear from Fig. 8a, as there are two peaks for skin friction coefficient for all cases. It is seen that the numerical friction shows some fluctuations, which is attributed to the circulation zone and followed by showing similar friction factor in the fully-developed regime. In addition, although the difference is not significant, the friction factor increases as the concentration of EGGNP increases, which is in agreement with many experimental results in different regimes of flow, meaning basefluid has the lowest friction factor. The second peak can be attributed to the secondary recirculation region. Fig. 8b is shown the ratio of skin friction factor of nanofluid to basefluid at different weight concentrations. It can be seen as the weight concentration increases, the ratio of the ratio of skin friction factor of nanofluid to basefluid increases. Fig. 8c presents the performance index of EGGNP-WEG for different weight concentration and Reynolds numbers. The performance index (e) is the ratio of the heat transfer rate to the pressure drop. Some studies (e.g., [38]) illustrates that the addition of nanoparticles increases the heat transfer rate enhancement and the pressure drop together, which is desirable and undesirable, respectively. Noticeably, the performance index results of all samples in Xmax for all Reynolds number is greater than 1, indicating the effectiveness of the prepared coolant over
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Fig. 8. (a) Prediction of skin friction factor, (b) the ratio of skin friction factor of EGGNP to basefluid, and (c) the performance index of the synthesized coolant versus weight concentrations of EGGNP for various Reynolds numbers.
a backward facing step. This figure also shows that mance index curves for different Reynolds number peaks for a weight concentration of 0.05%, and that by a decrease of the performance index for further the weight concentration of EGGNP.
the perforreach their is followed increase in
5. Conclusion This study analyses the recirculation phenomena in a turbulent flow downstream over a backward facing step. A new type of coolant including functionalized GNP with EG and synthesized and were tested to study the influences of graphene nanostructure and fluid flow on heat transfer, by changing the Reynolds number and weight fraction of flakes.
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Both thermo-physical data obtained experimentally and numerical simulation showed that the value and the position of maximum Nu only depends on Re in the turbulent regime, and is independent of weight fraction of nanoparticles. The skin friction coefficient results are also independent of weight fraction of EGGNP in coolant. The obtained results were resulted in: By considering both Nusselt number enhancement and pressure drop, the backward facing step shows the highest performance index in weight concentration of 0.05%. Concentration of nanoparticles has no effect on the position of the maximum heat transfer position and the reattachment position. Increasing weight concentration of EGGNP in basefluids can result in higher values of the fully developed Nusselt number and convective heat transfer coefficient. The higher Re number, the higher position of maximum Nu is and the higher the position of the fully developed Nusselt number is.
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