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An investigation of heat transfer in heat exchange devices with spirally-coiled twisted-ducts using nanofluid
Applied Thermal Engineering 143 (2018) 358–375
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An investigation of heat transfer in heat exchange devices with spirallycoiled twisted-ducts using nanofluid
T
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M. Khoshvaght-Aliabadia, , S.F. Khalighb, Z. Tavassolia a b
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran Department of Chemistry, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran
H I GH L IG H T S
G R A P H I C A L A B S T R A C T
transport character• Thermo-fluidic istics of spirally-coiled twisted-tube are investigated.
and Cu/water are used as • Water working fluid. and coil-pitch have con• Twist-pitch siderable effects on performance of studied cases.
performance indexes of • Maximum 1.39 and 1.88 are recorded for water and nanofluid.
A R T I C LE I N FO
A B S T R A C T
Keywords: Spirally-coiled twisted-ducts Cu/water nanofluid Twist-pitch Coil-pitch
A new design of curved ducts namely spirally-coiled twisted-duct is introduced and analyzed both experimentally and numerically. Water and Cu/water nanofluid at two concentrations of 0.5% and 1% by mass are considered as working fluid. The results show that the dependence of thermo-fluidic transport characteristics on the geometry of spirally-coiled twisted-duct is strongly influenced by twist-pitch (tp) and coil-pitch (cp). The studied ranges are tp = 0.05, 0.1, and 0.15 m and cp = 0.015, 0.025, and 0.035 m. The maximum augmentations of Nusselt number and friction factor are recorded for the spirally-coiled twisted-ducts with the lowest twist-pitch and coil-pitch (i.e. tp = 0.05 and cp = 0.015). One of the key outcomes of this work is that the effect of twistpitch is more pronounced at higher Graetz numbers, while at lower Graetz numbers the effect of coil-pitch is more noticeable. Likewise, with the deployment of a performance index combining the enhancement in Nusselt number and corresponding augmentation in friction factor, the overall hydrothermal performance of spirallycoiled twisted-ducts is assessed. Among the studied cases, the spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m possesses the highest performance index of 1.39 at the maximum Graetz number. Also, a noticeable heat transfer enhancement due to suspension of copper nanoparticles in water is obtained with a certain augmentation in the pressure drop, and the enhancement is intensified with increasing the concentration of nanoparticles. The performance index enhances up to 1.88 when the 1.0% nanofluid is used in the spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m. Finally, using the obtained results, two correlations are established to model Nusselt number and friction factor inside the spirally-coiled twisted-ducts for the Graetz number range of 14–58.
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Corresponding author at: Postal address: 36199-43189, Iran. E-mail address: [email protected] (M. Khoshvaght-Aliabadi).
https://doi.org/10.1016/j.applthermaleng.2018.07.112 Received 3 April 2018; Received in revised form 16 July 2018; Accepted 23 July 2018 Available online 23 July 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 143 (2018) 358–375
M. Khoshvaght-Aliabadi et al.
ρ
Nomenclature Ac At Cp cp dh h l m p Q T tp u, v, w V x, y, z
density, kg/m3
Subscripts
frontal surface area, m2 total surface area, m2 specific heat capacity, J/kg K coil-pitch, m hydraulic diameter, m heat transfer coefficient, W/m2 K duct length, m mass flow rate, kg/s pressure, Pa heat transfer rate, W temperature, K twist-pitch, m velocity components, m/s velocity, m/s coordinates
b in out w
bulk inlet outlet wall
Dimensionless groups f Gr Nu Pr Re
Friction factor Graetz number Nusselt number Prandtl number Reynolds number
Acronyms
Greek symbols η κ μ ν α
EEWL FVM LMTD PNFC R&D SIMPLE
performance factor thermal conductivity, W/m K dynamic viscosity, kg/m s kinematic viscosity, m2/s thermal diffusivity, m2/s
1. Introduction
Electrical Explosion of Wires in Liquid Finite Volume Method Logarithmic Mean Temperature Difference Payamavaran Nanotechnology Fardanegar Research and Development Semi Implicit Method for Pressure Linked Equation
duct, and it was enhanced with decreasing of the helical radius. Etghani and Baboli [2] studied helical ducts embedded inside a shell with different geometrical and operating parameters. A better thermal performance was detected at higher cold and hot flow rates and lower coilpitches. Kurnia et al. [3] investigated three different cross-section shapes, including circular, ellipse and square, on the performance of helical duct. It was found that the square cross-section had the highest entropy, followed by ellipse and circular ones. Some studies focused on the use of turbulators or inserts as passive technique inside the curved ducts. For instance, Panahi and Zamzamian [4] used the helical wire as a turbulator inside the helical duct. Their results showed that the applied technique could significantly enhance the overall thermal performance of the helical duct with an increase in the pressure drop. As the other enhanced technique, the nanofluid was tested as the working fluid inside the curved ducts. Bizhaem and Abbassi [5] conducted numerical simulations on Al2O3/water nanofluid flow inside a helical duct. The findings disclosed that water and nanofluid have
Curved ducts have compact structure and good hydrothermal performance, so they have been widely used in various industrial and engineering applications, such as heat exchangers, solar systems, chemical reactors, food processes, etc. As shown in Fig. 1, helical, serpentine, and spiral geometries are well known configurations of curved ducts. The transport phenomena (i.e. momentum, heat, and mass) occurring in these geometries are more complex than those in straight ducts. As a fluid passes through the helical, serpentine, or spiral ducts, the presence of curvatures in the fluid path leads to centrifugal forces thereby rotational flows are induced which have significant ability to increase the rate of transport phenomena. Actually, the performance of curved ducts strongly depend on the behavior of generated rotational flows. Zhao et al. [1] simulated turbulent flow and heat transfer of supercritical water in vertical helical ducts. It was found that the heat transfer coefficient for helical ducts was higher than that for straight
Fig. 1. Well known configurations of curved ducts. 359
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almost the same velocity profiles with significant difference in the temperature profiles. Khoshvaght-Aliabadi et al. [6] conducted experiments on Cu/water nanofluid flow through helical micro-ducts with
different coil-pitches. It was concluded that the overall hydrothermal performance of helical micro-ducts were improved as the concentration of nanoparticles was increased. A similar study was conducted on
Fig. 2. Schematic of fabricated spirally-coiled twisted-tubes. 360
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nanoparticles in aqueous carboxymethyl cellulose for the use in a shell and helical duct heat exchanger. It was detected that the CuO nanoparticles showed better heat transfer than the other two types. Three nanoparticles of Al2O3, CuO and TiO2 in water as working fluid through a shell and helical duct heat exchanger were also tested by Srinivas and Vinod [12,13]. They also examined the simultaneous application of helical and Al2O3/water nanofluid in an agitated heat exchanger. It was observed that higher stirrer speed and shell-side fluid temperature resulted in more energy savings. In the other work [14], the performance of agitated heat exchanger was checked by using serpentine ducts and three different metallic nanofluids. It was found that the thermal performance of Cu/water nanofluid was more intensive than Fe/water and Ag/water nanofluids. Wu et al. [15,16] analyzed the performance of multi-walled carbon nanotube nanofluid in a double-pipe helically
serpentine micro-ducts by the same team [7]. Likewise, Rakhsha et al. [8] studied the turbulent flow of CuO/water nanofluid inside a helical duct under the constant wall surface temperature condition. The flow and heat transfer of Cu/water nanofluid in the serpentine ducts with variable straight sections were examined by Khoshvaght-Aliabadi and Alizadeh [9]. It was reported that creating short straight sections at the beginning of serpentine ducts enhanced both the heat transfer coefficient and the pressure drop values. Also, the Cu/water nanofluid increased the heat transfer rate, and the maximum performance index of 1.18 was obtained. Bhanvase et al. [10] tested water based PANI (polyaniline) nanofluid in a vertical helical duct. The heat transfer coefficient enhancements of 10.52% and 69.62% were obtained for the nanofluid at 0.1% and 0.5% volume fractions, respectively. Naik and Vinod [11] studied three different nanofluids of Fe2O3, Al2O3, and CuO
Fig. 3. (a) Schematic diagram of experimental set-up (b) Actual representation of experimental setup. 361
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Fig. 3. (continued)
coiled heat exchanger. A numerical study on the pulsating laminar flow of Al2O3/water nanofluid inside a helical microchannel heat sink with a porous medium was carried out by Sivasankaran and Narrein [17]. Kahani et al. [18] performed experiments on Al2O3/water and TiO2/ water nanofluids inside three helical ducts with different coil-diameters. They explained that due to greater thermal conductivity of Al2O3/water nanofluid compared to TiO2/water nanofluid, Al2O3/ water nanofluid showed better thermal performance. Jamshidi et al. [19] applied the Taguchi method to find the optimum operating conditions of the helical duct working with Al2O3/water nanofluid. All above mentioned studies were conducted for the nanofluid flow inside the helical and serpentine ducts, and studies in open literature on the spiral ducts are very scarce. For instance, Jamal-Abad et al. [20] tested Cu/water and Al/water nanofluids in a spiral duct. However, the other Refs. [21–23] used the conventional fluids as heat transfer media. Naphon [21] conducted numerical and experimental studies on water flow in a horizontal spiral duct. An increment about 1.5 times was reported for both the Nusselt number and the pressure drop of the spiral duct compared with the straight duct. Altaç and Altun [22] tested air and water flow in the spiral ducts with four different curvature ratios. It was found that in the studied range of Reynolds number, the heat transfer was enhanced 2–4 times over straight duct. Finally, Patil [23] applied the spiral tunes for the flow and heat transfer of petroleum base oils. The above literature survey clarifies that compared to the frequent studies on the vertically curved ducts (i.e. helical), only few investigations were reported on the horizontally curved ducts (i.e. serpentine and spiral). Likewise, none of them focused on the spirallycoiled twisted-duct particularly in the presence of nanofluid, and it will be done in the present study. Hence, the thermo-fluidic transport
characteristics of the spirally-coiled twisted-duct are experimentally studied for water as well as Cu/water nanofluid under the constant wall temperature, and numerical simulations are conducted to obtain the distributions of velocity vector and temperature contour. 2. Configurations of spirally-coiled twisted-ducts For the spirally-coiled twisted-duct, which is the geometry under consideration in the present study, the twist-pitch (tp) and the coil-pitch (cp) are the specific design parameters. Hence, the influence of these parameters is investigated and discussed. Fig. 2 shows the considered and tested spirally-coiled twisted-ducts. All geometries are created from straight aluminum ducts with square cross-section of 0.005 m × 0.005 m and thickness of 0.001 m. The creating procedure consists of two parts; (I) twisting the straight ducts to create twisted ducts at three different twist-pitches of 0.05, 0.1, and 0.15 m (II) coiling the twisted ducts to create spirally-coiled twisted-ducts at three different coil-pitches of 0.015, 0.025, and 0.035 m. As depicted in Fig. 2, the spirally-coiled twisted-duct with middle values of twist-pitch and coil-pitch (i.e. tp = 0.1 m and cp = 0.025 m, Case A) is considered as reference case, also a spirally-coiled duct with the same dimension of the reference case is considered as base line for overall performance evaluation. Note that, in all cases the working fluid starts to flow from the innermost coil and flows out from the outermost coil. Also, all cases have five 180° turns (i.e. curved parts) in order to provide adequate axial length for description of thermo-fluidic transport characteristics. 3. Experimental part Schematic diagram and actual representation of the experimental 362
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setup are shown in Fig. 3(a and b). It consists of working fluid transmission state, test chamber, cooling unit, measurement instruments, and data acquisition system. The working fluid restored inside an open container is derived to the loop by a centrifugal pump. The transmission pipelines and fittings are stainless-steel with 10 mm size. The flow rate of working fluid is controlled by adjusting a set of needle valve and rotameter. The working fluid flows through transmission pipelines and enters the test section. The test section is a spirally-coiled twisted-duct which is horizontally located in the test chamber and totally surrounded by the water steam. The connections of the test chamber are planned such that the test section can be changed easily. The surface of test section is maintained at a constant temperature condition by saturated water steam produced with the help of two electrical heaters. The power of electrical heaters is provided by a set of voltage adjuster and watt meter. The temperature and pressure of test chamber are adjusted and controlled to the desired levels by T-type thermocouple + temperature controller and solenoid valve + pressure controller. The temperature and pressure of water steam inside the test chamber are maintained at the constant values of 95 °C and 1 bar, respectively. Also, the level of liquid water inside the test chamber is controlled by level meter. The inlet/outlet temperatures and pressures of working fluid are measured by using two T-type thermocouples and two pressure transmitters. The K-type thermocouples used to measure the surface temperature are placed at the equal distances on the test section. Their signals are logged by 8 channels data logger. The maximum deviation between the first and the last surface temperature measurements is found to be less than 1 °C. After passing the test section, the working fluid reaches to the cooling unit where it is cooled to the temperature of primary container. The cooling process has two steps; cooling in a plate heat exchanger with tap water, which its flow rate is controlled with a rotameter, and cooling in a radiator + fan with ambient air. Finally, the exact flow rate of the working fluid through the loop is evaluated by an ultrasonic flow meter. Experiments are conducted at five different Graetz numbers. For each Graetz number, the inlet temperature of working fluid is adjusted to achieve the desired value of 25 °C by using the cooling unit. After the steadystate condition, the signals from the measurement instruments are recorded by the data acquisition system. In the current work, the working fluid is the Cu/water nanofluid at three concentrations of 0% (i.e. water as base fluid), 0.5%, and 1% by mass. A promising one-step technique, namely EEWL, is applied to prepare uniform and stable nanofluids. Through the EEWL technique, copper nanoparticles are generated and directly dispersed in the base fluid by explosion of a wire at high voltage of 0.5–1 kV. The nanofluids with desired concentrations are adjusted and then sonicated by an ultrasonic processor for 2 h at 400 W and 24 kHz. The EEWL technique is implemented in R&D division of PNF Co., Iran [24] using a manufactured device namely PNC1k system. Specifications of the EEWL technique and the PNC1K system are presented in Fig. 4(a and b). Also, details of characterization and measurement of the Cu/water nanofluid properties are available in Refs. [25–27]. Therefore to prevent from duplication they are not presented here. As shown in Fig. 5, the prepared Cu/water nanofluids are stable for 3 days without any visible settlement, then the Cu nanoparticles start to sediment.
Fig. 4. (a) Details of EEWL (b) PNC1K system [24].
obtaining the working fluid temperature and pressure differences between the inlet and the outlet. For instance, the grids employed for the spirally-coiled twisted-duct with tp = 0.1 m and cp = 0.025 m are 168,750, 300,000, 507,670, 918,750, 1,200,000, 1,518,750, 1,953,350, 2,700,000, 3,168,750, 4,218,750, and 4,800,000. The results at the maximum Graetz number are shown in Fig. 7. It is clear that both the temperature and the pressure results become independent of grid number after 3,168,750 and further increment will not have noticeable effects. As the best trade-off between the results accuracy and the computations time, a grid number around 3,000,000 is used for all models. Some assumptions are considered before introducing the conservation equations; (I) the computational domain is 3D, (II) the working fluid is incompressible and Newtonian, (III) the flow is single-phase, steady-state, and laminar, (IV) the natural and radiation mechanisms are neglected, (V) the gravity and viscous dissipation are not considered. The resulting governing equations are as follows;
4. Numerical part In order to analyze the heat transfer and fluid flow in the spirallycoiled twisted-ducts, a numerical simulation is also carried out for the base fluid (i.e. water) at comparable geometrical parameters and equal operating conditions with the experiments. The models are produced 3D and meshed using hexagonal type structured grids. As shown in Fig. 6, higher grids concentration is employed at the interface between fluid and internal wall of spirally-coiled twisted-ducts to attain higher accuracy in the results. The mesh independence study is performed on all models by 363
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Fig. 5. Procedure of Cu/water nanofluid sedimentation.
Fig. 6. Representations of computational domain and grids concentration. 364
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Fig. 7. Effects of grid number on temperature and pressure results.
• Continuity equation ∇. V = 0
where h is the heat transfer coefficient as below, (1)
h=
• Momentum equations 1 (V . ∇) V = − ∇p + ν ∇2 V ρ
(2)
Q = mCp (Tout −Tin ) (3)
(Tw−Tb )LMTD =
As defined in Fig. 6, the inlet temperature of working fluid and the wall temperature of the spirally-coiled twisted-ducts are maintained at constant values (i.e. T = Tin and T = Tw). The velocity component of the working fluid normal to the entrance surface of models is set based on the Graetz numbers (i.e. u = uin), and all velocity components at the wall of spirally-coiled twisted-ducts are considered no-slip and assumed to zero (i.e. u = v = w = 0). At the exit surface of models, the diffusion fluxes for all variables are considered to be zero (i.e. ∂u/∂n = ∂v/ ∂n = ∂w/∂n = ∂T/∂n = 0). The continuity, momentum and energy equations as well as boundary conditions in 3D models are solved using the FVM and SIMPLE. The second-order upwind differencing scheme is used for the convective terms. An iterative approach is applied until the convergence is obtained (i.e. the residual of all objective variables reaches to 10−5). Almost 500–1000 iterations are done to get the solution. This takes 180–240 min with an eight-core processor (2.69 GHz) and 32 GB of RAM.
f=
hdh κ
(10)
Δp = pin −pout
(11)
In the foregoing relations, ρ, μ, and κ are the thermo-physical properties of the working fluid, l is the length of spirally-coiled twistedduct, Ac and At are the frontal and total surface area of spirally-coiled twisted-duct, m is the mass flow rate, Tw is the average wall temperature on spirally-coiled twisted duct, and the subscripts in and out refer to inlet and outlet conditions. Likewise, in order to investigate the overall hydrothermal performance of the spirally-coiled twisted-ducts, the following performance index is also used [28], 1 3
NuSpirally − coiled twisted tube ⎞ ⎛ fSpirally − coiled tube ⎞ η = ⎜⎛ ⎟ ⎜ ⎟ ⎝ NuSpirally − coiled tube ⎠ ⎝ fSpirally − coiled twisted tube ⎠
(12)
The main reason for the uncertainties in the experimental data is due to the measuring errors of quantities, such as flow rate, temperatures, and pressures. Uncertainty values are estimated based on the accuracy of each instrument and the following equation [29],
(4)
2
δE = (5)
2
2
⎛ ∂E ea ⎞ + ⎛ ∂E eb ⎞ + ⎛ ∂E ec ⎞ + ... ⎝ ∂a ⎠ ⎝ ∂b ⎠ ⎝ ∂c ⎠
(13)
where a, b, c, … are the measuring data with the obtained or given uncertainties of ea, eb, ec, ….… The derived results show that the average uncertainties of Graetz number, Nusselt number, and friction factor due to measurement errors in this study are less than 4%.
The Nusselt number is written as follows,
Nu =
(9)
2Δpdh ρuin2 l
where dh is the hydraulic diameter as below,
4Ac l At
ΔTw − in−ΔTw − out log(ΔTw − in ΔTw − out )
where Δp is the pressure drop as below,
The relation between the inlet velocity and the Reynolds number is defined as follows,
dh =
(8)
The friction factor is attained as follows,
5. Data reduction
ρuin dh Re = μ
(7)
where Q and (Tw − Tb)LMTD are, respectively, the convection heat transfer rate and the logarithmic mean temperature difference of walland-bulk fluid as below,
• Energy equation (V . ∇) T = α ∇2 T
Q At (Tw−Tb )LMTD
(6) 365
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6. Results and discussions
28.4%, and 21.7% higher than that found in the original shape of spirally-coiled duct, respectively. Actually, the thermal improvement in spirally-coiled twisted-ducts is attributed to the combined impacts of rotational flows induced by both geometries (i.e. twisted-duct and spiral-coil). Fig. 11 compares the upstream 3D-streamlines of spirally-coiled twisted-ducts with those of original shape of spirally-coiled duct at the maximum Graetz numbers. It can be seen that the streamlines are almost straight in the original case and gradually become disordered as the twist-pitch of spirally-coiled twisted-duct increases. This intensifies rotational flows which provides longer flow path and improves the thermal performance. As depicted in the streamlines, the intensive mixing of fluid in the spirally-coiled twisted-ducts results to rapid change in velocity magnitude which leads to higher pressure gradient and flow resistance than the original case. Moreover, the velocity contours clarify that there are some small scales of rotational flows appearing in the corner parts of spirally-coiled twisted-ducts crosssection which indicates an important difference from the original case. Both the velocity and the temperature distributions in the cross-sections of original case are symmetric while those of spirally-coiled twistedducts are not symmetric and become tortuous with the increase of twistpitch. The specific design parameters of twist-pitch (tp) and coil-pitch (cp) show a significant role in the thermal performance of the spirally-coiled twisted-ducts as it is found that the cases with smaller twist-pitch and coil-pitch generally yield higher values of the heat transfer coefficient than the ones with larger twist-pitch and coil-pitch. This is related to two subjects; (I) the stronger interaction between the rotational flows generated by the twisted-duct and those generated by the spiral-coil as mentioned above (II) the smaller twist-pitch and coil-pitch which help to intensify flow velocity and shear force through the spirally-coiled twisted-duct resulting in superior convective mixing between the hot region near the wall and the cold region in the center. Effects of the twist-pitch and the coil-pitch on velocity and temperature contours of the spirally-coiled twisted-ducts are displayed in Fig. 12. Note that, the velocity and temperature legends are similar to Fig. 11 and the 3rd and 6th planes in this figure are represented as inlet and outlet parts of the spirally-coiled twisted-ducts, respectively. Also, the temperature contours encompass both the axial and the normal representations. The numerical results specify that the velocity contours (i.e. flow pattern) are different for each case depending on the spirally-coiled twisted-duct configuration; thereby affecting the temperature contours. Obviously, at the entrance of different cases, the working fluid has the highest velocity and centrifugal force in the center part of spirally-coiled twisted-ducts. However, it is visible in the velocity contours of Fig. 12
6.1. Validation Due to a lack of data for the spirally-coiled twisted-ducts, first, the Nusselt number of water flow in the spirally-coiled duct is considered to validate the accuracy of the current experimental data and numerical results against those of predicted by Patil correlation [23],
Nu = 2.96Gz 0.545 for 3 ⩽ Gz ⩽ 786 and 12 < Re < 6013
(14)
The dimensionless Graetz number is defined as,
Gz =
mCp κl
d π = RePr ⎛ h ⎞ ⎛ ⎞ ⎝ l ⎠⎝ 4 ⎠
(15)
Fig. 8 shows the outcomes of the comparison. A reasonable agreement is found from the comparison between the current results and the predicted values by Eq. (14). However, it can be clearly seen that the results obtained from the numerical part are very well agreement with data recorded from the experimental part. Across the whole range of Graetz number, the average deviation is within ± 5%. It clarifies that the adopted numerical simulation can simulate reasonably well the experimental procedure. Hence, it will be employed to conduct a detailed analysis to describe thermo-fluidic transport characteristics of the spirally-coiled twisted-ducts. The current experimental data for 0.5% Cu/water nanofluid flow in the spirally-coiled duct are also compared with those obtained for a spirally-coiled duct with circular cross-section by Jamal-Abad et al. [20] in Fig. 9. The Nusselt number values have the deviation within ± 10%. This deviation may be attributed to different operating conditions and geometrical parameters. 6.2. Effects of geometrical parameters As presented in Fig. 2, the spirally-coiled twisted-ducts considered in the current work are tp = 0.1 m and cp = 0.025 m (Case A as reference model), tp = 0.05 m and cp = 0.025 m (Case B), tp = 0.15 m and cp = 0.025 m (Case C), tp = 0.1 m and cp = 0.015 m (Case D), and tp = 0.1 m and cp = 0.035 m (Case E). In order to investigate the thermal characteristic of considered cases, the average heat transfer coefficient values are evaluated against to the Graetz number in Fig. 10. The thermal outcomes demonstrate that the use of twisted-ducts in spiral-coil results in considerably higher heat transfer coefficient that the use of the straight-duct particularly at higher Graetz numbers. For instance, at the maximum Graetz numbers, the heat transfer coefficient in Case A, Case B, Case C, Case D, and Case E is 25.1%, 50.1%, 9.9%,
Fig. 8. Comparison between current work and Patil correlation [23] for Nusselt number of water flow through spirally-coiled-tube. 366
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Fig. 9. Comparison between current work and Jamal-Abad et al. [20] for Nusselt number of 0.5% Cu/water nanofluid flow through spirally-coiled tube.
Fig. 10. Heat transfer coefficient – Graetz number.
twisted-duct at the wall are kept constant, the outlet temperature of working fluid decreases with increasing the Graetz number. Certainly, as shown in Fig. 10, the heat transfer rate is enhanced as the Graetz number goes up, but the increasing rate of heat transfer is less than that of working fluid flow rate [21]. Therefore, the outlet temperature of the working fluid is higher at lower Graetz numbers, and it is reduced with increasing the Graetz number. The mentioned phenomena suggest that both the twist-pitch and the coil-pitch are the key factors for the thermal improvement in the spirally-coiled twisted-ducts. However, it is found that at the studied ranges the effect of coil-pitch is more than that of twist-pitch; the heat transfer coefficient increases averagely 17.9% for the coil-pitch decrement from 0.035 m to 0.015 m, and it increases averagely 9.3% for the twist-pitch decrement from 0.015 m to 0.005 m. In order to create a better insight, variations of the ratio of Nusselt number for different cases to that for the reference one (i.e. Case A) are plotted in Fig. 14. The results of the pressure drop for all studied cases are revealed in Fig. 15. As expected, the pressure drop augments with increasing the Graetz number, and the pressure drop of spirally-coiled twisted-ducts is higher than that of spirally-coiled duct due to more complexity in rotational flows. Evidently, at the same coil-pitch, the pressure drop increases with decreasing the twist-pitch due to more rotation in the flow
that at the distance away from the entrance, the centrifugal force pushes the working fluid away from the center part to the twisted walls. It results that the maximum velocity shifts from the center part and occurs near the inner wall of spirally-coiled twisted-ducts. It has an important effect on the heat transfer enhancement and shifts the maximum temperature toward the outer curvatures. This phenomena intensify as the Graetz number goes up. For instance, the effects of Graetz number on the velocity and temperature contours of reference one (i.e. Case A) are depicted in Fig. 13. It can be seen that at higher Graetz number, the fluid mixing is enhanced through the spirally-coiled twisted-duct and more uniform temperature filed is obtained. The velocity contours show that the center part of flow (red1 region) in higher Graetz number is smaller than in lower Graetz number, which means that more parts of working fluid are induced in rotational flows and the mixing between fluids at the core and the wall regions is enhanced. Considering the data obtained from the experimental part and those from the numerical results, when the temperature of working fluid at the inlet and temperature of spirally-coiled
1 For interpretation of color in Fig. 13, the reader is referred to the web version of this article.
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Fig. 11. A comparison on velocity and temperature contours between spirally-coiled twisted-tubes and original spirally-coiled tube.
path; ΔpCase B > ΔpCase A > ΔpCase C. Also, at the same twist-pitch, the pressure drop increases with increasing the coil-pitch due to the longer flow path; ΔpCase E > ΔpCase A > ΔpCase D. Actually, at the same turns
of coil, the flow path increases with increasing the coil-pitch. This specifies that both the twist-pitch and the coil-pitch are the key factors in the pressure drop of spirally-coiled twisted-ducts. However, at the 368
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Fig. 12. Effects of twist-pitch and coil-pitch on velocity contours (Top) and temperature contours (Bottom) of spirally-coiled twisted-tubes at maximum Graetz numbers.
different cases to that for the reference one (i.e. Case A) is computed and plotted against to the Graetz number in Fig. 16. Among the studied cases, the use of spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m (Case B) results in the maximum values which are higher than those associated with the use of spirally-coiled twisted-duct at
same Graetz number, the pressure drop values of Case D and spirallycoiled duct are comparable, and the pressure drop values of Case A, Case B, Case C, and Case E are averagely 4.6%, 15.9%, 1.9%, and 16.6% above those of spirally-coiled duct. A normalized friction factor defined as the ratio of friction factor for 369
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Fig. 13. Effects of Graetz number on velocity contours (Top) and temperature contours (Bottom) of reference model (i.e. Case A).
Fig. 14. Nusselt number ratio – Graetz number.
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Fig. 15. Pressure drop – Graetz number.
Fig. 16. Friction factor ratio – Graetz number.
Fig. 17. Performance index – Graetz number.
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Fig. 18. Performance index ratio – Graetz number.
viscosity and density of nanofluid augments the pressure drop. However, the influence of heat transfer enhancement may overcome the influence of pressure drop augmentation by adding copper nanoparticles in water. According to Fig. 19(c), the net effects of nanofluid improve the overall hydrothermal performance of spirally-coiled twisted-duct compared to water. This figure elucidates that the Cu/ water nanofluids perform better than water for the spirally-coiled twisted-duct. Also, the overall performance of spirally-coiled twistedduct is improved with increasing the nanoparticles concentration and Graetz number. However, after the Graetz number around 30, the performance index of nanolfuids decreases compared to that of water. In order to save the space, the plots corresponding to the other cases are not presented, and the average variations of heat transfer coefficient, pressure drop, and performance index with nanoparticle concentration are tabulated in Table 1. It is obvious that at the studied range of Graetz number, the effects of nanolfuid on thermal and hydraulic characteristics of the spirally-coiled twisted-duct enhances as both the twist-pitch and the coil-pitch decrease. For instance, the maximum variations are recorded for Case B which has the lowest twist-pitch.
tp = 0.1 m and cp = 0.015 m (Case D). It is also reveal that the effect of the twist-pitch on the friction factor of spirally-coiled twisted-duct is considerably higher than that of coil-pitch. The overall hydrothermal performance results of the spirally-coiled twisted-ducts are shown in Fig. 17. In general, the performance index of spirally-coiled twisted-ducts is enhanced with increasing the Graetz number. Therefore, the effect of twisting duct in promoting the heat transfer at higher Graetz numbers is more significant than that at lower Graetz numbers. In common, at the Graetz numbers higher than 25, the performance index gets values higher than unity. For instance, at the maximum Graetz number the performance index in Case A, Case B, Case C, Case D, and Case E is 1.21, 1.39, 1.09, 1.23, and 1.19, respectively. It implies that the use of a spirally-coiled twisted-duct is efficient than the use of the spirally-coiled duct form the considered hydrothermal performance index point of view. The performance index increases with decreasing both the twistpitch and the coil-pitch, because according to Figs. 14 and 16, the increase of Nusselt number is more dominant than that of friction factor as the twist-pitch and the coil-pitch decrease. As compared to the reference model, the results presented in Fig. 18 disclose that the effect of twist-pitch on the hydrothermal performance of spirally-coiled twistedduct is more pronounced at higher Graetz numbers. In contrast, at lower Graetz numbers, the effect of coil-pitch is more noticeable.
6.4. Correlations Although the interest in curved ducts is on the rise, there are very few correlations for prediction of thermal and hydraulic characteristics. The current work deals with the laminar flow of water as well as Cu/ water nanofluid through a new introduced curved geometry called spirally-coiled twisted-duct. The obtained data are used in order to introduce correlations on Nusselt number and friction factor. The proposed correlations, which are function of geometrical parameters and operating conditions and valid for the Graetz number between 14 and 58, are as follows,
6.3. Effects of Cu/water nanofluid In order to further improve the performance of spirally-coiled twisted-ducts, the Cu/water nanofluid is tested through the studied cases. The mass concentrations of Cu/water nanofluid are chosen as 0.5% and 1.0%. Fig. 19(a–c) illustrates the effects of nanofluid concentration on heat transfer coefficient, pressure drop, and performance index of the reference case (i.e. Case A). It reveals that adding low mass concentration of copper nanoparticles to water leads to a noticeable enhancement in the heat transfer coefficient between 6% and 28% with a certain penalty in the pressure drop between 3% and 6%. The heat transfer enhancements are due to the higher thermal conductivity of the nanofluid and the role of Brownian motion of nanoparticles. Also, at higher mass concentration, the nanoparticles have larger surface area and molecular collisions leading to higher momentum and energy transports. In general, the presence of copper nanoparticles explains two opposing effects on thermal and hydraulic characteristics of the spirally-coiled twisted-duct; the favorable effect which is driven by high thermal conductivity of nanofluid enhances the heat transfer coefficient, and the undesirable effect which is driven by high dynamic
cp Nu = 1.267Gr 0.839 ⎜⎛ ⎟⎞ ⎝ tp ⎠
0.154
(16)
−0.044
cp f = 0.177Gr −0.547 ⎜⎛ ⎟⎞ ⎝ tp ⎠
(17)
An excellent agreement between the predicted data and the obtained results with the mean absolute error of 6.2% for the Nusselt number and 7.2% for the friction factor is recorded. For instance, Fig. 20(a and b) shows the comparison between the predicted data and the obtained results when water is as working fluid. 372
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Fig. 19. (a) Heat transfer coefficient – Graetz number (b) Pressure drop – Graetz number (c) Performance index – Graetz number of reference case (i.e. Case A).
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7. Conclusions
Table 1 Average variations of heat transfer coefficient, pressure drop, and performance index with nanoparticle concentration for different cases (%). TST
Parameter
0.5% nanofluid
1.0% nanofluid
Case A tp = 0.1 m cp = 0.025 m
h Δp η
8.7 2.6 7.8
26.4 5.3 24.6
Case B tp = 0.05 m cp = 0.025 m
h Δp η
18.1 3.5 15.9
36.9 7.6 32.4
Case C tp = 0.15 m cp = 0.025 m
h Δp η
6.2 2.3 6.9
23.1 4.8 21.1
Case D tp = 0.1 m cp = 0.015 m
h Δp η
9.4 2.7 8.5
28.2 5.4 26.2
Case E tp = 0.1 m cp = 0.035 m
h Δp η
8.5 2.6 7.6
25.4 5.3 23.4
Thermo-fluidic transport characteristics of a new design of curved ducts, namely spirally-coiled twisted-duct, are investigated both experimentally and numerically. The results are compared with the original shape of spirally-coiled duct. Water and Cu/water nanofluid are considered as working fluid. The following conclusions can be made from the outcomes of the current study,
• Both the experiments and the simulations are performed under la• •
• •
minar flow regime and constant wall temperature condition. The validation procedure is made by comparing available correlation and experimental data, and the average deviation within ± 10% is obtained. Considerable enhancements in the heat transfer coefficient are recorded for the spirally-coiled twisted-duct compared with the original shape. For instance, at the maximum Graetz numbers they are about 25.1%, 50.1%, 9.9%, 28.4%, and 21.7% for Case A, Case B, Case C, Case D, and Case E, respectively. The overall hydrothermal performance of spirally-coiled twistedduct improves as the twist-pitch and coil-pitch are decreased; at lower Graetz numbers the best performance is recorded for the case with lowest coil-pitch (i.e. Case D) and at higher Graetz numbers the best performance is recorded for the case with lowest twist-pitch (i.e. Case B). The Cu/water nanofluids are prepared by the EEWL technique and they are found very stable. The nanofluids have higher heat transfer coefficient and pressure drop compared to pure water. Likewise, the nanofluid with the higher concentration provides higher values. The results clarify that the effects of nanofluid flow in the spirallycoiled twisted-duct are more intensified at lower twist-pitch and coil-pitch.
Finally, this study can create applied guidelines to design more efficient and compact heat exchangers. References [1] H. Zhao, X. Li, X. Wu, Numerical investigation of supercritical water turbulent flow and heat transfer characteristics in vertical helical tubes, J. Supercrit. Fluids 127 (2017) 48–61. [2] M.M. Etghani, S.A.H. Baboli, Numerical investigation and optimization of heat transfer and exergy loss in shell and helical tube heat exchanger, Appl. Therm. Eng. 121 (2017) 294–301. [3] J.C. Kurnia, A.P. Sasmito, T. Shamim, A.S. Mujumdar, Numerical investigation of heat transfer and entropy generation of laminar flow in helical tubes with various cross sections, Appl. Therm. Eng. 102 (2016) 849–860. [4] D. Panahi, K. Zamzamian, Heat transfer enhancement of shell-and-coiled tube heat exchanger utilizing helical wire turbulator, Appl. Therm. Eng. 115 (2017) 607–615. [5] H.K. Bizhaem, A. Abbassi, Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model, Adv. Powder Technol. 28 (9) (2017) 2110–2125. [6] M. Khoshvaght-Aliabadi, S. Pazdar, O. Sartipzadeh, Experimental investigation of water based nanofluid containing copper nanoparticles across helical microtubes, Int. Commun. Heat Mass Transfer 70 (2016) 84–92. [7] M. Khoshvaght-Aliabadi, F. Rahimpour, O. Sartipzadeh, S. Pazdar, Heat transfer enhancement by combination of serpentine curves and nanofluid flow in microtube, Exp. Heat Transfer 30 (3) (2017) 235–252. [8] M. Rakhsha, F. Akbaridoust, A. Abbassi, S.A. Majid, Experimental and numerical investigations of turbulent forced convection flow of nano-fluid in helical coiled tubes at constant surface temperature, Powder Technol. 283 (2015) 178–189. [9] M. Khoshvaght-Aliabadi, A. Alizadeh, An experimental study of Cu–water nanofluid flow inside serpentine tubes with variable straight-section lengths, Exp. Therm Fluid Sci. 61 (2015) 1–11. [10] B.A. Bhanvase, S.D. Sayankar, A. Kapre, P.J. Fule, S.H. Sonawane, Experimental investigation on intensified convective heat transfer coefficient of water based PANI nanofluid in vertical helical coiled heat exchanger, Appl. Therm. Eng. 128 (2018) 134–140. [11] B.A.K. Naik, A.V. Vinod, Heat transfer enhancement using non-Newtonian nanofluids in a shell and helical coil heat exchanger, Exp. Therm Fluid Sci. 90 (2018) 132–142.
Fig. 20. Comparison between predicted data and obtained results (a) Nusselt number (b) Friction factor.
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[12] T. Srinivas, A.V. Vinod, Heat transfer intensification in a shell and helical coil heat exchanger using water-based nanofluids, Chem. Eng. Process. Process Intensif. 102 (2016) 1–8. [13] T. Srinivas, A.V. Vinod, Performance of an agitated helical coil heat exchanger using Al2O3/water nanofluid, Exp. Therm Fluid Sci. 51 (2013) 77–83. [14] M. Khoshvaght-Aliabadi, M. Nouri, O. Sartipzadeh, M. Salami, Performance of agitated serpentine heat exchanger using metallic nanofluids, Chem. Eng. Res. Des. 109 (2016) 53–64. [15] Z.Wu.L. Wang, B. Sundén, L. Wadsö, Aqueous carbon nanotube nanofluids and their thermal performance in a helical heat exchanger, Appl. Therm. Eng. 96 (2016) 364–371. [16] Z. Wu, L. Wang, B. Sundén, Pressure drop and convective heat transfer of water and nanofluids in a double-pipe helical heat exchanger, Appl. Therm. Eng. 60 (1–2) (2013) 266–274. [17] S. Sivasankaran, K. Narrein, Numerical investigation of two-phase laminar pulsating nanofluid flow in helical microchannel filled with a porous medium, Int. Commun. Heat Mass Transfer 75 (2016) 86–91. [18] M. Kahani, S. Zeinali Heris, S.M. Mousavi, Comparative study between metal oxide nanopowders on thermal characteristics of nanofluid flow through helical coils, Powder Technol. 246 (2013) 82–92. [19] N. Jamshidi, M. Farhadi, K. Sedighi, D.D. Ganji, Optimization of design parameters for nanofluids flowing inside helical coils, Int. Commun. Heat Mass Transfer 39 (2) (2012) 311–317. [20] M.T. Jamal-Abad, A. Zamzamian, M. Dehghan, Experimental studies on the heat
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transfer and pressure drop characteristics of Cu–water and Al–water nanofluids in a spiral coil, Exp. Therm Fluid Sci. 47 (2013) 206–212. P. Naphon, Study on the heat transfer and flow characteristics in a spiral-coil tube, Int. Commun. Heat Mass Transfer 38 (2011) 69–74. Z. Altaç, Ö. Altun, Hydrodynamically and thermally developing laminar flow in spiral coil tubes, Int. J. Therm. Sci. 77 (2014) 96–107. R.H. Patil, Experimental studies on heat transfer to Newtonian fluids through spiral coils, Exp. Therm Fluid Sci. 84 (2017) 144–155. Payamavaran Nanotechnology Fardanegar (PNF) Nano Engineering & Manufacturing Co.. M. Khoshvaght-Aliabadi, P. Rahnama, A. Zanganeh, M.H. Akbari, Experimental study on metallic water nanofluids flow inside rectangular duct equipped with circular pins (pin channel), Exp. Therm Fluid Sci. 72 (2016) 18–30. M. Khoshvaght-Aliabadi, H. Shabanpour, A. Alizadeh, O. Sartipzadeh, Experimental assessment of different inserts inside straight tubes: nanofluid as working media, Chem. Eng. Process. Process Intensif. 97 (2015) 1–11. M. Khoshvaght-Aliabadi, M. Eskandari, Influence of twist length variations on thermal–hydraulic specifications of twisted-tape inserts in presence of Cu–water nanofluid, Exp. Therm Fluid Sci. 61 (2015) 230–240. R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transf. 24 (1981) 715–726. J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, second ed., University Science Books, 1997.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
An investigation of heat transfer in heat exchange devices with spirallycoiled twisted-ducts using nanofluid
T
⁎
M. Khoshvaght-Aliabadia, , S.F. Khalighb, Z. Tavassolia a b
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran Department of Chemistry, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran
H I GH L IG H T S
G R A P H I C A L A B S T R A C T
transport character• Thermo-fluidic istics of spirally-coiled twisted-tube are investigated.
and Cu/water are used as • Water working fluid. and coil-pitch have con• Twist-pitch siderable effects on performance of studied cases.
performance indexes of • Maximum 1.39 and 1.88 are recorded for water and nanofluid.
A R T I C LE I N FO
A B S T R A C T
Keywords: Spirally-coiled twisted-ducts Cu/water nanofluid Twist-pitch Coil-pitch
A new design of curved ducts namely spirally-coiled twisted-duct is introduced and analyzed both experimentally and numerically. Water and Cu/water nanofluid at two concentrations of 0.5% and 1% by mass are considered as working fluid. The results show that the dependence of thermo-fluidic transport characteristics on the geometry of spirally-coiled twisted-duct is strongly influenced by twist-pitch (tp) and coil-pitch (cp). The studied ranges are tp = 0.05, 0.1, and 0.15 m and cp = 0.015, 0.025, and 0.035 m. The maximum augmentations of Nusselt number and friction factor are recorded for the spirally-coiled twisted-ducts with the lowest twist-pitch and coil-pitch (i.e. tp = 0.05 and cp = 0.015). One of the key outcomes of this work is that the effect of twistpitch is more pronounced at higher Graetz numbers, while at lower Graetz numbers the effect of coil-pitch is more noticeable. Likewise, with the deployment of a performance index combining the enhancement in Nusselt number and corresponding augmentation in friction factor, the overall hydrothermal performance of spirallycoiled twisted-ducts is assessed. Among the studied cases, the spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m possesses the highest performance index of 1.39 at the maximum Graetz number. Also, a noticeable heat transfer enhancement due to suspension of copper nanoparticles in water is obtained with a certain augmentation in the pressure drop, and the enhancement is intensified with increasing the concentration of nanoparticles. The performance index enhances up to 1.88 when the 1.0% nanofluid is used in the spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m. Finally, using the obtained results, two correlations are established to model Nusselt number and friction factor inside the spirally-coiled twisted-ducts for the Graetz number range of 14–58.
⁎
Corresponding author at: Postal address: 36199-43189, Iran. E-mail address: [email protected] (M. Khoshvaght-Aliabadi).
https://doi.org/10.1016/j.applthermaleng.2018.07.112 Received 3 April 2018; Received in revised form 16 July 2018; Accepted 23 July 2018 Available online 23 July 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
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ρ
Nomenclature Ac At Cp cp dh h l m p Q T tp u, v, w V x, y, z
density, kg/m3
Subscripts
frontal surface area, m2 total surface area, m2 specific heat capacity, J/kg K coil-pitch, m hydraulic diameter, m heat transfer coefficient, W/m2 K duct length, m mass flow rate, kg/s pressure, Pa heat transfer rate, W temperature, K twist-pitch, m velocity components, m/s velocity, m/s coordinates
b in out w
bulk inlet outlet wall
Dimensionless groups f Gr Nu Pr Re
Friction factor Graetz number Nusselt number Prandtl number Reynolds number
Acronyms
Greek symbols η κ μ ν α
EEWL FVM LMTD PNFC R&D SIMPLE
performance factor thermal conductivity, W/m K dynamic viscosity, kg/m s kinematic viscosity, m2/s thermal diffusivity, m2/s
1. Introduction
Electrical Explosion of Wires in Liquid Finite Volume Method Logarithmic Mean Temperature Difference Payamavaran Nanotechnology Fardanegar Research and Development Semi Implicit Method for Pressure Linked Equation
duct, and it was enhanced with decreasing of the helical radius. Etghani and Baboli [2] studied helical ducts embedded inside a shell with different geometrical and operating parameters. A better thermal performance was detected at higher cold and hot flow rates and lower coilpitches. Kurnia et al. [3] investigated three different cross-section shapes, including circular, ellipse and square, on the performance of helical duct. It was found that the square cross-section had the highest entropy, followed by ellipse and circular ones. Some studies focused on the use of turbulators or inserts as passive technique inside the curved ducts. For instance, Panahi and Zamzamian [4] used the helical wire as a turbulator inside the helical duct. Their results showed that the applied technique could significantly enhance the overall thermal performance of the helical duct with an increase in the pressure drop. As the other enhanced technique, the nanofluid was tested as the working fluid inside the curved ducts. Bizhaem and Abbassi [5] conducted numerical simulations on Al2O3/water nanofluid flow inside a helical duct. The findings disclosed that water and nanofluid have
Curved ducts have compact structure and good hydrothermal performance, so they have been widely used in various industrial and engineering applications, such as heat exchangers, solar systems, chemical reactors, food processes, etc. As shown in Fig. 1, helical, serpentine, and spiral geometries are well known configurations of curved ducts. The transport phenomena (i.e. momentum, heat, and mass) occurring in these geometries are more complex than those in straight ducts. As a fluid passes through the helical, serpentine, or spiral ducts, the presence of curvatures in the fluid path leads to centrifugal forces thereby rotational flows are induced which have significant ability to increase the rate of transport phenomena. Actually, the performance of curved ducts strongly depend on the behavior of generated rotational flows. Zhao et al. [1] simulated turbulent flow and heat transfer of supercritical water in vertical helical ducts. It was found that the heat transfer coefficient for helical ducts was higher than that for straight
Fig. 1. Well known configurations of curved ducts. 359
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almost the same velocity profiles with significant difference in the temperature profiles. Khoshvaght-Aliabadi et al. [6] conducted experiments on Cu/water nanofluid flow through helical micro-ducts with
different coil-pitches. It was concluded that the overall hydrothermal performance of helical micro-ducts were improved as the concentration of nanoparticles was increased. A similar study was conducted on
Fig. 2. Schematic of fabricated spirally-coiled twisted-tubes. 360
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nanoparticles in aqueous carboxymethyl cellulose for the use in a shell and helical duct heat exchanger. It was detected that the CuO nanoparticles showed better heat transfer than the other two types. Three nanoparticles of Al2O3, CuO and TiO2 in water as working fluid through a shell and helical duct heat exchanger were also tested by Srinivas and Vinod [12,13]. They also examined the simultaneous application of helical and Al2O3/water nanofluid in an agitated heat exchanger. It was observed that higher stirrer speed and shell-side fluid temperature resulted in more energy savings. In the other work [14], the performance of agitated heat exchanger was checked by using serpentine ducts and three different metallic nanofluids. It was found that the thermal performance of Cu/water nanofluid was more intensive than Fe/water and Ag/water nanofluids. Wu et al. [15,16] analyzed the performance of multi-walled carbon nanotube nanofluid in a double-pipe helically
serpentine micro-ducts by the same team [7]. Likewise, Rakhsha et al. [8] studied the turbulent flow of CuO/water nanofluid inside a helical duct under the constant wall surface temperature condition. The flow and heat transfer of Cu/water nanofluid in the serpentine ducts with variable straight sections were examined by Khoshvaght-Aliabadi and Alizadeh [9]. It was reported that creating short straight sections at the beginning of serpentine ducts enhanced both the heat transfer coefficient and the pressure drop values. Also, the Cu/water nanofluid increased the heat transfer rate, and the maximum performance index of 1.18 was obtained. Bhanvase et al. [10] tested water based PANI (polyaniline) nanofluid in a vertical helical duct. The heat transfer coefficient enhancements of 10.52% and 69.62% were obtained for the nanofluid at 0.1% and 0.5% volume fractions, respectively. Naik and Vinod [11] studied three different nanofluids of Fe2O3, Al2O3, and CuO
Fig. 3. (a) Schematic diagram of experimental set-up (b) Actual representation of experimental setup. 361
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Fig. 3. (continued)
coiled heat exchanger. A numerical study on the pulsating laminar flow of Al2O3/water nanofluid inside a helical microchannel heat sink with a porous medium was carried out by Sivasankaran and Narrein [17]. Kahani et al. [18] performed experiments on Al2O3/water and TiO2/ water nanofluids inside three helical ducts with different coil-diameters. They explained that due to greater thermal conductivity of Al2O3/water nanofluid compared to TiO2/water nanofluid, Al2O3/ water nanofluid showed better thermal performance. Jamshidi et al. [19] applied the Taguchi method to find the optimum operating conditions of the helical duct working with Al2O3/water nanofluid. All above mentioned studies were conducted for the nanofluid flow inside the helical and serpentine ducts, and studies in open literature on the spiral ducts are very scarce. For instance, Jamal-Abad et al. [20] tested Cu/water and Al/water nanofluids in a spiral duct. However, the other Refs. [21–23] used the conventional fluids as heat transfer media. Naphon [21] conducted numerical and experimental studies on water flow in a horizontal spiral duct. An increment about 1.5 times was reported for both the Nusselt number and the pressure drop of the spiral duct compared with the straight duct. Altaç and Altun [22] tested air and water flow in the spiral ducts with four different curvature ratios. It was found that in the studied range of Reynolds number, the heat transfer was enhanced 2–4 times over straight duct. Finally, Patil [23] applied the spiral tunes for the flow and heat transfer of petroleum base oils. The above literature survey clarifies that compared to the frequent studies on the vertically curved ducts (i.e. helical), only few investigations were reported on the horizontally curved ducts (i.e. serpentine and spiral). Likewise, none of them focused on the spirallycoiled twisted-duct particularly in the presence of nanofluid, and it will be done in the present study. Hence, the thermo-fluidic transport
characteristics of the spirally-coiled twisted-duct are experimentally studied for water as well as Cu/water nanofluid under the constant wall temperature, and numerical simulations are conducted to obtain the distributions of velocity vector and temperature contour. 2. Configurations of spirally-coiled twisted-ducts For the spirally-coiled twisted-duct, which is the geometry under consideration in the present study, the twist-pitch (tp) and the coil-pitch (cp) are the specific design parameters. Hence, the influence of these parameters is investigated and discussed. Fig. 2 shows the considered and tested spirally-coiled twisted-ducts. All geometries are created from straight aluminum ducts with square cross-section of 0.005 m × 0.005 m and thickness of 0.001 m. The creating procedure consists of two parts; (I) twisting the straight ducts to create twisted ducts at three different twist-pitches of 0.05, 0.1, and 0.15 m (II) coiling the twisted ducts to create spirally-coiled twisted-ducts at three different coil-pitches of 0.015, 0.025, and 0.035 m. As depicted in Fig. 2, the spirally-coiled twisted-duct with middle values of twist-pitch and coil-pitch (i.e. tp = 0.1 m and cp = 0.025 m, Case A) is considered as reference case, also a spirally-coiled duct with the same dimension of the reference case is considered as base line for overall performance evaluation. Note that, in all cases the working fluid starts to flow from the innermost coil and flows out from the outermost coil. Also, all cases have five 180° turns (i.e. curved parts) in order to provide adequate axial length for description of thermo-fluidic transport characteristics. 3. Experimental part Schematic diagram and actual representation of the experimental 362
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setup are shown in Fig. 3(a and b). It consists of working fluid transmission state, test chamber, cooling unit, measurement instruments, and data acquisition system. The working fluid restored inside an open container is derived to the loop by a centrifugal pump. The transmission pipelines and fittings are stainless-steel with 10 mm size. The flow rate of working fluid is controlled by adjusting a set of needle valve and rotameter. The working fluid flows through transmission pipelines and enters the test section. The test section is a spirally-coiled twisted-duct which is horizontally located in the test chamber and totally surrounded by the water steam. The connections of the test chamber are planned such that the test section can be changed easily. The surface of test section is maintained at a constant temperature condition by saturated water steam produced with the help of two electrical heaters. The power of electrical heaters is provided by a set of voltage adjuster and watt meter. The temperature and pressure of test chamber are adjusted and controlled to the desired levels by T-type thermocouple + temperature controller and solenoid valve + pressure controller. The temperature and pressure of water steam inside the test chamber are maintained at the constant values of 95 °C and 1 bar, respectively. Also, the level of liquid water inside the test chamber is controlled by level meter. The inlet/outlet temperatures and pressures of working fluid are measured by using two T-type thermocouples and two pressure transmitters. The K-type thermocouples used to measure the surface temperature are placed at the equal distances on the test section. Their signals are logged by 8 channels data logger. The maximum deviation between the first and the last surface temperature measurements is found to be less than 1 °C. After passing the test section, the working fluid reaches to the cooling unit where it is cooled to the temperature of primary container. The cooling process has two steps; cooling in a plate heat exchanger with tap water, which its flow rate is controlled with a rotameter, and cooling in a radiator + fan with ambient air. Finally, the exact flow rate of the working fluid through the loop is evaluated by an ultrasonic flow meter. Experiments are conducted at five different Graetz numbers. For each Graetz number, the inlet temperature of working fluid is adjusted to achieve the desired value of 25 °C by using the cooling unit. After the steadystate condition, the signals from the measurement instruments are recorded by the data acquisition system. In the current work, the working fluid is the Cu/water nanofluid at three concentrations of 0% (i.e. water as base fluid), 0.5%, and 1% by mass. A promising one-step technique, namely EEWL, is applied to prepare uniform and stable nanofluids. Through the EEWL technique, copper nanoparticles are generated and directly dispersed in the base fluid by explosion of a wire at high voltage of 0.5–1 kV. The nanofluids with desired concentrations are adjusted and then sonicated by an ultrasonic processor for 2 h at 400 W and 24 kHz. The EEWL technique is implemented in R&D division of PNF Co., Iran [24] using a manufactured device namely PNC1k system. Specifications of the EEWL technique and the PNC1K system are presented in Fig. 4(a and b). Also, details of characterization and measurement of the Cu/water nanofluid properties are available in Refs. [25–27]. Therefore to prevent from duplication they are not presented here. As shown in Fig. 5, the prepared Cu/water nanofluids are stable for 3 days without any visible settlement, then the Cu nanoparticles start to sediment.
Fig. 4. (a) Details of EEWL (b) PNC1K system [24].
obtaining the working fluid temperature and pressure differences between the inlet and the outlet. For instance, the grids employed for the spirally-coiled twisted-duct with tp = 0.1 m and cp = 0.025 m are 168,750, 300,000, 507,670, 918,750, 1,200,000, 1,518,750, 1,953,350, 2,700,000, 3,168,750, 4,218,750, and 4,800,000. The results at the maximum Graetz number are shown in Fig. 7. It is clear that both the temperature and the pressure results become independent of grid number after 3,168,750 and further increment will not have noticeable effects. As the best trade-off between the results accuracy and the computations time, a grid number around 3,000,000 is used for all models. Some assumptions are considered before introducing the conservation equations; (I) the computational domain is 3D, (II) the working fluid is incompressible and Newtonian, (III) the flow is single-phase, steady-state, and laminar, (IV) the natural and radiation mechanisms are neglected, (V) the gravity and viscous dissipation are not considered. The resulting governing equations are as follows;
4. Numerical part In order to analyze the heat transfer and fluid flow in the spirallycoiled twisted-ducts, a numerical simulation is also carried out for the base fluid (i.e. water) at comparable geometrical parameters and equal operating conditions with the experiments. The models are produced 3D and meshed using hexagonal type structured grids. As shown in Fig. 6, higher grids concentration is employed at the interface between fluid and internal wall of spirally-coiled twisted-ducts to attain higher accuracy in the results. The mesh independence study is performed on all models by 363
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Fig. 5. Procedure of Cu/water nanofluid sedimentation.
Fig. 6. Representations of computational domain and grids concentration. 364
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Fig. 7. Effects of grid number on temperature and pressure results.
• Continuity equation ∇. V = 0
where h is the heat transfer coefficient as below, (1)
h=
• Momentum equations 1 (V . ∇) V = − ∇p + ν ∇2 V ρ
(2)
Q = mCp (Tout −Tin ) (3)
(Tw−Tb )LMTD =
As defined in Fig. 6, the inlet temperature of working fluid and the wall temperature of the spirally-coiled twisted-ducts are maintained at constant values (i.e. T = Tin and T = Tw). The velocity component of the working fluid normal to the entrance surface of models is set based on the Graetz numbers (i.e. u = uin), and all velocity components at the wall of spirally-coiled twisted-ducts are considered no-slip and assumed to zero (i.e. u = v = w = 0). At the exit surface of models, the diffusion fluxes for all variables are considered to be zero (i.e. ∂u/∂n = ∂v/ ∂n = ∂w/∂n = ∂T/∂n = 0). The continuity, momentum and energy equations as well as boundary conditions in 3D models are solved using the FVM and SIMPLE. The second-order upwind differencing scheme is used for the convective terms. An iterative approach is applied until the convergence is obtained (i.e. the residual of all objective variables reaches to 10−5). Almost 500–1000 iterations are done to get the solution. This takes 180–240 min with an eight-core processor (2.69 GHz) and 32 GB of RAM.
f=
hdh κ
(10)
Δp = pin −pout
(11)
In the foregoing relations, ρ, μ, and κ are the thermo-physical properties of the working fluid, l is the length of spirally-coiled twistedduct, Ac and At are the frontal and total surface area of spirally-coiled twisted-duct, m is the mass flow rate, Tw is the average wall temperature on spirally-coiled twisted duct, and the subscripts in and out refer to inlet and outlet conditions. Likewise, in order to investigate the overall hydrothermal performance of the spirally-coiled twisted-ducts, the following performance index is also used [28], 1 3
NuSpirally − coiled twisted tube ⎞ ⎛ fSpirally − coiled tube ⎞ η = ⎜⎛ ⎟ ⎜ ⎟ ⎝ NuSpirally − coiled tube ⎠ ⎝ fSpirally − coiled twisted tube ⎠
(12)
The main reason for the uncertainties in the experimental data is due to the measuring errors of quantities, such as flow rate, temperatures, and pressures. Uncertainty values are estimated based on the accuracy of each instrument and the following equation [29],
(4)
2
δE = (5)
2
2
⎛ ∂E ea ⎞ + ⎛ ∂E eb ⎞ + ⎛ ∂E ec ⎞ + ... ⎝ ∂a ⎠ ⎝ ∂b ⎠ ⎝ ∂c ⎠
(13)
where a, b, c, … are the measuring data with the obtained or given uncertainties of ea, eb, ec, ….… The derived results show that the average uncertainties of Graetz number, Nusselt number, and friction factor due to measurement errors in this study are less than 4%.
The Nusselt number is written as follows,
Nu =
(9)
2Δpdh ρuin2 l
where dh is the hydraulic diameter as below,
4Ac l At
ΔTw − in−ΔTw − out log(ΔTw − in ΔTw − out )
where Δp is the pressure drop as below,
The relation between the inlet velocity and the Reynolds number is defined as follows,
dh =
(8)
The friction factor is attained as follows,
5. Data reduction
ρuin dh Re = μ
(7)
where Q and (Tw − Tb)LMTD are, respectively, the convection heat transfer rate and the logarithmic mean temperature difference of walland-bulk fluid as below,
• Energy equation (V . ∇) T = α ∇2 T
Q At (Tw−Tb )LMTD
(6) 365
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6. Results and discussions
28.4%, and 21.7% higher than that found in the original shape of spirally-coiled duct, respectively. Actually, the thermal improvement in spirally-coiled twisted-ducts is attributed to the combined impacts of rotational flows induced by both geometries (i.e. twisted-duct and spiral-coil). Fig. 11 compares the upstream 3D-streamlines of spirally-coiled twisted-ducts with those of original shape of spirally-coiled duct at the maximum Graetz numbers. It can be seen that the streamlines are almost straight in the original case and gradually become disordered as the twist-pitch of spirally-coiled twisted-duct increases. This intensifies rotational flows which provides longer flow path and improves the thermal performance. As depicted in the streamlines, the intensive mixing of fluid in the spirally-coiled twisted-ducts results to rapid change in velocity magnitude which leads to higher pressure gradient and flow resistance than the original case. Moreover, the velocity contours clarify that there are some small scales of rotational flows appearing in the corner parts of spirally-coiled twisted-ducts crosssection which indicates an important difference from the original case. Both the velocity and the temperature distributions in the cross-sections of original case are symmetric while those of spirally-coiled twistedducts are not symmetric and become tortuous with the increase of twistpitch. The specific design parameters of twist-pitch (tp) and coil-pitch (cp) show a significant role in the thermal performance of the spirally-coiled twisted-ducts as it is found that the cases with smaller twist-pitch and coil-pitch generally yield higher values of the heat transfer coefficient than the ones with larger twist-pitch and coil-pitch. This is related to two subjects; (I) the stronger interaction between the rotational flows generated by the twisted-duct and those generated by the spiral-coil as mentioned above (II) the smaller twist-pitch and coil-pitch which help to intensify flow velocity and shear force through the spirally-coiled twisted-duct resulting in superior convective mixing between the hot region near the wall and the cold region in the center. Effects of the twist-pitch and the coil-pitch on velocity and temperature contours of the spirally-coiled twisted-ducts are displayed in Fig. 12. Note that, the velocity and temperature legends are similar to Fig. 11 and the 3rd and 6th planes in this figure are represented as inlet and outlet parts of the spirally-coiled twisted-ducts, respectively. Also, the temperature contours encompass both the axial and the normal representations. The numerical results specify that the velocity contours (i.e. flow pattern) are different for each case depending on the spirally-coiled twisted-duct configuration; thereby affecting the temperature contours. Obviously, at the entrance of different cases, the working fluid has the highest velocity and centrifugal force in the center part of spirally-coiled twisted-ducts. However, it is visible in the velocity contours of Fig. 12
6.1. Validation Due to a lack of data for the spirally-coiled twisted-ducts, first, the Nusselt number of water flow in the spirally-coiled duct is considered to validate the accuracy of the current experimental data and numerical results against those of predicted by Patil correlation [23],
Nu = 2.96Gz 0.545 for 3 ⩽ Gz ⩽ 786 and 12 < Re < 6013
(14)
The dimensionless Graetz number is defined as,
Gz =
mCp κl
d π = RePr ⎛ h ⎞ ⎛ ⎞ ⎝ l ⎠⎝ 4 ⎠
(15)
Fig. 8 shows the outcomes of the comparison. A reasonable agreement is found from the comparison between the current results and the predicted values by Eq. (14). However, it can be clearly seen that the results obtained from the numerical part are very well agreement with data recorded from the experimental part. Across the whole range of Graetz number, the average deviation is within ± 5%. It clarifies that the adopted numerical simulation can simulate reasonably well the experimental procedure. Hence, it will be employed to conduct a detailed analysis to describe thermo-fluidic transport characteristics of the spirally-coiled twisted-ducts. The current experimental data for 0.5% Cu/water nanofluid flow in the spirally-coiled duct are also compared with those obtained for a spirally-coiled duct with circular cross-section by Jamal-Abad et al. [20] in Fig. 9. The Nusselt number values have the deviation within ± 10%. This deviation may be attributed to different operating conditions and geometrical parameters. 6.2. Effects of geometrical parameters As presented in Fig. 2, the spirally-coiled twisted-ducts considered in the current work are tp = 0.1 m and cp = 0.025 m (Case A as reference model), tp = 0.05 m and cp = 0.025 m (Case B), tp = 0.15 m and cp = 0.025 m (Case C), tp = 0.1 m and cp = 0.015 m (Case D), and tp = 0.1 m and cp = 0.035 m (Case E). In order to investigate the thermal characteristic of considered cases, the average heat transfer coefficient values are evaluated against to the Graetz number in Fig. 10. The thermal outcomes demonstrate that the use of twisted-ducts in spiral-coil results in considerably higher heat transfer coefficient that the use of the straight-duct particularly at higher Graetz numbers. For instance, at the maximum Graetz numbers, the heat transfer coefficient in Case A, Case B, Case C, Case D, and Case E is 25.1%, 50.1%, 9.9%,
Fig. 8. Comparison between current work and Patil correlation [23] for Nusselt number of water flow through spirally-coiled-tube. 366
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Fig. 9. Comparison between current work and Jamal-Abad et al. [20] for Nusselt number of 0.5% Cu/water nanofluid flow through spirally-coiled tube.
Fig. 10. Heat transfer coefficient – Graetz number.
twisted-duct at the wall are kept constant, the outlet temperature of working fluid decreases with increasing the Graetz number. Certainly, as shown in Fig. 10, the heat transfer rate is enhanced as the Graetz number goes up, but the increasing rate of heat transfer is less than that of working fluid flow rate [21]. Therefore, the outlet temperature of the working fluid is higher at lower Graetz numbers, and it is reduced with increasing the Graetz number. The mentioned phenomena suggest that both the twist-pitch and the coil-pitch are the key factors for the thermal improvement in the spirally-coiled twisted-ducts. However, it is found that at the studied ranges the effect of coil-pitch is more than that of twist-pitch; the heat transfer coefficient increases averagely 17.9% for the coil-pitch decrement from 0.035 m to 0.015 m, and it increases averagely 9.3% for the twist-pitch decrement from 0.015 m to 0.005 m. In order to create a better insight, variations of the ratio of Nusselt number for different cases to that for the reference one (i.e. Case A) are plotted in Fig. 14. The results of the pressure drop for all studied cases are revealed in Fig. 15. As expected, the pressure drop augments with increasing the Graetz number, and the pressure drop of spirally-coiled twisted-ducts is higher than that of spirally-coiled duct due to more complexity in rotational flows. Evidently, at the same coil-pitch, the pressure drop increases with decreasing the twist-pitch due to more rotation in the flow
that at the distance away from the entrance, the centrifugal force pushes the working fluid away from the center part to the twisted walls. It results that the maximum velocity shifts from the center part and occurs near the inner wall of spirally-coiled twisted-ducts. It has an important effect on the heat transfer enhancement and shifts the maximum temperature toward the outer curvatures. This phenomena intensify as the Graetz number goes up. For instance, the effects of Graetz number on the velocity and temperature contours of reference one (i.e. Case A) are depicted in Fig. 13. It can be seen that at higher Graetz number, the fluid mixing is enhanced through the spirally-coiled twisted-duct and more uniform temperature filed is obtained. The velocity contours show that the center part of flow (red1 region) in higher Graetz number is smaller than in lower Graetz number, which means that more parts of working fluid are induced in rotational flows and the mixing between fluids at the core and the wall regions is enhanced. Considering the data obtained from the experimental part and those from the numerical results, when the temperature of working fluid at the inlet and temperature of spirally-coiled
1 For interpretation of color in Fig. 13, the reader is referred to the web version of this article.
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Fig. 11. A comparison on velocity and temperature contours between spirally-coiled twisted-tubes and original spirally-coiled tube.
path; ΔpCase B > ΔpCase A > ΔpCase C. Also, at the same twist-pitch, the pressure drop increases with increasing the coil-pitch due to the longer flow path; ΔpCase E > ΔpCase A > ΔpCase D. Actually, at the same turns
of coil, the flow path increases with increasing the coil-pitch. This specifies that both the twist-pitch and the coil-pitch are the key factors in the pressure drop of spirally-coiled twisted-ducts. However, at the 368
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Fig. 12. Effects of twist-pitch and coil-pitch on velocity contours (Top) and temperature contours (Bottom) of spirally-coiled twisted-tubes at maximum Graetz numbers.
different cases to that for the reference one (i.e. Case A) is computed and plotted against to the Graetz number in Fig. 16. Among the studied cases, the use of spirally-coiled twisted-duct at tp = 0.05 m and cp = 0.025 m (Case B) results in the maximum values which are higher than those associated with the use of spirally-coiled twisted-duct at
same Graetz number, the pressure drop values of Case D and spirallycoiled duct are comparable, and the pressure drop values of Case A, Case B, Case C, and Case E are averagely 4.6%, 15.9%, 1.9%, and 16.6% above those of spirally-coiled duct. A normalized friction factor defined as the ratio of friction factor for 369
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Fig. 13. Effects of Graetz number on velocity contours (Top) and temperature contours (Bottom) of reference model (i.e. Case A).
Fig. 14. Nusselt number ratio – Graetz number.
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Fig. 15. Pressure drop – Graetz number.
Fig. 16. Friction factor ratio – Graetz number.
Fig. 17. Performance index – Graetz number.
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Fig. 18. Performance index ratio – Graetz number.
viscosity and density of nanofluid augments the pressure drop. However, the influence of heat transfer enhancement may overcome the influence of pressure drop augmentation by adding copper nanoparticles in water. According to Fig. 19(c), the net effects of nanofluid improve the overall hydrothermal performance of spirally-coiled twisted-duct compared to water. This figure elucidates that the Cu/ water nanofluids perform better than water for the spirally-coiled twisted-duct. Also, the overall performance of spirally-coiled twistedduct is improved with increasing the nanoparticles concentration and Graetz number. However, after the Graetz number around 30, the performance index of nanolfuids decreases compared to that of water. In order to save the space, the plots corresponding to the other cases are not presented, and the average variations of heat transfer coefficient, pressure drop, and performance index with nanoparticle concentration are tabulated in Table 1. It is obvious that at the studied range of Graetz number, the effects of nanolfuid on thermal and hydraulic characteristics of the spirally-coiled twisted-duct enhances as both the twist-pitch and the coil-pitch decrease. For instance, the maximum variations are recorded for Case B which has the lowest twist-pitch.
tp = 0.1 m and cp = 0.015 m (Case D). It is also reveal that the effect of the twist-pitch on the friction factor of spirally-coiled twisted-duct is considerably higher than that of coil-pitch. The overall hydrothermal performance results of the spirally-coiled twisted-ducts are shown in Fig. 17. In general, the performance index of spirally-coiled twisted-ducts is enhanced with increasing the Graetz number. Therefore, the effect of twisting duct in promoting the heat transfer at higher Graetz numbers is more significant than that at lower Graetz numbers. In common, at the Graetz numbers higher than 25, the performance index gets values higher than unity. For instance, at the maximum Graetz number the performance index in Case A, Case B, Case C, Case D, and Case E is 1.21, 1.39, 1.09, 1.23, and 1.19, respectively. It implies that the use of a spirally-coiled twisted-duct is efficient than the use of the spirally-coiled duct form the considered hydrothermal performance index point of view. The performance index increases with decreasing both the twistpitch and the coil-pitch, because according to Figs. 14 and 16, the increase of Nusselt number is more dominant than that of friction factor as the twist-pitch and the coil-pitch decrease. As compared to the reference model, the results presented in Fig. 18 disclose that the effect of twist-pitch on the hydrothermal performance of spirally-coiled twistedduct is more pronounced at higher Graetz numbers. In contrast, at lower Graetz numbers, the effect of coil-pitch is more noticeable.
6.4. Correlations Although the interest in curved ducts is on the rise, there are very few correlations for prediction of thermal and hydraulic characteristics. The current work deals with the laminar flow of water as well as Cu/ water nanofluid through a new introduced curved geometry called spirally-coiled twisted-duct. The obtained data are used in order to introduce correlations on Nusselt number and friction factor. The proposed correlations, which are function of geometrical parameters and operating conditions and valid for the Graetz number between 14 and 58, are as follows,
6.3. Effects of Cu/water nanofluid In order to further improve the performance of spirally-coiled twisted-ducts, the Cu/water nanofluid is tested through the studied cases. The mass concentrations of Cu/water nanofluid are chosen as 0.5% and 1.0%. Fig. 19(a–c) illustrates the effects of nanofluid concentration on heat transfer coefficient, pressure drop, and performance index of the reference case (i.e. Case A). It reveals that adding low mass concentration of copper nanoparticles to water leads to a noticeable enhancement in the heat transfer coefficient between 6% and 28% with a certain penalty in the pressure drop between 3% and 6%. The heat transfer enhancements are due to the higher thermal conductivity of the nanofluid and the role of Brownian motion of nanoparticles. Also, at higher mass concentration, the nanoparticles have larger surface area and molecular collisions leading to higher momentum and energy transports. In general, the presence of copper nanoparticles explains two opposing effects on thermal and hydraulic characteristics of the spirally-coiled twisted-duct; the favorable effect which is driven by high thermal conductivity of nanofluid enhances the heat transfer coefficient, and the undesirable effect which is driven by high dynamic
cp Nu = 1.267Gr 0.839 ⎜⎛ ⎟⎞ ⎝ tp ⎠
0.154
(16)
−0.044
cp f = 0.177Gr −0.547 ⎜⎛ ⎟⎞ ⎝ tp ⎠
(17)
An excellent agreement between the predicted data and the obtained results with the mean absolute error of 6.2% for the Nusselt number and 7.2% for the friction factor is recorded. For instance, Fig. 20(a and b) shows the comparison between the predicted data and the obtained results when water is as working fluid. 372
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Fig. 19. (a) Heat transfer coefficient – Graetz number (b) Pressure drop – Graetz number (c) Performance index – Graetz number of reference case (i.e. Case A).
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7. Conclusions
Table 1 Average variations of heat transfer coefficient, pressure drop, and performance index with nanoparticle concentration for different cases (%). TST
Parameter
0.5% nanofluid
1.0% nanofluid
Case A tp = 0.1 m cp = 0.025 m
h Δp η
8.7 2.6 7.8
26.4 5.3 24.6
Case B tp = 0.05 m cp = 0.025 m
h Δp η
18.1 3.5 15.9
36.9 7.6 32.4
Case C tp = 0.15 m cp = 0.025 m
h Δp η
6.2 2.3 6.9
23.1 4.8 21.1
Case D tp = 0.1 m cp = 0.015 m
h Δp η
9.4 2.7 8.5
28.2 5.4 26.2
Case E tp = 0.1 m cp = 0.035 m
h Δp η
8.5 2.6 7.6
25.4 5.3 23.4
Thermo-fluidic transport characteristics of a new design of curved ducts, namely spirally-coiled twisted-duct, are investigated both experimentally and numerically. The results are compared with the original shape of spirally-coiled duct. Water and Cu/water nanofluid are considered as working fluid. The following conclusions can be made from the outcomes of the current study,
• Both the experiments and the simulations are performed under la• •
• •
minar flow regime and constant wall temperature condition. The validation procedure is made by comparing available correlation and experimental data, and the average deviation within ± 10% is obtained. Considerable enhancements in the heat transfer coefficient are recorded for the spirally-coiled twisted-duct compared with the original shape. For instance, at the maximum Graetz numbers they are about 25.1%, 50.1%, 9.9%, 28.4%, and 21.7% for Case A, Case B, Case C, Case D, and Case E, respectively. The overall hydrothermal performance of spirally-coiled twistedduct improves as the twist-pitch and coil-pitch are decreased; at lower Graetz numbers the best performance is recorded for the case with lowest coil-pitch (i.e. Case D) and at higher Graetz numbers the best performance is recorded for the case with lowest twist-pitch (i.e. Case B). The Cu/water nanofluids are prepared by the EEWL technique and they are found very stable. The nanofluids have higher heat transfer coefficient and pressure drop compared to pure water. Likewise, the nanofluid with the higher concentration provides higher values. The results clarify that the effects of nanofluid flow in the spirallycoiled twisted-duct are more intensified at lower twist-pitch and coil-pitch.
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Fig. 20. Comparison between predicted data and obtained results (a) Nusselt number (b) Friction factor.
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