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vortex-generator plate-fin (CVGPF)
Accepted Manuscript Title: Thermal-hydraulic characteristics of plate-fin heat exchangers with corrugated/vortex-generator plate-fin (CVGPF) Author: M. Khoshvaght-Aliabadi, M. Khoshvaght, P. Rahnama PII: DOI: Reference:
S1359-4311(16)00026-0 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.135 ATE 7549
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
2-10-2015 29-12-2015
Please cite this article as: M. Khoshvaght-Aliabadi, M. Khoshvaght, P. Rahnama, Thermalhydraulic characteristics of plate-fin heat exchangers with corrugated/vortex-generator plate-fin (CVGPF), Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.135. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermal-hydraulic characteristics of plate-fin heat exchangers with corrugated/vortex-generator plate-fin (CVGPF)
M. Khoshvaght-Aliabadi 1,*, M. Khoshvaght 2, P. Rahnama 1 1,*
2
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran. Department of Agricultural Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran.
*(Corresponding author): E-mail: [email protected] Phone: +98 9151811311, Fax: +98 5147244818, Postal address: 36199-43189.
Highlights
Thermal-hydraulic performance of PFHEs is evaluated with CPF and VGPF.
A new design for plate-fins as CVGPF is proposed and evaluated.
CVGPF channel has a better performance compared to CPF and VGPF channels.
Performance of all the channels increase with mass fraction of ethylene glycol.
Correlations are developed for Nusselt number and friction of plate-fins.
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Graphical Abstract
Abstract Plate-fin heat exchangers (PFHEs), after tubular heat exchangers, are the most common types of heat exchange instruments in thermal engineering applications. In the present work, a new design of the plate-fin namely corrugated/vortex-generator plate-fin (CVGPF) is proposed and studied. It is designed based on the corrugated plate-fin (CPF) and the vortex-generator plate-fin (VGPF) configurations. It is anticipated that this enhanced plate-fin can be a great choice in the PFHEs. Influences of the most effective geometrical parameters of CPF, VGPF, and CVGPF on thermal-hydraulic performances of the PFHEs are investigated and appraised. Water/ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) are selected as working fluid to examine the effects of coolant. The results show that at the same geometrical and operating conditions, the CVGPF channel has the best thermal-hydraulic performances, and the CPF and VGPF channels come in the second and third, respectively. It is also detected that the working fluid with the higher mass fraction of ethylene glycol has lower values of Nusselt number, and the effect of that on the friction factor is not considerable. However, the overall thermal2 Page 2 of 35
hydraulic performances of all plate-fins improve, as the mass fraction of ethylene glycol in the working fluid increases.
Keywords: Plate-fin heat exchanger; Heat transfer enhancement; Corrugated/vortex-generator; Experimental study.
1. Introduction Nowadays, plate-fin heat exchangers (PFHEs) are recognized as one of the most efficient, standard, and compact type of heat transfer devices. These instruments have unique features and considerable advantages when compared with other heat exchangers. In the PFHEs, different demands of thermal load can be obtained by adding or removing of the plate-fins (flexible thermal design is a good feature in chemical/petrochemical industries), operating conditions can be justified well (good temperature control is an importance issue in cryogenic and aerospace industries), and plate-fins can be cleaned up easily (extreme hygiene is necessary for food or pharmaceutical industries) [1]. Heat and hydraulic characteristics of the PFHEs are strongly influenced by the configuration and geometrical parameters of extended surfaces, i.e. plate-fins [2]. Based on different applications, various types of the plate-fins such as plain, perforated, offset-strip, louvered, corrugated, vortex-generator, or pin are used in the PFHEs. Numerous experimental and numerical studies were conducted on characteristics of each configuration of plate-fins. A compressive review on the PFHEs can be found in [3, 4]. However, some related reports on the PFHEs will be reviewed here. Kotcioglu et al. [5] conducted an experimental investigation for optimization of design parameters in a PFHE with rectangular duct using Taguchi method. Effects of the six design parameters (ratio of the duct channel width to the height, ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity, and pressure 3 Page 3 of 35
drop) were investigated. Thermal-hydraulic performances of a PFHE with the vortex-generator channels were investigated by Khoshvaght-Aliabadi et al. [6]. Influences of the seven effective geometrical parameters (wings height, wings width, channel length, longitudinal wings pitch, transverse wings pitch, wings attach angle, and wings attack angle) for the three conventional coolants (water, oil, and ethylene glycol) were evaluated at the laminar flow regime. Among the studied design parameters, the wings height was the most effective parameter. Sinha et al. [7] investigated the heat transfer enhancement of a PFHE using two rows of winglet type vortex generators. Five different strategic placements of the vortex-generator (common-flow up in series, common-flow down in series, combined, inline rows of winglet, and staggered rows of winglet) were considered. The common-flow up in series was the best in terms of the heat transfer as well as quality factor. The application of Bees algorithm in the optimum design of a cross flow PFHE with the offset strip fin was investigated by Zarea et al. [8]. Hot and cold flow length, number of fin layers, fin frequency, fin height, fin strip length and fin thickness were introduced as optimization variables. The results shown that Bees algorithm can find the optimum configuration with higher accuracy in comparison with Genetic algorithm, Particle Swarm optimization, Imperialist Competitive algorithm, and preliminary design. Pressure drop and heat transfer characteristics of a titanium brazed PFHE with the offset strip fins were studied by Fernández-Seara et al. [9]. An experimental program was conducted by using firstly, water on both sides of the heat exchanger and secondly, 10–30 wt% ethylene glycol aqueous solutions as working fluids. An empirical correlation was proposed to determine the single-phase convection heat transfer coefficients. Effects of the two passive heat transfer enhancement techniques namely vortex-generator and nanofluid on the performance of a PFHE were examined numerically by Khoshvaght-Aliabadi et al. [10]. It was shown that the mixture model had a
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closer prediction of the convective heat transfer coefficient to the experimental data. A general study on the performance of a PFHE with the offset strip fins was carried out by Yang and Li [11]. Effects of the geometrical three-dimensionality were analyzed in a distinctive way to understand the general behavior of the PEHE performance. Based on the literature review, it is found that there are very limited experimental studies on the corrugated and vortex-generator plate-fins. On the other hand, our previous comparative study [12] indicates that a better heat transfer in comparison to pressure drop in a PFHE belongs to the corrugated plate-fin (CPF) and vortex-generator plate-fin (VGPF). It motivates the current work to combine these plate-fins and generate a new design of the plate-fin as corrugated/vortexgenerator plate-fin (CVGPF). This study tries to analyze the thermal-hydraulic performances of the CPF, VGPF, and CVGPF in a PFHE by using the water-ethylene glycol mixtures as working fluid. The studied factors are the geometrical parameters (corrugation amplitude/length and winglet height/pitch), working fluid composition (100:0, 90:10, and 75:25 by mass), and volumetric flow rate (7.5 to 10.5 L/min). Experimental tests are performed in a pre-calibrated close loop setup with the ability to produce a constant wall temperature condition.
2. Tested plate-fins and coolants Usually, the complicated geometries of the plate-fins are fabricated by stamping from thin metal sheets. In the present study, all the tested plate-fins, i.e. corrugated plate-fin (CPF), vortexgenerator plate-fin (VGPF), and corrugated/vortex-generator pate-fin (CVGPF), are made from aluminum sheets with the length of 0.5 m and width of 1.6×10-2 m. The sheets thickness of 5×104
m is chosen to avoid an additional friction that might be occurred by thicker sheets. Our
previous studies [13, 14] show that the ratio of corrugation amplitude to corrugation length (γ =
5 Page 5 of 35
a/l) and the ratio of winglet height to winglet pitch (η = h/p) are the most effective geometrical parameters of the CPFs and VGPFs, respectively. Therefore, as depicted in Fig. 1, these geometrical ratios are examined at three levels. To create a physically meaningful and reliably comparative study, the studied combined plate-fins, i.e. CVGPFs, are fabricated at the same values of geometrical parameters. The considered values for the geometrical parameters of platefins are tabulated in Table 1. A coolant is a working fluid which flows through a heat transfer device to transfer the heat to other devices or dissipate it. A high thermal conductivity, low viscosity and low cost are the considerable advantages of a perfect working fluid. The most common working fluid is the water. Its low cost makes it a suitable heat transfer medium. Also, the ethylene glycol is another working fluid that is extensively used as an anti-freeze or anti-boil in heat transfer devices. Therefore, the water-ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) are the working fluids used to investigate the effect of coolant. The effective thermos-physical properties of the working fluids are systematically measured as function of ethylene glycol weight fraction. The thermal conductivity (κ), dynamic viscosity (μ), heat capacity (Cp) and density (ρ) are measured, respectively, using Decagon Devices/KD2 Pro system, Physica MCR 301 Anton Paar/rheometer, C80D Setaram/differential scanning calorimeter, and set of CPA 1003S Sartorius/digital electronic balance and pycnometer [15].
Please insert Fig. 1 here Please insert Table 1 here
3. Experimental setup
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The current experiments are conducted in the constant wall temperature condition. It is a commonly encountered condition in experimental thermal studies [16, 17]. To have a real and uniform temperature on the test section, a two-phase chamber is required. Therefore, an experimental setup with the ability to produce a constant wall temperature condition is prepared. The experimental setup is a close flow system, as schematically shown in Fig. 2. The working fluid restored in the storage tank is driven with a centrifugal pump through the system. In order to protect the equipment, a pressure relief valve is incorporated into the flow line. The flow rate passing through the system is controlled by using a needle valve, and it is measured by using a high sensitive ultrasonic flow meter. The test fluid flow length is a straight copper duct with the internal square cross section area of 2.56×10-4 m2, thickness of 1.0×10-3 m, and length of 1.2 m; 0.85 m is considered as the hydrodynamic entry section and 0.35 m is the heat transfer section. The hydrodynamic entry section is well insulated in order to eliminate the heat transfer with the ambient. The bulk temperature measurements at the inlet and outlet of the test section are made using two T-type thermocouples. Two sensitive pressure transmitters are also added to the test fluid flow length to obtain the pressure drop. Five K-type thermocouples are placed at equally spaced locations along the heat transfer section length to measure the wall temperature. After the test section, the fluid is cooled back to the inlet temperature via the cooling loop, which consists of a plate heat exchanger, a reservoir, a centrifugal pump, and a rotameter. For each test, it is essential to record the temperatures, pressures, and volumetric flow rate across the test section. As depicted in the figure, a data recording system is employed. A photograph of the applied experimental setup is presented in Fig. 2(b). Also, details about setup components are tabulated in Table 2.
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Please insert Fig. 2 here Please insert Table 2 here
4. Data reduction The equation of the convective heat transfer rate is used to compute the heat absorbed by the flowing fluid, Q c o n v V C
p
(T b ,o u t T b , in )
(1)
where, ρ, V, Cp, Tb,out and Tb,in represent the density, volumetric flow rate, specific heat capacity, inlet and outlet bulk temperatures of the working fluid, respectively. The effective heat transfer coefficient is estimated from the ratio of the convective heat transfer rate to the total surface area and logarithmic mean temperature difference of the wall-and-bulk fluid, h
Q conv
(2)
A (T w T b ) L M T D
(T w T b ) L M T D
Tw
b , in
lo g T w
Tw
b , in
b ,o u t
Tw
b ,o u t
(3)
where, ∆Tw–b,in and ∆Tw–b,out denote the differences between the wall temperature and the bulk fluid temperature at the inlet and outlet of the heat transfer section. Also, the average Nusselt number is defined as, hD
Nu
h
(4)
The thermal performance can be illustrated in a non-dimensional form, namely Colburn factor, j
Nu Re Pr
(5)
1 3
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The pressure drop is estimated from the experimental observations and theoretical formula as given below, P P in Po u t
(6)
To appraise the hydraulic performance, the friction factor is estimated from the pressure drop values by using the following equation, 2D h P
f
L u
(7)
2
where, u is the inlet velocity which is evaluated from the volumetric flow rate and cross section area. The uncertainties for the calculated results are evaluated according to the propagation analysis [18]. The maximum uncertainties obtained for the averaged Nusselt number and friction factor are about 4.9% and 6.4%, respectively.
5. Results and discussion Experiments are initially conducted for the water flow inside the empty duct to check the consistency of results. The present experimental results are validated by comparing with the single-phase fluid correlations, which are frequently referred in literature, in terms of the average Nusselt number and friction factor, (a) Equation of Gnielinski [19] f R e 1000 Pr 2
Nu
f 1 1 2 .7 2
(8)
1 2
Pr
2 3
1
where,
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f 1 .5 8 ln R e 3 .8 2
2
(9)
2300 < Re < 5 × 106 and 0.5 < Pr < 2000. (b) Equation of Notter-Rouse [20] N u 5 0 .0 1 5 R e
0 .8 5 6
Pr
0 .3 4 7
(10)
(c) Equation of Petukov [21] f 0 .7 9 ln R e 1 .6 4
2
(11)
3000 < Re < 5 × 106. The comparison of the values calculated through Eqs. (8) to (11) and their deviations with the current experimental results are presented in Fig. 3(a–b). The comparison shows a good agreement between the present experimental results and the previous empirical data so that at the range of studied, it lies within ±10% error.
Please insert Fig. 3 here
The variations of heat transfer coefficient versus the mass flow rate for water flow through studied plate-fin channels are presented in Fig. 4(a–c). The results of empty duct are also present for comparison. As anticipated, for all the cases, the heat transfer coefficient increases as the flow rate goes up. However, the effect of flow rate on the thermal performance of plate-fin channels is different. For instance, as the flow rate increases from the minimum to the maximum, the heat transfer coefficient of the CPF and VGPF channels at the middle value of dimensionless parameters, i.e. γ = η = 0.202, enhances about 29.8% and 34.7%, respectively. It is interesting to note that the effect of flow rate on the thermal performance of CVGPF channels is more than the CPF and VGPF channels; the heat transfer coefficient of CVGPF channel with λ = 0.041 10 Page 10 of 35
enhances about 37.6%, when the flow rate varies from the minimum to the maximum. It is found that at a given flow rate, the heat transfer coefficient gets higher values for the CPF and VGPF channels with the greater values of γ and η. In fact, as the dimensionless parameter of γ increases, the corrugations effect in the CPF channel intensifies. It leads to a larger flow path and stronger swirl flows in the CPF channel. Our previous study [13] shows that the strength of swirl flows depends strongly on the corrugation amplitude and length. Also, as the dimensionless parameter of η increases, the winglets effect in the VGPF channel intensifies. It causes a heavy exchange of core and wall fluids, leading to the higher enhancement of heat transfer between the flowing fluid and the channel walls. It is shown that the winglet height and pitch affect meaningfully the performance of VGPF channel [10].
Please insert Fig. 4 here
It can be found from Fig. 4(a–c) that at the same operating condition, the CVGPF channel has the highest values of the heat transfer coefficient, and the CPF and VGPF channels come in the second and third, respectively. For a better insight, Nusselt number enhancement of the platefin channels compared to the empty duct versus Reynolds number for water flow is shown in Fig. 5. The results confirm that all the plate-fin channels have higher Nusselt number in comparison with the empty duct, since the heat transfer coefficient in the plate-fin channels enhances by thermal boundary layer interruption with corrugations and winglets. In the CPF and VGPF channels, the longitudinal, transverse, and normal swirl flows may be generated in the corrugations and behind the winglets. These swirl flows make a heavy exchange of core and wall fluids, leading to the enhancement of heat transfer coefficient thereby Nusselt number. The
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enhancement in NuPF/NuEmpty duct ratio for the CVGPF channel is obvious compared to the other ones. Over the tested range of Reynolds number, Nusselt number of the CPF, VGPF, and CVGPF channels averagely increase by about 34.1% for γ = 0.317, 63.3% for γ = 0.202, and 76.6% for γ = 0.258, 25.7% for η = 0.086, 39.7% for η = 0.202, and 53.2% for η = 0.411, 49.3% for λ = 0.056, 69.9% for λ = 0.041, and 83.7% for λ = 0.022. It is worth to note that for all the plate-fin channels, the ratio of NuPF/NuEmpty duct gives higher values, as Reynolds number goes up. A possible mechanism for this appreciable Nusselt number enhancement is due to increasing number and size of swirl flows in these channels, because the strength of swirl flows depends on the Reynolds number.
Please insert Fig. 5 here
The measured flow pressure drops along the plate-fin channels are also used to study the hydraulic performance of the plate-fin channels. The variations of measured pressure drop with the mass flow rate are shown in Fig. 6(a–c). It can be observed that the pressure drop gradually increases with the flow rate increasing. It is found that the pressure drop of CPF channel is much higher than that of VGPF channel. It is attributed to noticeable flow blockage produced by corrugations in the channel equipped with the CPFs. Another point is the considerable effect of geometrical parameters on the pressure drop of the CPF channel compare to the VGPF channel. Likewise, the presence of winglets on corrugations is the main reason for the additional pressure drop of the CVGPF channel compared to the CPF channel. It is interesting to find that the effect of winglets on the pressure drop of corrugated plate is more than that of the plain one. As an example, embedding winglets with the height of 4 mm on the corrugated plate increases the
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pressure drop along the channel about 59.6%, while embedding the same winglets on the plain plate increases the pressure drop about 50.1%.
Please insert Fig. 6 here
As shown in Fig 7, the fPF/fEmpty duct ratio values of all the models are higher than one and decrease with Reynolds number. Over the tested range of Reynolds number, the friction factor of CPF, VGPF, and CVGPF channels averagely increase by about 19.8% for γ = 0.317, 279.3% for γ = 0.202, and 780.7% for γ = 0.258, 7.7% for η = 0.086, 150.1% for η = 0.202, and 212.2% for η = 0.411, 71.4% for λ = 0.056, 446.3% for λ = 0.041, and 801.3% for λ = 0.022.
Please insert Fig. 7 here
To investigate the effect of coolant, the variations of Nusselt number and friction factor of water/ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) across the plate-fin channels are presented in Fig. 8(a–b). The results show that Nusselt number decreases, as the mass fraction of ethylene glycol increases in the coolant. It can be explained that at the same mass flow rate, the working fluid with lower percentage of the ethylene glycol (lower Prandtl number) absorbs more heat compared to the working fluid with higher percentage of the ethylene glycol (higher Prandtl number). Therefore, the working fluid with the composition of 100:0 of the water/ethylene glycol mixture shows the highest Nusselt number, and the working fluids with the composition of 90:10 and 75:25 come in the second and third, respectively. It is found that the effect of coolant on the thermal performance of CVGPF channel is more than that of CPF and
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VGPF channels. For instance, when water is replaced with 90:10 and 75:25 water/ethylene glycol mixtures in the CVGPF, Nusselt number varies averagely about 5.6% and 14.7%, respectively. For the same replacements, Nusselt number varies about 4.3% and 12.1% for the CPF channel and 3.4% and 8.5% for the VGPF channel. As revealed in Fig. 8(b), the friction factor values for the three working fluids closely fell onto the same curve for all the plate-fin channels. A similar result was reported for the other plate-fin channels like offset strip [22].
Please insert Fig. 8 here
However, based on the results of heat transfer and pressure drop separately, it is difficult to create a final and correct conclusion as to which geometry of plate-fin is better. Therefore, the following thermal-hydraulic performances factor is applied to evaluate different configurations and geometries of the plate-fins [23],
JF
j f
j
PF
PF
f
E m p ty d u c t
E m p ty d u c t
(12)
1 3
where, the subscripts PF and Empty duct represent a plate-fin channel and the empty duct, respectively. A comparison among the JF factor values versus the volumetric flow rate for different working fluids across the studied plate-fins is displayed in Fig. 9(a–c). The JF factor is a “the larger the better” parameter, and a high value of that indicates a geometry with the appropriate thermal-hydraulic performances. It is depicted that under the studied range, the highest values are found for the CVGPF channel and the CPF and VGPF channels come in the second and third, respectively. An overall scrutiny on the figure discloses that the JF factor values of all the channels increase with the mass fraction of ethylene glycol. It should be note 14 Page 14 of 35
that the difference between the CPF and the CVGPF channels decreases as the mass fraction of ethylene glycol increases. Another noticeable issue is the effect of geometrical parameters on the JF factor values. It is clear that the JF factor values decrease as the ratio of corrugation amplitude to corrugation length, i.e. γ, and the ratio of winglet height to winglet pitch, i.e. η, are increased. It means that the CPF and VGPF channels with the lower values of γ and η have a better thermal-hydraulic performances form the considered performance evaluation criterion point of view.
Please insert Fig. 9 here
Finally, the experimental data are used to develop correlations for Nusselt number and friction factor in the case of tested working fluids inside the plate-fin channels. The regression analysis coefficients are assessed with the help of classical least square method. The proposed correlations are valid for Reynolds number from 1700 to 13000, based on the applied working fluid. The correlations of Nusselt number and friction factor are derived as follows, N u or f a R e Pr b
c
,
, or
d
(13)
The constants of correlations (i.e. a, b, c, and d) are given in Table 3 for the tested plate-fin channels. It should be illustrated that the data obtained from the proposed correlations and experimental results are in a good agreement, so that approximately 98% of the experimental data are correlated within ±15%. For instance, a comparison between the experimental data and the predicted values of Nusselt number is made in Fig. 10.
Please insert Table 3 here 15 Page 15 of 35
Please insert Fig. 10 here
6. Conclusions Employing complex channels and enhanced working fluids has been proven to be very effective ways on plate-fin heat exchangers (PFHEs). In the present study, the thermal-hydraulic performances of two mostly use plate-fins, namely corrugated plate-fin (CPF) and vortexgenerator plate-fin (VGPF), are analyzed. Then, a new design for the plate-fins is proposed as corrugated/vortex-generator plate-fin (CVGPF), and its performance is compared with the CPF and VGPF channels. The experimental results are validated based on the previous correlations. The results confirm that all the plate-fin channels have higher Nusselt number in comparison with the empty duct. Also, the enhancement in thermal performance of the PFHE with the CVGPF channel is obvious compared to the CPF and VGPF channels. Over the tested range of flow rate, the maximum enhancement in Nusselt number is about 76.6% for the CPF channel, 53.2% for the VGPF channel, and 83.7% for the CVGPF channel compared to the empty duct. It is interesting to find that the effect of winglets on the friction factor of corrugated plate is more than that of the plain one. Another point is the considerable effect of geometrical parameters on the friction factor of the CPF channel compare to the VGPF channel. The results show that Nusselt number decreases as the mass fraction of ethylene glycol increases in the coolant. It is found that the effect of coolant on the thermal performance of CVGPF channel is more than that of CPF and VGPF channels. However, the friction factor values for the three working fluids closely fell onto the same curve for all the plate-fin channels. The current study shows that using the complex channels instead of the plain one enhances Nusselt number with a penalty in the friction factor. However, Nusselt number and friction factor are two independent parameters that
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are not related together by an equation. Therefore, a thermal-hydraulic performance evaluation criterion is considered that can relate these parameters and provide conditions for the comparison. It is depicted that under the studied range, the highest values of considered performance evaluation criterion are found for the CVGPF channel, and the CPF and VGPF channels come in the second and third, respectively. The performance evaluation criterion values of all the channels increase with the mass fraction of ethylene glycol. Also, it decrease as the ratio of corrugation amplitude to corrugation length and the ratio of winglet height to winglet pitch increase. Finally, correlations are proposed for Nusselt number and friction factor of the considered plate-fins.
Acknowledgements This research was carried out in Advanced Research Laboratory of Chemical Engineering Department of Islamic Azad University (IAU) of Shahrood Branch, Iran.
Nomenclature A
total surface area, m2
a
corrugation amplitude, m
Cp
specific heat capacity, J.kg-1.K-1
Dh
hydraulic diameter, m
h
winglet pitch, m
L
channel length, m
l
corrugation length, m
Qconv
convective heat transfer rate, W
17 Page 17 of 35
P
pressure, Pa
p
winglet pitch, m
∆P
pressure drop, Pa
T
temperature, K
u
velocity, m.s-1
V
volumetric flow rate, m3.s-1
Greek symbols ρ
density, kg.m-3
μ
dynamic viscosity, Pa.s
κ
thermal conductivity, W.m-1.K-1
γ
ratio of corrugation amplitude to corrugation length
η
ratio of winglet height to winglet pitch
λ
γ/η
Dimensionless groups f
Fanning friction factor
j
Colburn factor
Nu
Nusselt number
Re
Reynolds number
Pr
Prandtl number
Subscripts
18 Page 18 of 35
b
bulk fluid
in
inlet
out
outlet
LMTD
logarithmic mean temperature difference
PF
plate-fin
w
wall
Acronyms CPF
Corrugated plate-fin
CVGPF
Corrugated/vortex-generator plate-fin
PFHE
Plate-fin heat exchangers
VGPF
Vortex-generator plate-fin
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M. Fakoor Pakdaman, M.A. Akhavan-Behabadi, P. Razi, An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes, Experimental Thermal and Fluid Science 40 (2012) 103–111.
[17]
M. Khoshvaght-Aliabadi, F. Hormozi, A. Zamzamian, Experimental analysis of thermal– hydraulic performance of copper–water nanofluid flow in different plate-fin channels, Experimental Thermal and Fluid Science 52 (2014) 248–258.
21 Page 21 of 35
[18]
H.W. Coleman, W.G. Steele, Experimentation, validation, and uncertainty analysis for engineers, John Wiley & Sons, New York, 2009.
[19]
V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (1976) 359–368.
[20]
R.H. Notter, M.W. Rouse, A solution to the Graetz problem – III. Fully developed region heat transfer rates, Chemical Engineering Science 27 (1972) 2073–2093.
[21]
B.S. Petukhov, Heat transfer and friction in turbulent pipe flow with variable physical properties, In: Hartnett JP, Irvine TF, editors. Advances in Heat Transfer. New York: Academic Press (1970) 504–64.
[22]
M.S. Kim, J. Lee, S.J. Yook, K.S. Lee, Correlations and optimization of a heat exchanger with offset-strip fins, International Journal of Heat and Mass Transfer 54 (2011) 2073– 2079.
[23]
J.Y. Yun, K.S. Lee, Influence of design parameters on the heat transfer and flow friction characteristics of the heat exchanger with slit fins, International Journal of Heat and Mass Transfer 43 (14) (2000) 2529–2539.
22 Page 22 of 35
Caption of Figures:
Fig. 1. Generated and tested plate-fins.
23 Page 23 of 35
Data recording systems Pin Pout F
Safety pressure valve
Tin Tout
Selector switch
Tw P-o
T-o
T-i
T5
T4
T3
T2
T1
Hydrodynamic length (Insulated)
Level meter
Test section
P-i
Ultrasonic flow meter Three way
Heater 2
Ball valve
Heater 1
Relief valve Needle valve
Test chamber Drain
Cooling fluid reservoir
FI
PHE
Tap water outlet Storage tank Drain
Centrifugal pump
Rotameter
Centrifugal pump
(a)
24 Page 24 of 35
(b) Fig. 2. (a) Schematic (b) photograph representations of experimental setup.
25 Page 25 of 35
Nusselt number
120
105
Present experimental data Eq. (8) Eq. (10)
90
75
60 9000
10000
11000 Reynolds number
12000
13000
12000
13000
(a)
0.04
Friction factor
0.035
Present experimental data Eq. (9) Eq. (11)
0.03
0.025
0.02 9000
10000
11000 Reynolds number (b)
Fig. 3. Comparison between present experimental data and previous empirical correlations (a) Nusselt number (b) Friction factor.
26 Page 26 of 35
Heat transfer coefficient (W/m2.K)
Empty duct
γ=0.137
γ=0.202
γ=0.258
6000
5000
4000
3000
Min. error: 0.8% Max. error: 3.2%
2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(a)
Heat transfer coefficient (W/m2.K)
Empty duct
η=0.086
η=0.202
η=0.411
6000
5000
4000
3000
Min. error: 1.1% Max. error: 2.5% 2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(b)
27 Page 27 of 35
Heat transfer coefficient (W/m2.K)
Empty duct
λ=0.056
λ=0.041
λ=0.022
6000
5000
4000
3000
Min. error: 0.9% Max. error: 3.6%
2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(c) Fig. 4. Heat transfer coefficient – Mass flow rate for water flow in plate-fin channels (a) CPF (b) VGPF (c) CVGPF.
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
Nu PF / Nu Empty duct
2.5 2 1.5 1 0.5 0 7773.55
8291.79
8810.03
9328.27
9846.50
10364.74 10882.98
Reynolds number
Fig. 5. Nusselt number enhancement – Reynolds number of plate-fin channels compare to empty duct.
28 Page 28 of 35
Empty duct
γ=0.137
γ=0.202
γ=0.258
Pressure drop (Pa)
10000 8000
Min. error: 0.04% Max. error: 0.09%
6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.17
0.18
Mass flow rate (kg/s)
(a) Empty duct
η=0.086
η=0.202
η=0.411
Pressure drop (Pa)
10000
Min. error: 0.02% Max. error: 0.08%
8000 6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
Mass flow rate (kg/s)
(b)
29 Page 29 of 35
Empty duct
λ=0.056
λ=0.041
λ=0.022
Pressure drop (Pa)
10000 8000
Min. error: 0.05% Max. error: 0.08%
6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(c) Fig. 6. Pressure drop – Mass flow rate for water flow in plate-fin channels (a) CPF (b) VGPF (c) CVGPF.
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
10
f PF / f Empty duct
8 6 4 2 0 7773.55
8291.79
8810.03
9328.27
9846.50
10364.74
10882.98
Reynolds number
Fig. 7. Friction factor increase – Reynolds number of plate-fin channels compare to empty duct.
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Water across CPF 10% EG in water across CPF 25% EG in water across CPF Water across VGPF 10% EG in water across VGPF 25% EG in water across VGPF Water across CVGPF 10% EG in water across CVGPF 25% EG in water across CVGPF
Nusselt number
150
125
100
75 7
7.5
8
8.5
9
9.5
10
10.5
11
10
10.5
11
Volumetric flow rate (L/min)
(a)
Water across CPF 10% EG in water across CPF 25% EG in water across CPF Water across VGPF 10% EG in water across VGPF 25% EG in water across VGPF Water across CVGPF 10% EG in water across CVGPF 25% EG in water across CVGPF
Friction factor
0.3
0.2
0.1
0 7
7.5
8
8.5
9
9.5
Volumetric flow rate (L/min)
(b) Fig. 8. Effect of working fluid type on (a) Nusselt number (b) Friction factor of plate-fin channels at middle value of geometrical parameters, i.e. γ = η = 0.202.
31 Page 31 of 35
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(a) γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(b)
32 Page 32 of 35
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(c) Fig. 9. JF factor – Volumetric flow rate for different working fluids in plate-fin channels (a) water (b) 10% EG in water (c) 25% EG in water.
33 Page 33 of 35
Predicted values for Nusselt number
180
150
+15% 120
–15% 90
60 60
90
120
150
180
Experimental data for Nusselt number
Fig. 10. Comparison of experimental values for Nusselt number with those predicted by Eq. (13).
34 Page 34 of 35
Table 1. Geometrical parameters of plate-fins. Plate-fins Dimensionless parameter Level 1 Level 2 Level 3 1. CPF γ = a/l 0.137 0.202 0.258 2. VGPF η = h/p 0.086 0.202 0.411 3. CVGPF λ = ah/lp 0.056 0.041 0.022 Table 2.Specification, range, and accuracy of setup components. Component Specification Range Accuracy 1. Storage tank Stainless steel 0–6.75 lit – 2. Centrifugal pump PKm60, Pedrollo 0–40 lit/min – 3. Needle valve LMC, ASC.15 0–20 lit/min – 4. Relief valve Watts, 530-050 – – 5. Safety pressure valve 21T2BV28-F, BDA – – 6. Ultrasonic flow meter Flownetix® 100seriesTM 0–20 lit/min 0.05 lit/min 7. Bulk thermocouples T-type –50 to 200 °C 0.1 °C 8. Wall thermocouples K-type (Omega) –73 to 260 °C 0.1 °C 9. Pressure transmitters PSCH0.5BCIA, Sensys 0 to 10000 Pa 10 Pa 10. Ultrasonic flow meter indicator MT4W, Autonics – – 11. Bulk thermocouples indicator SU-105PRR, Samwon – – 12. Wall thermocouples indicator SU-105KRR, Samwon – – 13. Pressure transmitters indicator MT4W, Autonics – – 14. Rotameter LZT-1005G, MBLD 0–7 lit/min 0.25 lit/min 15. Plate heat exchanger B3-014C-12-3.0-H, Danfuss 0–10 lit/min – Table 3. Constants of Nusselt number and fiction factor correlations. Plate-fin a b c d 1. CPF Nu 5.695×10-2 0.762 0.669 0.408 f 12.236 –5.96×10-2 – 3.3351 2. VGPF Nu 5.033×10-3 0.923 0.832 9.839×10-2 -2 f 0.111 –1.412×10 – 0.437 3. CVGPF Nu 1.016×10-2 0.797 0.685 –0.229 f 1.718×10-3 –1.041×10-3 – –1.306
35 Page 35 of 35
S1359-4311(16)00026-0 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.135 ATE 7549
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
2-10-2015 29-12-2015
Please cite this article as: M. Khoshvaght-Aliabadi, M. Khoshvaght, P. Rahnama, Thermalhydraulic characteristics of plate-fin heat exchangers with corrugated/vortex-generator plate-fin (CVGPF), Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.135. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermal-hydraulic characteristics of plate-fin heat exchangers with corrugated/vortex-generator plate-fin (CVGPF)
M. Khoshvaght-Aliabadi 1,*, M. Khoshvaght 2, P. Rahnama 1 1,*
2
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran. Department of Agricultural Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran.
*(Corresponding author): E-mail: [email protected] Phone: +98 9151811311, Fax: +98 5147244818, Postal address: 36199-43189.
Highlights
Thermal-hydraulic performance of PFHEs is evaluated with CPF and VGPF.
A new design for plate-fins as CVGPF is proposed and evaluated.
CVGPF channel has a better performance compared to CPF and VGPF channels.
Performance of all the channels increase with mass fraction of ethylene glycol.
Correlations are developed for Nusselt number and friction of plate-fins.
1 Page 1 of 35
Graphical Abstract
Abstract Plate-fin heat exchangers (PFHEs), after tubular heat exchangers, are the most common types of heat exchange instruments in thermal engineering applications. In the present work, a new design of the plate-fin namely corrugated/vortex-generator plate-fin (CVGPF) is proposed and studied. It is designed based on the corrugated plate-fin (CPF) and the vortex-generator plate-fin (VGPF) configurations. It is anticipated that this enhanced plate-fin can be a great choice in the PFHEs. Influences of the most effective geometrical parameters of CPF, VGPF, and CVGPF on thermal-hydraulic performances of the PFHEs are investigated and appraised. Water/ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) are selected as working fluid to examine the effects of coolant. The results show that at the same geometrical and operating conditions, the CVGPF channel has the best thermal-hydraulic performances, and the CPF and VGPF channels come in the second and third, respectively. It is also detected that the working fluid with the higher mass fraction of ethylene glycol has lower values of Nusselt number, and the effect of that on the friction factor is not considerable. However, the overall thermal2 Page 2 of 35
hydraulic performances of all plate-fins improve, as the mass fraction of ethylene glycol in the working fluid increases.
Keywords: Plate-fin heat exchanger; Heat transfer enhancement; Corrugated/vortex-generator; Experimental study.
1. Introduction Nowadays, plate-fin heat exchangers (PFHEs) are recognized as one of the most efficient, standard, and compact type of heat transfer devices. These instruments have unique features and considerable advantages when compared with other heat exchangers. In the PFHEs, different demands of thermal load can be obtained by adding or removing of the plate-fins (flexible thermal design is a good feature in chemical/petrochemical industries), operating conditions can be justified well (good temperature control is an importance issue in cryogenic and aerospace industries), and plate-fins can be cleaned up easily (extreme hygiene is necessary for food or pharmaceutical industries) [1]. Heat and hydraulic characteristics of the PFHEs are strongly influenced by the configuration and geometrical parameters of extended surfaces, i.e. plate-fins [2]. Based on different applications, various types of the plate-fins such as plain, perforated, offset-strip, louvered, corrugated, vortex-generator, or pin are used in the PFHEs. Numerous experimental and numerical studies were conducted on characteristics of each configuration of plate-fins. A compressive review on the PFHEs can be found in [3, 4]. However, some related reports on the PFHEs will be reviewed here. Kotcioglu et al. [5] conducted an experimental investigation for optimization of design parameters in a PFHE with rectangular duct using Taguchi method. Effects of the six design parameters (ratio of the duct channel width to the height, ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity, and pressure 3 Page 3 of 35
drop) were investigated. Thermal-hydraulic performances of a PFHE with the vortex-generator channels were investigated by Khoshvaght-Aliabadi et al. [6]. Influences of the seven effective geometrical parameters (wings height, wings width, channel length, longitudinal wings pitch, transverse wings pitch, wings attach angle, and wings attack angle) for the three conventional coolants (water, oil, and ethylene glycol) were evaluated at the laminar flow regime. Among the studied design parameters, the wings height was the most effective parameter. Sinha et al. [7] investigated the heat transfer enhancement of a PFHE using two rows of winglet type vortex generators. Five different strategic placements of the vortex-generator (common-flow up in series, common-flow down in series, combined, inline rows of winglet, and staggered rows of winglet) were considered. The common-flow up in series was the best in terms of the heat transfer as well as quality factor. The application of Bees algorithm in the optimum design of a cross flow PFHE with the offset strip fin was investigated by Zarea et al. [8]. Hot and cold flow length, number of fin layers, fin frequency, fin height, fin strip length and fin thickness were introduced as optimization variables. The results shown that Bees algorithm can find the optimum configuration with higher accuracy in comparison with Genetic algorithm, Particle Swarm optimization, Imperialist Competitive algorithm, and preliminary design. Pressure drop and heat transfer characteristics of a titanium brazed PFHE with the offset strip fins were studied by Fernández-Seara et al. [9]. An experimental program was conducted by using firstly, water on both sides of the heat exchanger and secondly, 10–30 wt% ethylene glycol aqueous solutions as working fluids. An empirical correlation was proposed to determine the single-phase convection heat transfer coefficients. Effects of the two passive heat transfer enhancement techniques namely vortex-generator and nanofluid on the performance of a PFHE were examined numerically by Khoshvaght-Aliabadi et al. [10]. It was shown that the mixture model had a
4 Page 4 of 35
closer prediction of the convective heat transfer coefficient to the experimental data. A general study on the performance of a PFHE with the offset strip fins was carried out by Yang and Li [11]. Effects of the geometrical three-dimensionality were analyzed in a distinctive way to understand the general behavior of the PEHE performance. Based on the literature review, it is found that there are very limited experimental studies on the corrugated and vortex-generator plate-fins. On the other hand, our previous comparative study [12] indicates that a better heat transfer in comparison to pressure drop in a PFHE belongs to the corrugated plate-fin (CPF) and vortex-generator plate-fin (VGPF). It motivates the current work to combine these plate-fins and generate a new design of the plate-fin as corrugated/vortexgenerator plate-fin (CVGPF). This study tries to analyze the thermal-hydraulic performances of the CPF, VGPF, and CVGPF in a PFHE by using the water-ethylene glycol mixtures as working fluid. The studied factors are the geometrical parameters (corrugation amplitude/length and winglet height/pitch), working fluid composition (100:0, 90:10, and 75:25 by mass), and volumetric flow rate (7.5 to 10.5 L/min). Experimental tests are performed in a pre-calibrated close loop setup with the ability to produce a constant wall temperature condition.
2. Tested plate-fins and coolants Usually, the complicated geometries of the plate-fins are fabricated by stamping from thin metal sheets. In the present study, all the tested plate-fins, i.e. corrugated plate-fin (CPF), vortexgenerator plate-fin (VGPF), and corrugated/vortex-generator pate-fin (CVGPF), are made from aluminum sheets with the length of 0.5 m and width of 1.6×10-2 m. The sheets thickness of 5×104
m is chosen to avoid an additional friction that might be occurred by thicker sheets. Our
previous studies [13, 14] show that the ratio of corrugation amplitude to corrugation length (γ =
5 Page 5 of 35
a/l) and the ratio of winglet height to winglet pitch (η = h/p) are the most effective geometrical parameters of the CPFs and VGPFs, respectively. Therefore, as depicted in Fig. 1, these geometrical ratios are examined at three levels. To create a physically meaningful and reliably comparative study, the studied combined plate-fins, i.e. CVGPFs, are fabricated at the same values of geometrical parameters. The considered values for the geometrical parameters of platefins are tabulated in Table 1. A coolant is a working fluid which flows through a heat transfer device to transfer the heat to other devices or dissipate it. A high thermal conductivity, low viscosity and low cost are the considerable advantages of a perfect working fluid. The most common working fluid is the water. Its low cost makes it a suitable heat transfer medium. Also, the ethylene glycol is another working fluid that is extensively used as an anti-freeze or anti-boil in heat transfer devices. Therefore, the water-ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) are the working fluids used to investigate the effect of coolant. The effective thermos-physical properties of the working fluids are systematically measured as function of ethylene glycol weight fraction. The thermal conductivity (κ), dynamic viscosity (μ), heat capacity (Cp) and density (ρ) are measured, respectively, using Decagon Devices/KD2 Pro system, Physica MCR 301 Anton Paar/rheometer, C80D Setaram/differential scanning calorimeter, and set of CPA 1003S Sartorius/digital electronic balance and pycnometer [15].
Please insert Fig. 1 here Please insert Table 1 here
3. Experimental setup
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The current experiments are conducted in the constant wall temperature condition. It is a commonly encountered condition in experimental thermal studies [16, 17]. To have a real and uniform temperature on the test section, a two-phase chamber is required. Therefore, an experimental setup with the ability to produce a constant wall temperature condition is prepared. The experimental setup is a close flow system, as schematically shown in Fig. 2. The working fluid restored in the storage tank is driven with a centrifugal pump through the system. In order to protect the equipment, a pressure relief valve is incorporated into the flow line. The flow rate passing through the system is controlled by using a needle valve, and it is measured by using a high sensitive ultrasonic flow meter. The test fluid flow length is a straight copper duct with the internal square cross section area of 2.56×10-4 m2, thickness of 1.0×10-3 m, and length of 1.2 m; 0.85 m is considered as the hydrodynamic entry section and 0.35 m is the heat transfer section. The hydrodynamic entry section is well insulated in order to eliminate the heat transfer with the ambient. The bulk temperature measurements at the inlet and outlet of the test section are made using two T-type thermocouples. Two sensitive pressure transmitters are also added to the test fluid flow length to obtain the pressure drop. Five K-type thermocouples are placed at equally spaced locations along the heat transfer section length to measure the wall temperature. After the test section, the fluid is cooled back to the inlet temperature via the cooling loop, which consists of a plate heat exchanger, a reservoir, a centrifugal pump, and a rotameter. For each test, it is essential to record the temperatures, pressures, and volumetric flow rate across the test section. As depicted in the figure, a data recording system is employed. A photograph of the applied experimental setup is presented in Fig. 2(b). Also, details about setup components are tabulated in Table 2.
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Please insert Fig. 2 here Please insert Table 2 here
4. Data reduction The equation of the convective heat transfer rate is used to compute the heat absorbed by the flowing fluid, Q c o n v V C
p
(T b ,o u t T b , in )
(1)
where, ρ, V, Cp, Tb,out and Tb,in represent the density, volumetric flow rate, specific heat capacity, inlet and outlet bulk temperatures of the working fluid, respectively. The effective heat transfer coefficient is estimated from the ratio of the convective heat transfer rate to the total surface area and logarithmic mean temperature difference of the wall-and-bulk fluid, h
Q conv
(2)
A (T w T b ) L M T D
(T w T b ) L M T D
Tw
b , in
lo g T w
Tw
b , in
b ,o u t
Tw
b ,o u t
(3)
where, ∆Tw–b,in and ∆Tw–b,out denote the differences between the wall temperature and the bulk fluid temperature at the inlet and outlet of the heat transfer section. Also, the average Nusselt number is defined as, hD
Nu
h
(4)
The thermal performance can be illustrated in a non-dimensional form, namely Colburn factor, j
Nu Re Pr
(5)
1 3
8 Page 8 of 35
The pressure drop is estimated from the experimental observations and theoretical formula as given below, P P in Po u t
(6)
To appraise the hydraulic performance, the friction factor is estimated from the pressure drop values by using the following equation, 2D h P
f
L u
(7)
2
where, u is the inlet velocity which is evaluated from the volumetric flow rate and cross section area. The uncertainties for the calculated results are evaluated according to the propagation analysis [18]. The maximum uncertainties obtained for the averaged Nusselt number and friction factor are about 4.9% and 6.4%, respectively.
5. Results and discussion Experiments are initially conducted for the water flow inside the empty duct to check the consistency of results. The present experimental results are validated by comparing with the single-phase fluid correlations, which are frequently referred in literature, in terms of the average Nusselt number and friction factor, (a) Equation of Gnielinski [19] f R e 1000 Pr 2
Nu
f 1 1 2 .7 2
(8)
1 2
Pr
2 3
1
where,
9 Page 9 of 35
f 1 .5 8 ln R e 3 .8 2
2
(9)
2300 < Re < 5 × 106 and 0.5 < Pr < 2000. (b) Equation of Notter-Rouse [20] N u 5 0 .0 1 5 R e
0 .8 5 6
Pr
0 .3 4 7
(10)
(c) Equation of Petukov [21] f 0 .7 9 ln R e 1 .6 4
2
(11)
3000 < Re < 5 × 106. The comparison of the values calculated through Eqs. (8) to (11) and their deviations with the current experimental results are presented in Fig. 3(a–b). The comparison shows a good agreement between the present experimental results and the previous empirical data so that at the range of studied, it lies within ±10% error.
Please insert Fig. 3 here
The variations of heat transfer coefficient versus the mass flow rate for water flow through studied plate-fin channels are presented in Fig. 4(a–c). The results of empty duct are also present for comparison. As anticipated, for all the cases, the heat transfer coefficient increases as the flow rate goes up. However, the effect of flow rate on the thermal performance of plate-fin channels is different. For instance, as the flow rate increases from the minimum to the maximum, the heat transfer coefficient of the CPF and VGPF channels at the middle value of dimensionless parameters, i.e. γ = η = 0.202, enhances about 29.8% and 34.7%, respectively. It is interesting to note that the effect of flow rate on the thermal performance of CVGPF channels is more than the CPF and VGPF channels; the heat transfer coefficient of CVGPF channel with λ = 0.041 10 Page 10 of 35
enhances about 37.6%, when the flow rate varies from the minimum to the maximum. It is found that at a given flow rate, the heat transfer coefficient gets higher values for the CPF and VGPF channels with the greater values of γ and η. In fact, as the dimensionless parameter of γ increases, the corrugations effect in the CPF channel intensifies. It leads to a larger flow path and stronger swirl flows in the CPF channel. Our previous study [13] shows that the strength of swirl flows depends strongly on the corrugation amplitude and length. Also, as the dimensionless parameter of η increases, the winglets effect in the VGPF channel intensifies. It causes a heavy exchange of core and wall fluids, leading to the higher enhancement of heat transfer between the flowing fluid and the channel walls. It is shown that the winglet height and pitch affect meaningfully the performance of VGPF channel [10].
Please insert Fig. 4 here
It can be found from Fig. 4(a–c) that at the same operating condition, the CVGPF channel has the highest values of the heat transfer coefficient, and the CPF and VGPF channels come in the second and third, respectively. For a better insight, Nusselt number enhancement of the platefin channels compared to the empty duct versus Reynolds number for water flow is shown in Fig. 5. The results confirm that all the plate-fin channels have higher Nusselt number in comparison with the empty duct, since the heat transfer coefficient in the plate-fin channels enhances by thermal boundary layer interruption with corrugations and winglets. In the CPF and VGPF channels, the longitudinal, transverse, and normal swirl flows may be generated in the corrugations and behind the winglets. These swirl flows make a heavy exchange of core and wall fluids, leading to the enhancement of heat transfer coefficient thereby Nusselt number. The
11 Page 11 of 35
enhancement in NuPF/NuEmpty duct ratio for the CVGPF channel is obvious compared to the other ones. Over the tested range of Reynolds number, Nusselt number of the CPF, VGPF, and CVGPF channels averagely increase by about 34.1% for γ = 0.317, 63.3% for γ = 0.202, and 76.6% for γ = 0.258, 25.7% for η = 0.086, 39.7% for η = 0.202, and 53.2% for η = 0.411, 49.3% for λ = 0.056, 69.9% for λ = 0.041, and 83.7% for λ = 0.022. It is worth to note that for all the plate-fin channels, the ratio of NuPF/NuEmpty duct gives higher values, as Reynolds number goes up. A possible mechanism for this appreciable Nusselt number enhancement is due to increasing number and size of swirl flows in these channels, because the strength of swirl flows depends on the Reynolds number.
Please insert Fig. 5 here
The measured flow pressure drops along the plate-fin channels are also used to study the hydraulic performance of the plate-fin channels. The variations of measured pressure drop with the mass flow rate are shown in Fig. 6(a–c). It can be observed that the pressure drop gradually increases with the flow rate increasing. It is found that the pressure drop of CPF channel is much higher than that of VGPF channel. It is attributed to noticeable flow blockage produced by corrugations in the channel equipped with the CPFs. Another point is the considerable effect of geometrical parameters on the pressure drop of the CPF channel compare to the VGPF channel. Likewise, the presence of winglets on corrugations is the main reason for the additional pressure drop of the CVGPF channel compared to the CPF channel. It is interesting to find that the effect of winglets on the pressure drop of corrugated plate is more than that of the plain one. As an example, embedding winglets with the height of 4 mm on the corrugated plate increases the
12 Page 12 of 35
pressure drop along the channel about 59.6%, while embedding the same winglets on the plain plate increases the pressure drop about 50.1%.
Please insert Fig. 6 here
As shown in Fig 7, the fPF/fEmpty duct ratio values of all the models are higher than one and decrease with Reynolds number. Over the tested range of Reynolds number, the friction factor of CPF, VGPF, and CVGPF channels averagely increase by about 19.8% for γ = 0.317, 279.3% for γ = 0.202, and 780.7% for γ = 0.258, 7.7% for η = 0.086, 150.1% for η = 0.202, and 212.2% for η = 0.411, 71.4% for λ = 0.056, 446.3% for λ = 0.041, and 801.3% for λ = 0.022.
Please insert Fig. 7 here
To investigate the effect of coolant, the variations of Nusselt number and friction factor of water/ethylene glycol mixtures (100:0, 90:10, and 75:25 by mass) across the plate-fin channels are presented in Fig. 8(a–b). The results show that Nusselt number decreases, as the mass fraction of ethylene glycol increases in the coolant. It can be explained that at the same mass flow rate, the working fluid with lower percentage of the ethylene glycol (lower Prandtl number) absorbs more heat compared to the working fluid with higher percentage of the ethylene glycol (higher Prandtl number). Therefore, the working fluid with the composition of 100:0 of the water/ethylene glycol mixture shows the highest Nusselt number, and the working fluids with the composition of 90:10 and 75:25 come in the second and third, respectively. It is found that the effect of coolant on the thermal performance of CVGPF channel is more than that of CPF and
13 Page 13 of 35
VGPF channels. For instance, when water is replaced with 90:10 and 75:25 water/ethylene glycol mixtures in the CVGPF, Nusselt number varies averagely about 5.6% and 14.7%, respectively. For the same replacements, Nusselt number varies about 4.3% and 12.1% for the CPF channel and 3.4% and 8.5% for the VGPF channel. As revealed in Fig. 8(b), the friction factor values for the three working fluids closely fell onto the same curve for all the plate-fin channels. A similar result was reported for the other plate-fin channels like offset strip [22].
Please insert Fig. 8 here
However, based on the results of heat transfer and pressure drop separately, it is difficult to create a final and correct conclusion as to which geometry of plate-fin is better. Therefore, the following thermal-hydraulic performances factor is applied to evaluate different configurations and geometries of the plate-fins [23],
JF
j f
j
PF
PF
f
E m p ty d u c t
E m p ty d u c t
(12)
1 3
where, the subscripts PF and Empty duct represent a plate-fin channel and the empty duct, respectively. A comparison among the JF factor values versus the volumetric flow rate for different working fluids across the studied plate-fins is displayed in Fig. 9(a–c). The JF factor is a “the larger the better” parameter, and a high value of that indicates a geometry with the appropriate thermal-hydraulic performances. It is depicted that under the studied range, the highest values are found for the CVGPF channel and the CPF and VGPF channels come in the second and third, respectively. An overall scrutiny on the figure discloses that the JF factor values of all the channels increase with the mass fraction of ethylene glycol. It should be note 14 Page 14 of 35
that the difference between the CPF and the CVGPF channels decreases as the mass fraction of ethylene glycol increases. Another noticeable issue is the effect of geometrical parameters on the JF factor values. It is clear that the JF factor values decrease as the ratio of corrugation amplitude to corrugation length, i.e. γ, and the ratio of winglet height to winglet pitch, i.e. η, are increased. It means that the CPF and VGPF channels with the lower values of γ and η have a better thermal-hydraulic performances form the considered performance evaluation criterion point of view.
Please insert Fig. 9 here
Finally, the experimental data are used to develop correlations for Nusselt number and friction factor in the case of tested working fluids inside the plate-fin channels. The regression analysis coefficients are assessed with the help of classical least square method. The proposed correlations are valid for Reynolds number from 1700 to 13000, based on the applied working fluid. The correlations of Nusselt number and friction factor are derived as follows, N u or f a R e Pr b
c
,
, or
d
(13)
The constants of correlations (i.e. a, b, c, and d) are given in Table 3 for the tested plate-fin channels. It should be illustrated that the data obtained from the proposed correlations and experimental results are in a good agreement, so that approximately 98% of the experimental data are correlated within ±15%. For instance, a comparison between the experimental data and the predicted values of Nusselt number is made in Fig. 10.
Please insert Table 3 here 15 Page 15 of 35
Please insert Fig. 10 here
6. Conclusions Employing complex channels and enhanced working fluids has been proven to be very effective ways on plate-fin heat exchangers (PFHEs). In the present study, the thermal-hydraulic performances of two mostly use plate-fins, namely corrugated plate-fin (CPF) and vortexgenerator plate-fin (VGPF), are analyzed. Then, a new design for the plate-fins is proposed as corrugated/vortex-generator plate-fin (CVGPF), and its performance is compared with the CPF and VGPF channels. The experimental results are validated based on the previous correlations. The results confirm that all the plate-fin channels have higher Nusselt number in comparison with the empty duct. Also, the enhancement in thermal performance of the PFHE with the CVGPF channel is obvious compared to the CPF and VGPF channels. Over the tested range of flow rate, the maximum enhancement in Nusselt number is about 76.6% for the CPF channel, 53.2% for the VGPF channel, and 83.7% for the CVGPF channel compared to the empty duct. It is interesting to find that the effect of winglets on the friction factor of corrugated plate is more than that of the plain one. Another point is the considerable effect of geometrical parameters on the friction factor of the CPF channel compare to the VGPF channel. The results show that Nusselt number decreases as the mass fraction of ethylene glycol increases in the coolant. It is found that the effect of coolant on the thermal performance of CVGPF channel is more than that of CPF and VGPF channels. However, the friction factor values for the three working fluids closely fell onto the same curve for all the plate-fin channels. The current study shows that using the complex channels instead of the plain one enhances Nusselt number with a penalty in the friction factor. However, Nusselt number and friction factor are two independent parameters that
16 Page 16 of 35
are not related together by an equation. Therefore, a thermal-hydraulic performance evaluation criterion is considered that can relate these parameters and provide conditions for the comparison. It is depicted that under the studied range, the highest values of considered performance evaluation criterion are found for the CVGPF channel, and the CPF and VGPF channels come in the second and third, respectively. The performance evaluation criterion values of all the channels increase with the mass fraction of ethylene glycol. Also, it decrease as the ratio of corrugation amplitude to corrugation length and the ratio of winglet height to winglet pitch increase. Finally, correlations are proposed for Nusselt number and friction factor of the considered plate-fins.
Acknowledgements This research was carried out in Advanced Research Laboratory of Chemical Engineering Department of Islamic Azad University (IAU) of Shahrood Branch, Iran.
Nomenclature A
total surface area, m2
a
corrugation amplitude, m
Cp
specific heat capacity, J.kg-1.K-1
Dh
hydraulic diameter, m
h
winglet pitch, m
L
channel length, m
l
corrugation length, m
Qconv
convective heat transfer rate, W
17 Page 17 of 35
P
pressure, Pa
p
winglet pitch, m
∆P
pressure drop, Pa
T
temperature, K
u
velocity, m.s-1
V
volumetric flow rate, m3.s-1
Greek symbols ρ
density, kg.m-3
μ
dynamic viscosity, Pa.s
κ
thermal conductivity, W.m-1.K-1
γ
ratio of corrugation amplitude to corrugation length
η
ratio of winglet height to winglet pitch
λ
γ/η
Dimensionless groups f
Fanning friction factor
j
Colburn factor
Nu
Nusselt number
Re
Reynolds number
Pr
Prandtl number
Subscripts
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b
bulk fluid
in
inlet
out
outlet
LMTD
logarithmic mean temperature difference
PF
plate-fin
w
wall
Acronyms CPF
Corrugated plate-fin
CVGPF
Corrugated/vortex-generator plate-fin
PFHE
Plate-fin heat exchangers
VGPF
Vortex-generator plate-fin
References [1]
L. Wang, B. Sundén, R.M. Manglik, Plate Heat Exchangers: Design, Applications and Performance, WIT Press, Ashurst Lodge, 2007, 27–39.
[2]
M. Khoshvaght Aliabadi, F. Hormozi, Performance analysis of plate-fin heat exchangers: Different fin configurations and coolants, Journal of Thermophysics and Heat Transfer 27 (3) (2013) 515–525.
[3]
L. Sheik Ismail, R. Velraj, C. Ranganayakulu, Studies on pumping power in terms of pressure drop and heat transfer characteristics of compact plate-fin heat exchangers-A review, Renewable and Sustainable Energy Reviews 14 (1) (2010) 478–485.
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Z. Wang, Y. Li, Layer pattern thermal design and optimization for multistream plate-fin heat exchangers-A review, Renewable and Sustainable Energy Reviews 53 (2016) 500– 514.
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[6]
M. Khoshvaght-Aliabadi, S. Zangouei, F. Hormozi, Performance of a plate-fin heat exchanger with vortex-generator channels: 3D-CFD simulation and experimental validation, International Journal of Thermal Sciences 88 (2015) 180–192.
[7]
A. Sinha, K. Ashoke Raman, H. Chattopadhyay, G. Biswas, Effects of different orientations of winglet arrays on the performance of plate-fin heat exchangers, International Journal of Heat and Mass Transfer 57 (1) (2013) 202–214.
[8]
H. Zarea, F. Moradi Kashkooli, A. Mansuri Mehryan, M.R. Saffarian, E. Namvar Beherghani, Optimal design of plate-fin heat exchangers by a Bees Algorithm, Applied Thermal Engineering 69 (1–2) (2014) 267–277.
[9]
J. Fernández-Seara, R. Diz, F.J. Uhía, Pressure drop and heat transfer characteristics of a titanium brazed plate-fin heat exchanger with offset strip fins, Applied Thermal Engineering 51 (1–2) (2013) 502–511.
[10]
M. Khoshvaght-Aliabadi, F. Hormozi, A. Zamzamian, Effects of geometrical parameters on performance of plate-fin heat exchanger: Vortex-generator as core surface and nanofluid as working media, Applied Thermal Engineering 70 (1) (2014) 565–579.
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Y. Yang, Y. Li, General prediction of the thermal hydraulic performance for plate-fin heat exchanger with offset strip fins, International Journal of Heat and Mass Transfer 78 (2014) 860–870.
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M. Khoshvaght-Aliabadi, F. Hormozi, A. Zamzamian, Role of channel shape on performance of plate-fin heat exchangers: Experimental assessment, International Journal of Thermal Sciences 79 (2014) 183–193.
[13]
M. Khoshvaght-Aliabadi, Influence of different design parameters and Al2O3-water nanofluid flow on heat transfer and flow characteristics of sinusoidal-corrugated channels, Energy Conversion and Management 88 (2014) 96–105.
[14]
M. Khoshvaght-Aliabadi, O. Sartipzadeh, A. Alizadeh, An experimental study on vortexgenerator insert with different arrangements of delta-winglets, Energy 82 (2015) 629– 639.
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M. Khoshvaght-Aliabadi, M. Sahamiyan, M. Hesampour, O. Sartipzadeh, Experimental study on cooling performance of sinusoidal–wavy minichannel heat sink, Applied Thermal Engineering 92 (2016) 50–61.
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H.W. Coleman, W.G. Steele, Experimentation, validation, and uncertainty analysis for engineers, John Wiley & Sons, New York, 2009.
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V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (1976) 359–368.
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[22]
M.S. Kim, J. Lee, S.J. Yook, K.S. Lee, Correlations and optimization of a heat exchanger with offset-strip fins, International Journal of Heat and Mass Transfer 54 (2011) 2073– 2079.
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J.Y. Yun, K.S. Lee, Influence of design parameters on the heat transfer and flow friction characteristics of the heat exchanger with slit fins, International Journal of Heat and Mass Transfer 43 (14) (2000) 2529–2539.
22 Page 22 of 35
Caption of Figures:
Fig. 1. Generated and tested plate-fins.
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Data recording systems Pin Pout F
Safety pressure valve
Tin Tout
Selector switch
Tw P-o
T-o
T-i
T5
T4
T3
T2
T1
Hydrodynamic length (Insulated)
Level meter
Test section
P-i
Ultrasonic flow meter Three way
Heater 2
Ball valve
Heater 1
Relief valve Needle valve
Test chamber Drain
Cooling fluid reservoir
FI
PHE
Tap water outlet Storage tank Drain
Centrifugal pump
Rotameter
Centrifugal pump
(a)
24 Page 24 of 35
(b) Fig. 2. (a) Schematic (b) photograph representations of experimental setup.
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Nusselt number
120
105
Present experimental data Eq. (8) Eq. (10)
90
75
60 9000
10000
11000 Reynolds number
12000
13000
12000
13000
(a)
0.04
Friction factor
0.035
Present experimental data Eq. (9) Eq. (11)
0.03
0.025
0.02 9000
10000
11000 Reynolds number (b)
Fig. 3. Comparison between present experimental data and previous empirical correlations (a) Nusselt number (b) Friction factor.
26 Page 26 of 35
Heat transfer coefficient (W/m2.K)
Empty duct
γ=0.137
γ=0.202
γ=0.258
6000
5000
4000
3000
Min. error: 0.8% Max. error: 3.2%
2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(a)
Heat transfer coefficient (W/m2.K)
Empty duct
η=0.086
η=0.202
η=0.411
6000
5000
4000
3000
Min. error: 1.1% Max. error: 2.5% 2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(b)
27 Page 27 of 35
Heat transfer coefficient (W/m2.K)
Empty duct
λ=0.056
λ=0.041
λ=0.022
6000
5000
4000
3000
Min. error: 0.9% Max. error: 3.6%
2000 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(c) Fig. 4. Heat transfer coefficient – Mass flow rate for water flow in plate-fin channels (a) CPF (b) VGPF (c) CVGPF.
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
Nu PF / Nu Empty duct
2.5 2 1.5 1 0.5 0 7773.55
8291.79
8810.03
9328.27
9846.50
10364.74 10882.98
Reynolds number
Fig. 5. Nusselt number enhancement – Reynolds number of plate-fin channels compare to empty duct.
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Empty duct
γ=0.137
γ=0.202
γ=0.258
Pressure drop (Pa)
10000 8000
Min. error: 0.04% Max. error: 0.09%
6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.17
0.18
Mass flow rate (kg/s)
(a) Empty duct
η=0.086
η=0.202
η=0.411
Pressure drop (Pa)
10000
Min. error: 0.02% Max. error: 0.08%
8000 6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
Mass flow rate (kg/s)
(b)
29 Page 29 of 35
Empty duct
λ=0.056
λ=0.041
λ=0.022
Pressure drop (Pa)
10000 8000
Min. error: 0.05% Max. error: 0.08%
6000 4000 2000 0 0.12
0.13
0.14
0.15
0.16
0.17
0.18
Mass flow rate (kg/s)
(c) Fig. 6. Pressure drop – Mass flow rate for water flow in plate-fin channels (a) CPF (b) VGPF (c) CVGPF.
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
10
f PF / f Empty duct
8 6 4 2 0 7773.55
8291.79
8810.03
9328.27
9846.50
10364.74
10882.98
Reynolds number
Fig. 7. Friction factor increase – Reynolds number of plate-fin channels compare to empty duct.
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Water across CPF 10% EG in water across CPF 25% EG in water across CPF Water across VGPF 10% EG in water across VGPF 25% EG in water across VGPF Water across CVGPF 10% EG in water across CVGPF 25% EG in water across CVGPF
Nusselt number
150
125
100
75 7
7.5
8
8.5
9
9.5
10
10.5
11
10
10.5
11
Volumetric flow rate (L/min)
(a)
Water across CPF 10% EG in water across CPF 25% EG in water across CPF Water across VGPF 10% EG in water across VGPF 25% EG in water across VGPF Water across CVGPF 10% EG in water across CVGPF 25% EG in water across CVGPF
Friction factor
0.3
0.2
0.1
0 7
7.5
8
8.5
9
9.5
Volumetric flow rate (L/min)
(b) Fig. 8. Effect of working fluid type on (a) Nusselt number (b) Friction factor of plate-fin channels at middle value of geometrical parameters, i.e. γ = η = 0.202.
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γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(a) γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(b)
32 Page 32 of 35
γ=0.137
γ=0.202
γ=0.258
η=0.086
η=0.202
η=0.411
λ=0.056
λ=0.041
λ=0.022
3.5 3
JF factor
2.5 2 1.5 1 0.5 7.5
8
8.5
9
9.5
10
10.5
Volumetric flow rate (L/min)
(c) Fig. 9. JF factor – Volumetric flow rate for different working fluids in plate-fin channels (a) water (b) 10% EG in water (c) 25% EG in water.
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Predicted values for Nusselt number
180
150
+15% 120
–15% 90
60 60
90
120
150
180
Experimental data for Nusselt number
Fig. 10. Comparison of experimental values for Nusselt number with those predicted by Eq. (13).
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Table 1. Geometrical parameters of plate-fins. Plate-fins Dimensionless parameter Level 1 Level 2 Level 3 1. CPF γ = a/l 0.137 0.202 0.258 2. VGPF η = h/p 0.086 0.202 0.411 3. CVGPF λ = ah/lp 0.056 0.041 0.022 Table 2.Specification, range, and accuracy of setup components. Component Specification Range Accuracy 1. Storage tank Stainless steel 0–6.75 lit – 2. Centrifugal pump PKm60, Pedrollo 0–40 lit/min – 3. Needle valve LMC, ASC.15 0–20 lit/min – 4. Relief valve Watts, 530-050 – – 5. Safety pressure valve 21T2BV28-F, BDA – – 6. Ultrasonic flow meter Flownetix® 100seriesTM 0–20 lit/min 0.05 lit/min 7. Bulk thermocouples T-type –50 to 200 °C 0.1 °C 8. Wall thermocouples K-type (Omega) –73 to 260 °C 0.1 °C 9. Pressure transmitters PSCH0.5BCIA, Sensys 0 to 10000 Pa 10 Pa 10. Ultrasonic flow meter indicator MT4W, Autonics – – 11. Bulk thermocouples indicator SU-105PRR, Samwon – – 12. Wall thermocouples indicator SU-105KRR, Samwon – – 13. Pressure transmitters indicator MT4W, Autonics – – 14. Rotameter LZT-1005G, MBLD 0–7 lit/min 0.25 lit/min 15. Plate heat exchanger B3-014C-12-3.0-H, Danfuss 0–10 lit/min – Table 3. Constants of Nusselt number and fiction factor correlations. Plate-fin a b c d 1. CPF Nu 5.695×10-2 0.762 0.669 0.408 f 12.236 –5.96×10-2 – 3.3351 2. VGPF Nu 5.033×10-3 0.923 0.832 9.839×10-2 -2 f 0.111 –1.412×10 – 0.437 3. CVGPF Nu 1.016×10-2 0.797 0.685 –0.229 f 1.718×10-3 –1.041×10-3 – –1.306
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