- Email: [email protected]
Air inlet angle influence on the air-side heat transfer and flow friction characteristics of a finned oval tube heat exchanger
International Journal of Heat and Mass Transfer 145 (2019) 118702
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Air inlet angle influence on the air-side heat transfer and flow friction characteristics of a finned oval tube heat exchanger Linghong Tang a,d, Xueping Du b, Jie Pan c, Bengt Sundén d,⇑ a
School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, China School of Electric Power Engineering, China University of Mining and Technology, Xuzhou 112226, China c School of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, China d Division of Heat Transfer, Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden b
a r t i c l e
i n f o
Article history: Received 12 June 2019 Received in revised form 4 August 2019 Accepted 5 September 2019
Keywords: Finned oval tube heat exchanger Air cooling Air inlet angle Heat transfer and flow friction characteristics
a b s t r a c t In this study, the influence of various air inlet angles on the heat transfer and flow friction characteristics of a 2-row plain finned oval tube heat exchanger is analyzed by experimental and numerical methods. The experimental results show that an air inlet angle 45° provides the best heat transfer performance, and an air inlet angle 90° provides the smallest pressure drop, while an air inlet angle 30° provides the worst heat transfer performance associated with the largest pressure drop. The 3-D numerical simulation results indicate that with the decrease of the air inlet angle, the uniformity of the air velocity distribution in the z-direction of the heat exchanger becomes worse. The heat transfer characteristics at different air inlet angles are analyzed from the prospective of the field synergy principle and the effect of the air velocity distribution uniformity. The overall heat transfer performance is also evaluated by the JF factor under the same air mass flow rate. The results show that the air inlet angle 45° offers the best overall heat transfer performance, next is the air inlet angle 60°, while the air inlet angle 30° has the worst overall heat transfer performance. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Finned tube heat exchangers are extensively employed in chemical engineering, refrigeration, and HVAC (heating, ventilation and air conditioning) applications such as compressor intercoolers, air-coolers and fan coils. Circular tubes are widely used in finned tube heat exchangers, but it has been proved that using finned oval tube can effectively improve the overall heat transfer performance on the fin side. During the past few years, there are many investigations on the heat transfer and flow friction performance of finned oval tube heat exchangers. Leu et al. [1] numerically studied the air side performance of finned tube heat exchangers having circular tube and oval tube. Compared with the circular tube configuration, a 10% decrease of heat transfer performance was observed and a 41% decrease of pressure drop was seen for the oval tube configuration at a fixed fin geometry. Han et al. [2] also numerically studied the heat transfer and flow friction characteristics of finned circular and oval tube heat exchangers. The results revealed that using the finned oval tube could not only reduce the flow resistance but also improve the heat transfer capacity of the heat ⇑ Corresponding author. E-mail address: [email protected] (B. Sundén). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118702 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
exchangers. Hasan et al. [3] experimentally studied the performance of circular and oval tube heat exchangers with plain fins. The results indicated that the average Colburn factor for the oval tube was 89% of that for the circular tube, while the average friction factor for the oval tube was 46% of that for the circular tube. Zeeshan et al. [4] numerically evaluated the thermal hydraulic performance of fin tube heat exchangers with circular, oval and flat tubes having inline and staggered arrangement. The results showed that the increase in heat transfer coefficient of the optimal oval tube shape was 14.0% at lower air side Reynolds number (Re = 400) and 5.0% at higher air side Reynolds number (Re = 900). Also, the pressure drop was reduced by 39.9% at higher Reynolds number (Re = 900) compared to the circular tube shape with the inline arrangement. El Gharbi et al. [5] numerically investigated the heat transfer and the pressure drop characteristics and effectiveness of a cross-flow heat exchanger employing a staggered tube bank with different tube shapes. Three studied geometries were considered, i.e., circular, elliptic and wind-shaped. The results showed that when Re > 15000, the circular tube shape was clearly worse than the other two geometries, and for Re > 23000, the elliptic shape was the best. Furthermore, there are some investigations on the heat transfer and flow friction performance for different fin patterns [6–11].
2
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Nomenclature A Ac Afr Ai Ao a b cp Dc di do Fs f fF H hi ho JF j Kc Ke k L l m Nu P1 Pt Pr Q q Re t ! U
area, m2 the minimum flow area, m2 the frontal area, m2 heat transfer area of water side, m2 total surface area of air side, m2 half of length of major axis, mm half of length of short axis, mm specific heat at constant pressure, J/(kgK) fin collar outside diameter, mm equivalent inside diameter of oval tube, mm equivalent outside diameter of oval tube, mm fin spacing, mm Darcy friction factor Fanning friction factor height of front area, mm heat transfer coefficient of water side, W/(m2K) heat transfer coefficient of air side, W/(m2K) JF factor Colburn factor the entrance loss coefficient the exit loss coefficient overall heat transfer coefficient, W/(m2K) tube length, mm fin length, mm mass flow rate, kg/s Nusselt number longitudinal pitch, mm transverse pitch, mm Prandtl number heat transfer rate, W volume flow rate, m3/h Reynolds number temperature, K velocity vector, m/s
In order to save space, it is necessary to arrange heat exchangers obliquely in many cases, and then the air inlet flow direction is not orthogonal to the inlet surface of heat exchangers. The air inlet flow direction has a major effect on the heat transfer and flow friction performance of the air-coolers. There are some related reports on the heat transfer and flow friction performance of various air inlet flow directions. As described by Kröger [12], the finned tube bundles in large air-cooled condensers might be sloped at some angles up to 60° with the horizontal in order to save land area. Ahmad and Badr [13] numerically studied the mixed convection from an oval tube at different attack angles placed in a fluctuating free stream. Their study revealed that increasing the inclination angle from 0° to 90° tended to enhance the vortex shedding and the heat transfer rate. Zhang [14] numerically and experimentally investigated the flow maldistribution and thermal performance deterioration in cross-flow air to air heat exchangers. Liu et al. [15] numerically studied the effect of the air inlet angle on the heat transfer coefficient and pressure drop of the plate-fin heat exchangers. The numerical results showed that the different flow fields of the two special air inlet angles caused different effects on the heat transfer coefficient and pressure drop. Unger et al. [16] experimentally studied the heat transfer and flow characteristics of finned oval tubes. The experimental results showed that as the tube tilt angle rose from 0° to 40°, both the Nusselt number and friction factor increased. In our previous papers [17–19], the performance of finned oval tube heat exchangers with different air inlet angles were experimentally studied, but the details about heat transfer and flow char-
u, v, w W x, y, z
x, y, z velocity components, m/s width of front area, mm Cartesian co-ordinates
Greek symbols Dp pressure drop, Pa Dtm logarithmic mean temperature difference, K a intersection angle between the velocity and temperature gradient, deg d thickness, mm g fin efficiency go surface efficiency h air inlet angle, deg thermal conductivity, W/(mK) k dynamic viscosity of fluid, kg/(ms) l density, kg/m3 q r contraction ratio of the fin array / heat flux, W/m2 w correction factor of temperature difference Subscripts a air f fin fr frontal area i inside in inlet m mean max maximum value out outlet ref reference value t oval tube w water
acteristics were not clarified. Therefore, in this paper, the overall performance and local detailed characteristics of a 2-row finned oval tube heat exchanger with different air inlet angles are studied by experimental and numerical methods.
2. Experimental results and discussion 2.1. Experimental system The experimental system consists of two separate loops, i.e., an air loop and a hot water loop, as shown in Fig. 1. The air loop is provided to blow air across the finned bundles of test core which is placed in the test section. Air is induced to the wind tunnel by a frequency modulation blower. Air flows in turn through the entrance, transition section, contraction section and straightening section before reaching the test core. The regulation and uniform distribution of air flow are achieved along these three sections between the entrance and test core. After being heated by hot water, air leaves the test core and then flows through the flow metering duct before being discharged to the environment. The air side condition is determined by the air inlet temperature before arriving at the test core, the change of the air temperature through the core, and the air pressure drop through the core. The air inlet temperature and the temperature difference between inlet and outlet through the test core are measured by two sets of multipoint T-type copper-constantan thermocouple grids. Each set contains twelve calibrated thermocouples with an accuracy of ±0.2 K.
3
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 1. Schematic diagram of the experimental system.
Meanwhile, the air velocity is measured by a Pitot-tube meter, which is located in the flow metering duct far downstream of the test core, and the air static pressure before and after the test core are surveyed by a U-tube water column manometer, whose precision is ±1%. The Pitot-tube meter is connected to two different range microbarometer (at small flow rates) or U-tube water column manometer (at large flow rates). The hot water loop is designed to provide hot water at a temperature of 333.15 K through the oval tubes of the test core. Hot water is generated by electric heating rods in a water tank and driven to the test core by a pump. The calibrated E-type armored thermocouples with an accuracy of ±0.1 K are used to measure the water temperature, and there are four thermocouples placed at the water inlet and outlet on each side, respectively. Furthermore, the water flow rate is tested by a turbine flowmeter with a precision of 0.2%. At the same time, the pressure drop and outlet static pressure on the water side is measured with two Rosemount pressure transmitters with a precision of 0.1%, respectively. Suitable data acquisition systems and data collectors are also used for data collection and storage. The transient temperatures of water and air, water pressure drop and water flowmeter signals in the present study are transformed and recorded by a real-time hybrid recorder (Keityley-2700) with a sample rate of 100 Hz. Much attention is paid to the heat balance to ensure that steady state of the test core exists before collecting the data in the experiments. To reduce the heat loss to the surroundings, the experimental test core is covered by a thick foam insulation. During the data-acquisition procedure, each measured value is read at least five times, starting reading data no less than 40 min later when a working condition is changed. The arithmetic mean value of the recorded data for a certain working condition is used for checking the heat balance between the energy gain Qa of the air and the energy loss Qw of the water. Then the data with the smallest thermal equilibrium error between air side and water side will be saved. In all tests, the thermal equilibrium between air side and water side is within 5%.
The test core is a 2-row plain finned oval tube heat exchanger, and the detailed geometrical parameters of the test core are tabulated in Table 1 and schematically shown in Fig. 2. All tubes and fins are made of carbon steel. The fins are connected to the oval tube by brazing, so the contact thermal resistance could be neglected. Heat transfer and flow friction characteristics of the finned oval tube heat exchanger with various air inlet angles (30°、45°、60° and 90°, as shown in Fig. 3) are experimentally investigated in this study. 2.2. Data reduction The main purpose of the data reduction is to determine the air side heat transfer and friction characteristics, Nusselt number (Nu) and friction factor (f) of the heat exchangers from the experimental data. There are recorded at steady-state conditions during each test run. An objective is to find out corresponding power-law correlations of Nu vs. Re, and f vs. Re for each case. The thermal properties of air and water are determined at the average value of the inlet and outlet temperatures of air and water, respectively. The water side heat transfer rate Qw is given as
Table 1 Geometric dimensions of the plain finned oval tube heat exchanger. Parameters
Symbol/unit
Values
Transverse tube pitch Longitudinal tube pitch Tube thickness Fin thickness Fin space Short axis of oval tube Major axis of oval tube Width of front area Height of front area
Pt/mm Pl/mm dt/mm df/mm Fs/mm 2b/mm 2a/mm W/mm H/mm
26.7 55 1.5 0.35 2.5 14 36 600 320
4
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 2. Schematic view of the 2-row plain finned oval tube heat exchanger.
Fig. 3. Four different air inlet angles.
Q w ¼ qw qw cp;w t w;in tw;out
ð1Þ
where qw is the volume flow rate of water, qw is the density of water, cp,w is the specific heat at constant pressure of water, tw,in is the inlet temperature of water, and tw,out is the outlet temperature of water. The air-side heat transfer rate Qa is given as
Q a ¼ ma cp;a ta;out ta;in
ð2Þ
where ma is the mass flow rate of air, cp,a is the specific heat at constant pressure of air, ta,in is the inlet temperature of air, and ta,out is the outlet temperature of air. The total heat transfer rate is defined as the average of the water side and air side heat transfer rates
Q ave ¼ ðQ w þ Q a Þ=2
ð3Þ
The overall heat transfer coefficient, k, is calculated from the following relationship
k ¼ Q av e =ðw Ao Dtm Þ
ð4Þ
where w is the correction factor of the temperature difference, Ao is the total heat transfer area of the air side, including the area of fins and base tubes, and Dtm is the logarithmic mean temperature difference. The overall heat transfer resistance can be defined as
1 1 1 do 1 ¼ þ ln þ kAo hi Ai 2pkL di ho go Ao
ð5Þ
The water side heat transfer coefficient, hi, is evaluated from the Gnielinski’s formula [20]
" 2=3 # 0:11 kw ðf i =8Þ Redi 1000 Prw d Prw 1þ i hi ¼ pffiffiffiffiffiffiffiffiffi 2=3 di 1 þ 12:7 f =8 Pr 1 L Prw;t i w fi can be calculated as follows
ð6Þ
2 f i ¼ 1:82lgRedi 1:64
ð7Þ
The equivalent diameters for the oval tube, do and di, are given as follows
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 do ¼ 4ab= 2 a2 þ b
ð8Þ
di ¼ do 2dt
ð9Þ
where a is half of the length of major axis, and b is half of the length of short axis. In Eq. (5), go is the surface efficiency, which may be written in terms of the fin efficiency gf, fin surface area Af and total surface area Ao, as follows
go ¼ 1
Af ð1 gf Þ Ao
ð10Þ
gf denotes the fin efficiency and is calculated by the approximative method described by Schmidt [21]
gf ¼
tanhðmHÞ mH
ð11Þ
where
sffiffiffiffiffiffiffiffi 2ho m¼ kf df
ð12Þ
H ¼ Rc /
ð13Þ
Rc ¼ do =2
ð14Þ
/¼
Req Req 1 1 þ 0:35ln Rc Rc
ð15Þ
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
0:5 Req XM XL ¼ 1:27 0:3 Rc Rc XM
XL ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðPt =2Þ2 þ P 2l
ð16Þ
5
area Afr. Dc is the fin collar outside diameter, Dc = do + 2df. According to Kays and London [22], the entrance and exit loss coefficients Kc and Ke are 0.4 and 0.2. The uncertainties of Nusselt number and friction factor of the air side are 5.2% and 7.3%, respectively.
ð17Þ
2
2.3. Heat transfer and pressure drop comparisons
X M ¼ Pt =2
ð18Þ
where Pt is the transverse tube pitch, and Pl is the longitudinal tube pitch. It can be seen that the calculation formulas of gf include the air side heat transfer coefficient ho in above Eqs. (11) and (12), but both of them are unknown. They can be acquired by solving Eqs. (5) and (10)–(18) with an iterative method. The iteration process for calculating gf is shown in Fig. 4. The heat transfer and friction characteristics of the heat exchanger are presented in the following dimensionless forms.
Nu ¼ ho Dc =ka
ð19Þ
ReDc ¼ qa umax Dc =la
ð20Þ
j ¼ Nu= ReDc Pr1=3
ð21Þ
" Ac qm 2qin Dp qin 2 K þ 1 r 1 2 fF ¼ c Ao qin ðqin uin Þ2 qout
qin þ 1 r2 K e
ð22Þ
f ¼ 4f F
ð23Þ
qout
Figs. 5 and 6 show the variations of ho and Nu for various air inlet angles of the finned oval tube heat exchanger. From Figs. 5 and 6, it can be seen that the heat transfer performance increases with increasing air frontal velocity (or Reynolds number). The heat transfer coefficient and Nusselt number for the air inlet angle 45° are the highest among the four different air inlet angles. Those of the air inlet angle 60° take the second place, while those of the air inlet angle 30° are the lowest. Compared with the air inlet angle 90°, the average Nusselt numbers of the air inlet angle 60°, 45° and 30° increase 5.6%, 8.0% and 12.5% in the range of the studied Reynolds number, respectively. Figs. 7 and 8 illustrate the effect of the air inlet angles on the friction characteristics of the finned oval tube heat exchanger. From Figs. 7 and 8, the pressure drop and friction factor of the air inlet angle 30° are the highest among the four different air inlet angles. Those of the air inlet angle 45° take the second place, and
where umax is the velocity at the minimum free flow area, umax = ufr/
r. The term r is the ratio of the minimum flow area Ac to the frontal
Fig. 5. Heat transfer coefficient comparisons for different air inlet angles.
Fig. 4. Calculation process of gf.
Fig. 6. Nusselt number comparisons for different air inlet angles.
6
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
and local detailed characteristics can be obtained by numerical simulations. Such an approach is more conducive to study the heat transfer and flow characteristics of the finned oval tube heat exchanger at different air inlet angles. A schematic diagram of the physical model is shown in Fig. 9. The actual length of the computational domain is 7.5 times of the fin length. This means that the domain is extended 1.5 times of the fin length at the entrance section to ensure the inlet uniformity, and at the exit, the domain is extended 5 times of the fin length in order to make sure that the exit flow boundary has no flow recirculation. The governing equations for continuity, momentum and energy may be expressed in vectorial notation as
!
r q U / ¼ r C / r / þ S/
Fig. 7. Pressure drop comparisons for different air inlet angles.
Fig. 8. f-factor comparisons for different air inlet angles.
those of the air inlet angle 90° are the lowest. Compared with the air inlet angle 90°, the average f-factors of the air inlet angle 60°, 45° and 30° increase 4.7%, 10.0% and 28.0% in the range of the studied Reynolds number, respectively. Based on the experimental data, correlations of Nusselt number and f-factor are given in Table 2. 3. Numerical simulation results and discussion 3.1. Physical and mathematic model The above experimental data generally reflect the overall performance of the finned oval tube heat exchanger, but it is difficult to obtain the local characteristics. Both the overall performance
ð24Þ
In the above equation, the dependent variable, /, stands for the velocity components, temperature, k and e. The terms C/ and S/ represent the appropriate diffusion coefficients and the source terms, respectively. The particular expressions for /, C/ and S/ are summarized in Table 3. Because the governing equations are elliptic in spatial coordinates, boundary conditions are required for all boundaries of the computational domain. At the inlet boundary, the flow velocity uin is assumed to be uniform, and the temperature tin is taken to 293.15 K. At the downstream end of the computational domain, streamwise gradients (Neumann boundary conditions) of all the variables are set to zero. On the solid surfaces (tube, fin), no-slip conditions are used and a uniform tube inside-wall temperature tw are specified as 333.15 K, and the temperature distribution in the tube outside-wall will be determined by solving the conjugated heat transfer problem between air and tube in the computational domain. The commercial code ANSYS FLUENT 14.0 is used for the numerical solution of the Navier-Stokes and energy equations. A preprocessor Gambit 2.4 is used to mesh the computational domain for the solver. The grids for the air inlet angle 60° are shown in Fig. 10. FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This procedure involves subdividing the region in which the flow is to be solved into individual cells or control volumes so that the equations can be integrated numerically on a cell-by-cell basis to produce discrete algebraic (finite volume) equations. The air flow is assumed to be incompressible ideal gas, turbulent, quasi-steady, 3-D and exhibiting no viscous dissipation. All variables, including velocity components, pressure and temperature, are averaged for a control volume. The coupling between pressure and velocity is implemented by the SIMPLEC algorithm. The QUICK scheme is used for the spacial discretization of the momentum, turbulent kinetic energy, turbulent dissipation rate and energy equations in the simulations. The residuals are less than 10-4 and 10-8 for the continuity and energy equations, respectively, to ensure convergence of the computations. After validating the solution independency of the grid number, about 35,000,000 mesh element number is selected as a reference mesh size for different air inlet angles in this paper.
Table 2 Correlations of Nusselt number and f-factor. Inletangle
Nu = f(Re)
Maximumrelative error
f = f(Re)
Maximum relative error
90° 60° 45° 30°
Nu = 2.128Re0.402 Dc Nu = 2.183Re0.405 Dc Nu = 2.159Re0.409 Dc 0.608 Nu = 0.314ReDc
1.4% 1.6% 1.3% 2.0%
f = 37.239Re-0.481 Dc f = 19.893Re-0.403 Dc f = 16.936Re-0.379 Dc f = 131.583Re-0.597 Dc
1.1% 1.5% 1.4% 2.3%
7
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Table 3 Expressions for /, C/ and S/ [23]. /
C/
S/
1 u
0
0
l + lt
@ Su ¼ @p @x þ @x
v
l + lt
w
l + lt
@ l þ lt @@xv þ @z@ l þ lt @w @x þ @y @x @ @ Sv ¼ @p l þ lt @u l þ lt @@yv þ @z@ l þ lt @w @y þ @x @y þ @y @y @ @ Sw ¼ @p l þ lt @u l þ lt @@zv þ @z@ l þ lt @w @z þ @x @z þ @y @z
t k
l/Pr + lt/rt l + lt/rk l + lt/re
St Sk ¼ qGk qe Se ¼ ke ðc1 qGk c2 qeÞ
e l
where Gk ¼ qt
@u2 @x
þ
2 @v @y
þ
@w2 @z
þ
@u @y
þ @@xv
2
þ
@u @z
þ @w @x
2
þ
@v @z
þ @w @y
l þ lt
@u
2 , lt = clqk2/e, cl = 0.09, c1 = 1.14, c2 = 1.92, rt = 0.85, re = 1.3, rk = 1.0.
3.2. Code validation
Fig. 10. Grids of air inlet angle 60°.
Fig. 11. Nusselt number comparison for the air inlet angle 45°.
In order to validate the reliability of the numerical simulation procedure, numerical simulations with different turbulence models, i.e., standard k-e turbulence model, RNG k-e turbulence model, realizable k-e turbulence model and SST k-x turbulence model, are carried out for the same operating conditions as in the experiments. Figs. 11 and 12 show the comparisons between the simulation results and the experimental results for the air inlet angle 45°. Compared with the experimental data, the mean relative deviations of the Nusselt number and f-factor with different turbulence models (in turn standard k-e turbulence model, RNG k-e turbulence model, realizable k-e turbulence model and SST k-x turbulence model) are 3.0% and 4.9%, 2.7% and 5.7%, 7.4% and 6.3%, and 9.1% and 10.2%, respectively. The simulation results of standard k-e turbulence model and RNG k-e turbulence model both have good agreements with the experimental results, but standard k-e turbulence model has the best performance, so the standard k-e
Fig. 12. f-factor comparison for the air inlet angle 45°.
8
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 13. Computed velocity fields at central cross section in the y-direction.
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
9
turbulence model with standard wall functions is adopted in this paper.
3.3. Air velocity distribution in the heat exchanger To analyze the effect of various air inlet angles on the air side heat transfer and flow friction characteristics of the finned oval tube heat exchanger, the computed velocity fields at central cross section in the y-direction are given in Fig. 13. The air mass flow rate for the four different air inlet angles is the same, and the inlet velocity for the air inlet angle 90° is 1.8 m/s. From Fig. 13, it can be seen that with the decrease of the air inlet angle, the uniformity of the air velocity field at central cross section in the y-direction becomes worse. Obviously, the air velocity distribution in the y-direction of the heat exchanger is uniform, it is not necessary to illustrate the velocity field in the y-direction, and the velocity field in the zdirection is the main focus in this paper. Figs. 14 and 15 show the average velocity distributions of the channels between two adjacent oval tubes at different air inlet angles in the z-direction. z/H = 0 and z/H = 1 stand for the lower part and the upper part of the heat exchanger respectively, and x/L = 0.25 and x/L = 0.75 stand for the central position of the first row and the second row of the heat exchanger respectively. From Figs. 14 and 15, it can be seen that the air velocity distribution of each channel in the zdirection is the most uniform at the air inlet angle 90°. When the inlet angle is smaller than 90°, the local resistance loss coefficient of the upper part of the heat exchanger is larger, and it makes the air flow distribution different in different channels of the heat exchanger. Therefore, for the same air mass flow rate, the lower part of the heat exchanger distributes more air flow and the upper part distributes less air flow, which leads to a bad uniformity of the air velocity distribution in the z-direction.
Fig. 15. Velocity distribution in the z-direction at x/lf = 0.75 for different air inlet angles.
3.4. Numerical simulation results and discussion The heat transfer and friction characteristics for various air inlet angles are shown in Figs. 16 and 17, where the Reynolds number is taken as the abscissa. In Fig. 16, the Nusselt number for the air inlet angle 45° is the highest among the four air inlet angles at the same Reynolds number. The air inlet angle 60° takes the second place, and the air inlet angle 30° is the lowest. These results agree with the experimental results.
Fig. 16. Nusselt number comparisons for different air inlet angles. (Numerical results).
Fig. 17. f-factor comparisons for different air inlet angles. (Numerical results).
Fig. 14. Velocity distribution in the z-direction at x/lf = 0.25 for different air inlet angles.
The reasons why some cases when the air inlet angle is less than 90° can enhance the heat transfer performance may be explained by the theory of field synergy [24–27]. The heat flux /w can be defined as follows [24]
10
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Z /w ¼ qcp
dl
Z ! U gradt dy ¼ qcp
0
dl 0
! U jgradtjcosady
! ! ! ! U ¼u i þv j þwk gradt ¼
@t ! @t ! @t ! i þ j þ k @x @y @z
ð25Þ ð26Þ ð27Þ
where a is the intersection angle between the velocity and temperature gradients. The field synergy principle indicates that reducing the intersection angle a is the basic mechanism to enhance convective heat transfer. The smaller the intersection angle, the better the synergy characteristics. The word ‘‘synergy” indicates the cooperative characteristics of different forces or actions which exist in the same transport process. This idea was extended from parabolic flow to elliptic flow in Ref. [25], and numerical verifications were provided in Ref. [26] showing that the existing convective heat transfer enhancement mechanisms could be unified under the field synergy principle. A comprehensive review of the recent studies of the field synergy principle was provided in [27]. According to [28], the volume average synergy angle am in the whole flow field can be defined as
1 ! B U gradt C a ¼ arccos@ ! A U jgradtj
hand, the uniformity of the air velocity distribution in the zdirection for the inlet angle 30° is much worse than that for the inlet angle 90°, and as the effect of the uniformity of the air flow distribution is the dominant part, it causes a worse overall heat transfer performance. Compared with the experimental results in the range of the studied Reynolds number, the maximum relative deviations of the Nusselt number for the air inlet angles 90°, 60°, 45° and 30° are 4.3%, 4.1%, 4.7%, and 5.1%, respectively. On the other hand, Fig. 17 shows that the f-factor for the air inlet angle 30° is the highest among the four air inlet angles at the same Reynolds number, while that for the air inlet angle 90° is the lowest. The reason can be explained as follows. The air flow resistance from the inlet to outlet of the heat exchanger is determined by the frictional resistance of the channel surfaces and the local resistance of the heat exchanger. With the decrease of the air inlet angle, the uniformity of the air flow distribution becomes worse. This causes the frictional resistance in the heat exchanger to be larger. The greater the change of the air flow direction is, the larger is the local resistance. The maximum relative deviations of the f-factor for air inlet angles 90°, 60°, 45° and 30° between experimental results and simulation results are 6.8%, 5.3%, 5.3%, and 5.4%, respectively.
0
RRR hdv am ¼ RRRV dv V
ð28Þ
ð29Þ
Fig. 18 presents the volume average synergy angle am against Reynolds number under different air inlet angles. When the air inlet flow direction is not orthogonal to the inlet surface of heat exchangers, it induces the volume average synergy angle am less than that for the air inlet angle 90°. Therefore, the heat transfer performance is increased. The overall heat transfer performance is also affected by the uniformity of the air flow distribution. The more uniform the air flow distribution is, the better is the heat transfer performance. From Figs. 14 and 15, it can be seen that the symmetry of the velocity distribution between two adjacent oval tubes for inlet angles 60° and 45° is less worse than that for the inlet angle 90°. However, under these conditions, the effect of decreasing the intersection angle plays the dominant part of the overall heat transfer performance, so the overall heat transfer characteristics for inlet angles 60° and 45° are better than that for the inlet angle 90°. On the other
Fig. 18. am comparisons for different air inlet angles.
4. Heat transfer performance comparison As mentioned above, the air inlet angle 45° provides the best heat transfer performance, and the air inlet angle 90° provides the smallest pressure drop. Attention is now turned to the relative heat transfer performance of the heat exchanger with the same mass flow rate for various air inlet angles. JF factor, which is a dimensionless number of the larger-the-better characteristics, related to the j-factor and f-factor is successfully used to evaluate the thermal hydraulic performance of the heat exchanger. Considering different heat transfer area, the JF factor is defined as follows [29]
JF ¼
j=jref ðf =f ref Þ
1=3
ð30Þ
where jref and fref are the j-factor and f-factor, respectively, of the air inlet angle 90°. The comparison results are shown in Fig. 19, where the Reynolds number is taken as the abscissa. It can be seen clearly that the air inlet angle 45° offers the best overall heat transfer performance, next is the air inlet angle 60°, while the air inlet angle 30° has the worst overall heat transfer performance. Compared
Fig. 19. JF factor comparisons for different air inlet angles.
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
with the air inlet angle 90° in the range of the studied Reynolds number, the average relative deviations of the JF factor of the air inlet angles 60°, 45° and 30° are 5.2%, 5.8%, and 18.3%, respectively.
[5]
[6]
5. Conclusions [7]
In this study, the influence of various air inlet angles on the heat transfer and flow friction characteristics of a 2-row plain finned oval tube heat exchanger was analyzed by experimental and numerical methods. The overall heat transfer performance was evaluated by the JF factor. The main conclusions are drawn as follows:
[8]
[9]
[10]
1. Air inlet angle 45° provided the best heat transfer performance, air inlet angle 90° provided the smallest pressure drop, while air inlet angle of 30° provided the worst heat transfer performance associated with the largest pressure drop. 2. The effect of air inlet angles on the performance of heat transfer and pressure drop was analyzed by a numerical method. With the decrease of the air inlet angle, the uniformity of the air velocity distribution in the z-direction became worse. The heat transfer characteristics at different air inlet angles were analyzed from the prospective of the field synergy principle and the effect of the air velocity distribution uniformity. 3. The overall heat transfer performance was evaluated by the JF factor for the same mass flow condition. The air inlet angle 45° offered the best overall heat transfer performance, followed by the air inlet angle 60°, while the air inlet angle 30° showed the worst overall heat transfer performance.
[11]
[12] [13]
[14]
[15]
[16]
[17]
[18]
Declaration of Competing Interest
[19]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[20]
Acknowledgment
[22]
This work is supported by National Nature Science Foundation of China (Grant No. 51774237) and The Youth Scientific Research and Innovation Team of Xi’an Shiyou University (No. 2019QNKYCXTD10). References [1] J.S. Leu, M.S. Liu, J.S. Liaw, et al., A numerical investigation of louvered fin-andtube heat exchangers having circular and oval tube configurations, Int. J. Heat Mass Transf. 44 (22) (2001) 4235–4243. [2] H. Han, Y.L. He, Y.S. Li, et al., A numerical study on compact enhanced fin-andtube heat exchangers with oval and circular tube configurations, Int. J. Heat Mass Transf. 65 (2013) 686–695. [3] A. Hasan, K. Siren, Performance investigation of plain circular and oval tube evaporatively cooled heat exchangers, Appl. Therm. Eng. 24 (5–6) (2004) 777– 790. [4] M. Zeeshan, S. Nath, D. Bhanja, Numerical study to predict optimal configuration of fin and tube compact heat exchanger with various tube
[21]
[23] [24] [25]
[26]
[27]
[28]
[29]
11
shapes and spatial arrangements, Energy Convers. Manage. 148 (2017) 737– 752. N. El Gharbi, A. Kheiri, M. El Ganaoui, et al., Numerical optimization of heat exchangers with circular and non-circular shapes, Case Stud. Therm. Eng. 6 (2015) 194–203. A. Gholami, M.A. Wahid, M.A. Mohammed, Thermal–hydraulic performance of fin-and-oval tube compact heat exchangers with innovative design of corrugated fin patterns, Int. J. Heat Mass Transf. 106 (2017) 573–592. B. Lotfi, B. Sundén, Q.W. Wang, An investigation of the thermo-hydraulic performance of the smooth wavy fin-and-elliptical tube heat exchangers utilizing new type vortex generators, Appl. Energy 162 (2016) 1282–1302. X.B. Zhao, G.H. Tang, X.W. Ma, et al., Numerical investigation of heat transfer and erosion characteristics for H-type finned oval tube with longitudinal vortex generators and dimples, Appl. Energy 127 (2014) 93–104. N.H. Kim, K.J. Lee, Y.B. Jeong, Airside performance of oval tube heat exchangers having sine wave fins under wet condition, Appl. Therm. Eng. 66 (1–2) (2014) 580–589. D. Diaz, A. Valencia, Heat transfer in an oval tube heat exchanger with different kinds of longitudinal vortex generators, Heat Transf. Res. 48 (18) (2017) 1707– 1725. X.B. Zhao, G.H. Tang, Y.T. Shi, et al., Experimental study of heat transfer and pressure drop for H-type finned oval tube with longitudinal vortex generators and dimples under flue gas, Heat Transf. Eng. 39 (7–8) (2018) 608–616. D.G. Kröger, Air-cooled Heat Exchangers and Cooling Towers, PennWell Corporation, Tulsa, Oklahoma, 2004. E.H. Ahmad, H.M. Badr, Mixed convection from an elliptic tube at different angles of attack placed in a fluctuating free stream, Heat Transf. Eng. 23 (5) (2002) 45–61. L.Z. Zhang, Flow maldistribution and thermal performance deterioration in a cross-flow air to air heat exchanger with plate-fin cores, Int. J. Heat Mass Transf. 52 (19–20) (2009) 4500–4509. Z.Y. Liu, H. Li, L. Shi, et al., Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers, Appl. Therm. Eng. 89 (2015) 356–364. S. Unger, M. Beyer, M. Arlit, et al., An experimental investigation on the air-side heat transfer and flow resistance of finned short oval tubes at different tube tilt angles, Int. J. Therm. Sci. 140 (2019) 225–237. X.P. Du, M. Zeng, Z.Y. Dong, et al., Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers, Exp. Therm Fluid Sci. 52 (2014) 146–155. X.P. Du, M. Zeng, Q.W. Wang, et al., Experimental investigation of heat transfer and resistance characteristics of a finned oval-tube heat exchanger with different air inlet angles, Heat Transf. Eng. 35 (6–8) (2014) 703–710. X.P. Du, Y.T. Yin, M. Zeng, et al., An experimental investigation on air-side performances of finned tube heat exchangers for indirect air-cooling tower, Therm. Sci. 18 (3) (2014) 863–874. V. Gnielinski, New equations for heat and mass transfer in the turbulent flow in pipes and channels, NASA STI/recon Tech. Rep. A 75 (1975) 8–16. T.E. Schmidt, Heat transfer calculations for extended surfaces, Refrig. Eng.. 57 (1949) 351–357. W.M. Kays, A.L. London, Compact Heat Exchangers, McGraw-Hill, New York, 1984. H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education, 2007. Z.Y. Guo, D.Y. Li, B.X. Wang, A novel concept for convective heat transfer enhancement, Int. J. Heat Mass Transf. 41 (14) (1998) 2221–2225. W.Q. Tao, Z.Y. Guo, B.X. Wang, Field synergy principle for enhancing convective heat transfer-its extension and numerical verifications, Int. J. Heat Mass Transf. 45 (18) (2002) 3849–3856. W.Q. Tao, Y.L. He, Q.W. Wang, et al., A unified analysis on enhancing convective heat transfer with field synergy principle, Int. J. Heat Mass Transf. 45 (24) (2002) 4871–4879. Z.Y. Guo, W.Q. Tao, R.K. Shah, The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer, Int. J. Heat Mass Transf. 48 (9) (2005) 1797–1807. L.H. Tang, W.X. Chu, N. Ahmed, et al., A new configuration of winglet longitudinal vortex generator to enhance heat transfer in a rectangular channel, Appl. Therm. Eng. 104 (2016) 74–84. 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, Int. J. Heat Mass Transf. 43 (14) (2000) 2529–2539.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Air inlet angle influence on the air-side heat transfer and flow friction characteristics of a finned oval tube heat exchanger Linghong Tang a,d, Xueping Du b, Jie Pan c, Bengt Sundén d,⇑ a
School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, China School of Electric Power Engineering, China University of Mining and Technology, Xuzhou 112226, China c School of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, China d Division of Heat Transfer, Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden b
a r t i c l e
i n f o
Article history: Received 12 June 2019 Received in revised form 4 August 2019 Accepted 5 September 2019
Keywords: Finned oval tube heat exchanger Air cooling Air inlet angle Heat transfer and flow friction characteristics
a b s t r a c t In this study, the influence of various air inlet angles on the heat transfer and flow friction characteristics of a 2-row plain finned oval tube heat exchanger is analyzed by experimental and numerical methods. The experimental results show that an air inlet angle 45° provides the best heat transfer performance, and an air inlet angle 90° provides the smallest pressure drop, while an air inlet angle 30° provides the worst heat transfer performance associated with the largest pressure drop. The 3-D numerical simulation results indicate that with the decrease of the air inlet angle, the uniformity of the air velocity distribution in the z-direction of the heat exchanger becomes worse. The heat transfer characteristics at different air inlet angles are analyzed from the prospective of the field synergy principle and the effect of the air velocity distribution uniformity. The overall heat transfer performance is also evaluated by the JF factor under the same air mass flow rate. The results show that the air inlet angle 45° offers the best overall heat transfer performance, next is the air inlet angle 60°, while the air inlet angle 30° has the worst overall heat transfer performance. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Finned tube heat exchangers are extensively employed in chemical engineering, refrigeration, and HVAC (heating, ventilation and air conditioning) applications such as compressor intercoolers, air-coolers and fan coils. Circular tubes are widely used in finned tube heat exchangers, but it has been proved that using finned oval tube can effectively improve the overall heat transfer performance on the fin side. During the past few years, there are many investigations on the heat transfer and flow friction performance of finned oval tube heat exchangers. Leu et al. [1] numerically studied the air side performance of finned tube heat exchangers having circular tube and oval tube. Compared with the circular tube configuration, a 10% decrease of heat transfer performance was observed and a 41% decrease of pressure drop was seen for the oval tube configuration at a fixed fin geometry. Han et al. [2] also numerically studied the heat transfer and flow friction characteristics of finned circular and oval tube heat exchangers. The results revealed that using the finned oval tube could not only reduce the flow resistance but also improve the heat transfer capacity of the heat ⇑ Corresponding author. E-mail address: [email protected] (B. Sundén). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118702 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
exchangers. Hasan et al. [3] experimentally studied the performance of circular and oval tube heat exchangers with plain fins. The results indicated that the average Colburn factor for the oval tube was 89% of that for the circular tube, while the average friction factor for the oval tube was 46% of that for the circular tube. Zeeshan et al. [4] numerically evaluated the thermal hydraulic performance of fin tube heat exchangers with circular, oval and flat tubes having inline and staggered arrangement. The results showed that the increase in heat transfer coefficient of the optimal oval tube shape was 14.0% at lower air side Reynolds number (Re = 400) and 5.0% at higher air side Reynolds number (Re = 900). Also, the pressure drop was reduced by 39.9% at higher Reynolds number (Re = 900) compared to the circular tube shape with the inline arrangement. El Gharbi et al. [5] numerically investigated the heat transfer and the pressure drop characteristics and effectiveness of a cross-flow heat exchanger employing a staggered tube bank with different tube shapes. Three studied geometries were considered, i.e., circular, elliptic and wind-shaped. The results showed that when Re > 15000, the circular tube shape was clearly worse than the other two geometries, and for Re > 23000, the elliptic shape was the best. Furthermore, there are some investigations on the heat transfer and flow friction performance for different fin patterns [6–11].
2
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Nomenclature A Ac Afr Ai Ao a b cp Dc di do Fs f fF H hi ho JF j Kc Ke k L l m Nu P1 Pt Pr Q q Re t ! U
area, m2 the minimum flow area, m2 the frontal area, m2 heat transfer area of water side, m2 total surface area of air side, m2 half of length of major axis, mm half of length of short axis, mm specific heat at constant pressure, J/(kgK) fin collar outside diameter, mm equivalent inside diameter of oval tube, mm equivalent outside diameter of oval tube, mm fin spacing, mm Darcy friction factor Fanning friction factor height of front area, mm heat transfer coefficient of water side, W/(m2K) heat transfer coefficient of air side, W/(m2K) JF factor Colburn factor the entrance loss coefficient the exit loss coefficient overall heat transfer coefficient, W/(m2K) tube length, mm fin length, mm mass flow rate, kg/s Nusselt number longitudinal pitch, mm transverse pitch, mm Prandtl number heat transfer rate, W volume flow rate, m3/h Reynolds number temperature, K velocity vector, m/s
In order to save space, it is necessary to arrange heat exchangers obliquely in many cases, and then the air inlet flow direction is not orthogonal to the inlet surface of heat exchangers. The air inlet flow direction has a major effect on the heat transfer and flow friction performance of the air-coolers. There are some related reports on the heat transfer and flow friction performance of various air inlet flow directions. As described by Kröger [12], the finned tube bundles in large air-cooled condensers might be sloped at some angles up to 60° with the horizontal in order to save land area. Ahmad and Badr [13] numerically studied the mixed convection from an oval tube at different attack angles placed in a fluctuating free stream. Their study revealed that increasing the inclination angle from 0° to 90° tended to enhance the vortex shedding and the heat transfer rate. Zhang [14] numerically and experimentally investigated the flow maldistribution and thermal performance deterioration in cross-flow air to air heat exchangers. Liu et al. [15] numerically studied the effect of the air inlet angle on the heat transfer coefficient and pressure drop of the plate-fin heat exchangers. The numerical results showed that the different flow fields of the two special air inlet angles caused different effects on the heat transfer coefficient and pressure drop. Unger et al. [16] experimentally studied the heat transfer and flow characteristics of finned oval tubes. The experimental results showed that as the tube tilt angle rose from 0° to 40°, both the Nusselt number and friction factor increased. In our previous papers [17–19], the performance of finned oval tube heat exchangers with different air inlet angles were experimentally studied, but the details about heat transfer and flow char-
u, v, w W x, y, z
x, y, z velocity components, m/s width of front area, mm Cartesian co-ordinates
Greek symbols Dp pressure drop, Pa Dtm logarithmic mean temperature difference, K a intersection angle between the velocity and temperature gradient, deg d thickness, mm g fin efficiency go surface efficiency h air inlet angle, deg thermal conductivity, W/(mK) k dynamic viscosity of fluid, kg/(ms) l density, kg/m3 q r contraction ratio of the fin array / heat flux, W/m2 w correction factor of temperature difference Subscripts a air f fin fr frontal area i inside in inlet m mean max maximum value out outlet ref reference value t oval tube w water
acteristics were not clarified. Therefore, in this paper, the overall performance and local detailed characteristics of a 2-row finned oval tube heat exchanger with different air inlet angles are studied by experimental and numerical methods.
2. Experimental results and discussion 2.1. Experimental system The experimental system consists of two separate loops, i.e., an air loop and a hot water loop, as shown in Fig. 1. The air loop is provided to blow air across the finned bundles of test core which is placed in the test section. Air is induced to the wind tunnel by a frequency modulation blower. Air flows in turn through the entrance, transition section, contraction section and straightening section before reaching the test core. The regulation and uniform distribution of air flow are achieved along these three sections between the entrance and test core. After being heated by hot water, air leaves the test core and then flows through the flow metering duct before being discharged to the environment. The air side condition is determined by the air inlet temperature before arriving at the test core, the change of the air temperature through the core, and the air pressure drop through the core. The air inlet temperature and the temperature difference between inlet and outlet through the test core are measured by two sets of multipoint T-type copper-constantan thermocouple grids. Each set contains twelve calibrated thermocouples with an accuracy of ±0.2 K.
3
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 1. Schematic diagram of the experimental system.
Meanwhile, the air velocity is measured by a Pitot-tube meter, which is located in the flow metering duct far downstream of the test core, and the air static pressure before and after the test core are surveyed by a U-tube water column manometer, whose precision is ±1%. The Pitot-tube meter is connected to two different range microbarometer (at small flow rates) or U-tube water column manometer (at large flow rates). The hot water loop is designed to provide hot water at a temperature of 333.15 K through the oval tubes of the test core. Hot water is generated by electric heating rods in a water tank and driven to the test core by a pump. The calibrated E-type armored thermocouples with an accuracy of ±0.1 K are used to measure the water temperature, and there are four thermocouples placed at the water inlet and outlet on each side, respectively. Furthermore, the water flow rate is tested by a turbine flowmeter with a precision of 0.2%. At the same time, the pressure drop and outlet static pressure on the water side is measured with two Rosemount pressure transmitters with a precision of 0.1%, respectively. Suitable data acquisition systems and data collectors are also used for data collection and storage. The transient temperatures of water and air, water pressure drop and water flowmeter signals in the present study are transformed and recorded by a real-time hybrid recorder (Keityley-2700) with a sample rate of 100 Hz. Much attention is paid to the heat balance to ensure that steady state of the test core exists before collecting the data in the experiments. To reduce the heat loss to the surroundings, the experimental test core is covered by a thick foam insulation. During the data-acquisition procedure, each measured value is read at least five times, starting reading data no less than 40 min later when a working condition is changed. The arithmetic mean value of the recorded data for a certain working condition is used for checking the heat balance between the energy gain Qa of the air and the energy loss Qw of the water. Then the data with the smallest thermal equilibrium error between air side and water side will be saved. In all tests, the thermal equilibrium between air side and water side is within 5%.
The test core is a 2-row plain finned oval tube heat exchanger, and the detailed geometrical parameters of the test core are tabulated in Table 1 and schematically shown in Fig. 2. All tubes and fins are made of carbon steel. The fins are connected to the oval tube by brazing, so the contact thermal resistance could be neglected. Heat transfer and flow friction characteristics of the finned oval tube heat exchanger with various air inlet angles (30°、45°、60° and 90°, as shown in Fig. 3) are experimentally investigated in this study. 2.2. Data reduction The main purpose of the data reduction is to determine the air side heat transfer and friction characteristics, Nusselt number (Nu) and friction factor (f) of the heat exchangers from the experimental data. There are recorded at steady-state conditions during each test run. An objective is to find out corresponding power-law correlations of Nu vs. Re, and f vs. Re for each case. The thermal properties of air and water are determined at the average value of the inlet and outlet temperatures of air and water, respectively. The water side heat transfer rate Qw is given as
Table 1 Geometric dimensions of the plain finned oval tube heat exchanger. Parameters
Symbol/unit
Values
Transverse tube pitch Longitudinal tube pitch Tube thickness Fin thickness Fin space Short axis of oval tube Major axis of oval tube Width of front area Height of front area
Pt/mm Pl/mm dt/mm df/mm Fs/mm 2b/mm 2a/mm W/mm H/mm
26.7 55 1.5 0.35 2.5 14 36 600 320
4
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 2. Schematic view of the 2-row plain finned oval tube heat exchanger.
Fig. 3. Four different air inlet angles.
Q w ¼ qw qw cp;w t w;in tw;out
ð1Þ
where qw is the volume flow rate of water, qw is the density of water, cp,w is the specific heat at constant pressure of water, tw,in is the inlet temperature of water, and tw,out is the outlet temperature of water. The air-side heat transfer rate Qa is given as
Q a ¼ ma cp;a ta;out ta;in
ð2Þ
where ma is the mass flow rate of air, cp,a is the specific heat at constant pressure of air, ta,in is the inlet temperature of air, and ta,out is the outlet temperature of air. The total heat transfer rate is defined as the average of the water side and air side heat transfer rates
Q ave ¼ ðQ w þ Q a Þ=2
ð3Þ
The overall heat transfer coefficient, k, is calculated from the following relationship
k ¼ Q av e =ðw Ao Dtm Þ
ð4Þ
where w is the correction factor of the temperature difference, Ao is the total heat transfer area of the air side, including the area of fins and base tubes, and Dtm is the logarithmic mean temperature difference. The overall heat transfer resistance can be defined as
1 1 1 do 1 ¼ þ ln þ kAo hi Ai 2pkL di ho go Ao
ð5Þ
The water side heat transfer coefficient, hi, is evaluated from the Gnielinski’s formula [20]
" 2=3 # 0:11 kw ðf i =8Þ Redi 1000 Prw d Prw 1þ i hi ¼ pffiffiffiffiffiffiffiffiffi 2=3 di 1 þ 12:7 f =8 Pr 1 L Prw;t i w fi can be calculated as follows
ð6Þ
2 f i ¼ 1:82lgRedi 1:64
ð7Þ
The equivalent diameters for the oval tube, do and di, are given as follows
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 do ¼ 4ab= 2 a2 þ b
ð8Þ
di ¼ do 2dt
ð9Þ
where a is half of the length of major axis, and b is half of the length of short axis. In Eq. (5), go is the surface efficiency, which may be written in terms of the fin efficiency gf, fin surface area Af and total surface area Ao, as follows
go ¼ 1
Af ð1 gf Þ Ao
ð10Þ
gf denotes the fin efficiency and is calculated by the approximative method described by Schmidt [21]
gf ¼
tanhðmHÞ mH
ð11Þ
where
sffiffiffiffiffiffiffiffi 2ho m¼ kf df
ð12Þ
H ¼ Rc /
ð13Þ
Rc ¼ do =2
ð14Þ
/¼
Req Req 1 1 þ 0:35ln Rc Rc
ð15Þ
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
0:5 Req XM XL ¼ 1:27 0:3 Rc Rc XM
XL ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðPt =2Þ2 þ P 2l
ð16Þ
5
area Afr. Dc is the fin collar outside diameter, Dc = do + 2df. According to Kays and London [22], the entrance and exit loss coefficients Kc and Ke are 0.4 and 0.2. The uncertainties of Nusselt number and friction factor of the air side are 5.2% and 7.3%, respectively.
ð17Þ
2
2.3. Heat transfer and pressure drop comparisons
X M ¼ Pt =2
ð18Þ
where Pt is the transverse tube pitch, and Pl is the longitudinal tube pitch. It can be seen that the calculation formulas of gf include the air side heat transfer coefficient ho in above Eqs. (11) and (12), but both of them are unknown. They can be acquired by solving Eqs. (5) and (10)–(18) with an iterative method. The iteration process for calculating gf is shown in Fig. 4. The heat transfer and friction characteristics of the heat exchanger are presented in the following dimensionless forms.
Nu ¼ ho Dc =ka
ð19Þ
ReDc ¼ qa umax Dc =la
ð20Þ
j ¼ Nu= ReDc Pr1=3
ð21Þ
" Ac qm 2qin Dp qin 2 K þ 1 r 1 2 fF ¼ c Ao qin ðqin uin Þ2 qout
qin þ 1 r2 K e
ð22Þ
f ¼ 4f F
ð23Þ
qout
Figs. 5 and 6 show the variations of ho and Nu for various air inlet angles of the finned oval tube heat exchanger. From Figs. 5 and 6, it can be seen that the heat transfer performance increases with increasing air frontal velocity (or Reynolds number). The heat transfer coefficient and Nusselt number for the air inlet angle 45° are the highest among the four different air inlet angles. Those of the air inlet angle 60° take the second place, while those of the air inlet angle 30° are the lowest. Compared with the air inlet angle 90°, the average Nusselt numbers of the air inlet angle 60°, 45° and 30° increase 5.6%, 8.0% and 12.5% in the range of the studied Reynolds number, respectively. Figs. 7 and 8 illustrate the effect of the air inlet angles on the friction characteristics of the finned oval tube heat exchanger. From Figs. 7 and 8, the pressure drop and friction factor of the air inlet angle 30° are the highest among the four different air inlet angles. Those of the air inlet angle 45° take the second place, and
where umax is the velocity at the minimum free flow area, umax = ufr/
r. The term r is the ratio of the minimum flow area Ac to the frontal
Fig. 5. Heat transfer coefficient comparisons for different air inlet angles.
Fig. 4. Calculation process of gf.
Fig. 6. Nusselt number comparisons for different air inlet angles.
6
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
and local detailed characteristics can be obtained by numerical simulations. Such an approach is more conducive to study the heat transfer and flow characteristics of the finned oval tube heat exchanger at different air inlet angles. A schematic diagram of the physical model is shown in Fig. 9. The actual length of the computational domain is 7.5 times of the fin length. This means that the domain is extended 1.5 times of the fin length at the entrance section to ensure the inlet uniformity, and at the exit, the domain is extended 5 times of the fin length in order to make sure that the exit flow boundary has no flow recirculation. The governing equations for continuity, momentum and energy may be expressed in vectorial notation as
!
r q U / ¼ r C / r / þ S/
Fig. 7. Pressure drop comparisons for different air inlet angles.
Fig. 8. f-factor comparisons for different air inlet angles.
those of the air inlet angle 90° are the lowest. Compared with the air inlet angle 90°, the average f-factors of the air inlet angle 60°, 45° and 30° increase 4.7%, 10.0% and 28.0% in the range of the studied Reynolds number, respectively. Based on the experimental data, correlations of Nusselt number and f-factor are given in Table 2. 3. Numerical simulation results and discussion 3.1. Physical and mathematic model The above experimental data generally reflect the overall performance of the finned oval tube heat exchanger, but it is difficult to obtain the local characteristics. Both the overall performance
ð24Þ
In the above equation, the dependent variable, /, stands for the velocity components, temperature, k and e. The terms C/ and S/ represent the appropriate diffusion coefficients and the source terms, respectively. The particular expressions for /, C/ and S/ are summarized in Table 3. Because the governing equations are elliptic in spatial coordinates, boundary conditions are required for all boundaries of the computational domain. At the inlet boundary, the flow velocity uin is assumed to be uniform, and the temperature tin is taken to 293.15 K. At the downstream end of the computational domain, streamwise gradients (Neumann boundary conditions) of all the variables are set to zero. On the solid surfaces (tube, fin), no-slip conditions are used and a uniform tube inside-wall temperature tw are specified as 333.15 K, and the temperature distribution in the tube outside-wall will be determined by solving the conjugated heat transfer problem between air and tube in the computational domain. The commercial code ANSYS FLUENT 14.0 is used for the numerical solution of the Navier-Stokes and energy equations. A preprocessor Gambit 2.4 is used to mesh the computational domain for the solver. The grids for the air inlet angle 60° are shown in Fig. 10. FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This procedure involves subdividing the region in which the flow is to be solved into individual cells or control volumes so that the equations can be integrated numerically on a cell-by-cell basis to produce discrete algebraic (finite volume) equations. The air flow is assumed to be incompressible ideal gas, turbulent, quasi-steady, 3-D and exhibiting no viscous dissipation. All variables, including velocity components, pressure and temperature, are averaged for a control volume. The coupling between pressure and velocity is implemented by the SIMPLEC algorithm. The QUICK scheme is used for the spacial discretization of the momentum, turbulent kinetic energy, turbulent dissipation rate and energy equations in the simulations. The residuals are less than 10-4 and 10-8 for the continuity and energy equations, respectively, to ensure convergence of the computations. After validating the solution independency of the grid number, about 35,000,000 mesh element number is selected as a reference mesh size for different air inlet angles in this paper.
Table 2 Correlations of Nusselt number and f-factor. Inletangle
Nu = f(Re)
Maximumrelative error
f = f(Re)
Maximum relative error
90° 60° 45° 30°
Nu = 2.128Re0.402 Dc Nu = 2.183Re0.405 Dc Nu = 2.159Re0.409 Dc 0.608 Nu = 0.314ReDc
1.4% 1.6% 1.3% 2.0%
f = 37.239Re-0.481 Dc f = 19.893Re-0.403 Dc f = 16.936Re-0.379 Dc f = 131.583Re-0.597 Dc
1.1% 1.5% 1.4% 2.3%
7
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Table 3 Expressions for /, C/ and S/ [23]. /
C/
S/
1 u
0
0
l + lt
@ Su ¼ @p @x þ @x
v
l + lt
w
l + lt
@ l þ lt @@xv þ @z@ l þ lt @w @x þ @y @x @ @ Sv ¼ @p l þ lt @u l þ lt @@yv þ @z@ l þ lt @w @y þ @x @y þ @y @y @ @ Sw ¼ @p l þ lt @u l þ lt @@zv þ @z@ l þ lt @w @z þ @x @z þ @y @z
t k
l/Pr + lt/rt l + lt/rk l + lt/re
St Sk ¼ qGk qe Se ¼ ke ðc1 qGk c2 qeÞ
e l
where Gk ¼ qt
@u2 @x
þ
2 @v @y
þ
@w2 @z
þ
@u @y
þ @@xv
2
þ
@u @z
þ @w @x
2
þ
@v @z
þ @w @y
l þ lt
@u
2 , lt = clqk2/e, cl = 0.09, c1 = 1.14, c2 = 1.92, rt = 0.85, re = 1.3, rk = 1.0.
3.2. Code validation
Fig. 10. Grids of air inlet angle 60°.
Fig. 11. Nusselt number comparison for the air inlet angle 45°.
In order to validate the reliability of the numerical simulation procedure, numerical simulations with different turbulence models, i.e., standard k-e turbulence model, RNG k-e turbulence model, realizable k-e turbulence model and SST k-x turbulence model, are carried out for the same operating conditions as in the experiments. Figs. 11 and 12 show the comparisons between the simulation results and the experimental results for the air inlet angle 45°. Compared with the experimental data, the mean relative deviations of the Nusselt number and f-factor with different turbulence models (in turn standard k-e turbulence model, RNG k-e turbulence model, realizable k-e turbulence model and SST k-x turbulence model) are 3.0% and 4.9%, 2.7% and 5.7%, 7.4% and 6.3%, and 9.1% and 10.2%, respectively. The simulation results of standard k-e turbulence model and RNG k-e turbulence model both have good agreements with the experimental results, but standard k-e turbulence model has the best performance, so the standard k-e
Fig. 12. f-factor comparison for the air inlet angle 45°.
8
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Fig. 13. Computed velocity fields at central cross section in the y-direction.
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
9
turbulence model with standard wall functions is adopted in this paper.
3.3. Air velocity distribution in the heat exchanger To analyze the effect of various air inlet angles on the air side heat transfer and flow friction characteristics of the finned oval tube heat exchanger, the computed velocity fields at central cross section in the y-direction are given in Fig. 13. The air mass flow rate for the four different air inlet angles is the same, and the inlet velocity for the air inlet angle 90° is 1.8 m/s. From Fig. 13, it can be seen that with the decrease of the air inlet angle, the uniformity of the air velocity field at central cross section in the y-direction becomes worse. Obviously, the air velocity distribution in the y-direction of the heat exchanger is uniform, it is not necessary to illustrate the velocity field in the y-direction, and the velocity field in the zdirection is the main focus in this paper. Figs. 14 and 15 show the average velocity distributions of the channels between two adjacent oval tubes at different air inlet angles in the z-direction. z/H = 0 and z/H = 1 stand for the lower part and the upper part of the heat exchanger respectively, and x/L = 0.25 and x/L = 0.75 stand for the central position of the first row and the second row of the heat exchanger respectively. From Figs. 14 and 15, it can be seen that the air velocity distribution of each channel in the zdirection is the most uniform at the air inlet angle 90°. When the inlet angle is smaller than 90°, the local resistance loss coefficient of the upper part of the heat exchanger is larger, and it makes the air flow distribution different in different channels of the heat exchanger. Therefore, for the same air mass flow rate, the lower part of the heat exchanger distributes more air flow and the upper part distributes less air flow, which leads to a bad uniformity of the air velocity distribution in the z-direction.
Fig. 15. Velocity distribution in the z-direction at x/lf = 0.75 for different air inlet angles.
3.4. Numerical simulation results and discussion The heat transfer and friction characteristics for various air inlet angles are shown in Figs. 16 and 17, where the Reynolds number is taken as the abscissa. In Fig. 16, the Nusselt number for the air inlet angle 45° is the highest among the four air inlet angles at the same Reynolds number. The air inlet angle 60° takes the second place, and the air inlet angle 30° is the lowest. These results agree with the experimental results.
Fig. 16. Nusselt number comparisons for different air inlet angles. (Numerical results).
Fig. 17. f-factor comparisons for different air inlet angles. (Numerical results).
Fig. 14. Velocity distribution in the z-direction at x/lf = 0.25 for different air inlet angles.
The reasons why some cases when the air inlet angle is less than 90° can enhance the heat transfer performance may be explained by the theory of field synergy [24–27]. The heat flux /w can be defined as follows [24]
10
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
Z /w ¼ qcp
dl
Z ! U gradt dy ¼ qcp
0
dl 0
! U jgradtjcosady
! ! ! ! U ¼u i þv j þwk gradt ¼
@t ! @t ! @t ! i þ j þ k @x @y @z
ð25Þ ð26Þ ð27Þ
where a is the intersection angle between the velocity and temperature gradients. The field synergy principle indicates that reducing the intersection angle a is the basic mechanism to enhance convective heat transfer. The smaller the intersection angle, the better the synergy characteristics. The word ‘‘synergy” indicates the cooperative characteristics of different forces or actions which exist in the same transport process. This idea was extended from parabolic flow to elliptic flow in Ref. [25], and numerical verifications were provided in Ref. [26] showing that the existing convective heat transfer enhancement mechanisms could be unified under the field synergy principle. A comprehensive review of the recent studies of the field synergy principle was provided in [27]. According to [28], the volume average synergy angle am in the whole flow field can be defined as
1 ! B U gradt C a ¼ arccos@ ! A U jgradtj
hand, the uniformity of the air velocity distribution in the zdirection for the inlet angle 30° is much worse than that for the inlet angle 90°, and as the effect of the uniformity of the air flow distribution is the dominant part, it causes a worse overall heat transfer performance. Compared with the experimental results in the range of the studied Reynolds number, the maximum relative deviations of the Nusselt number for the air inlet angles 90°, 60°, 45° and 30° are 4.3%, 4.1%, 4.7%, and 5.1%, respectively. On the other hand, Fig. 17 shows that the f-factor for the air inlet angle 30° is the highest among the four air inlet angles at the same Reynolds number, while that for the air inlet angle 90° is the lowest. The reason can be explained as follows. The air flow resistance from the inlet to outlet of the heat exchanger is determined by the frictional resistance of the channel surfaces and the local resistance of the heat exchanger. With the decrease of the air inlet angle, the uniformity of the air flow distribution becomes worse. This causes the frictional resistance in the heat exchanger to be larger. The greater the change of the air flow direction is, the larger is the local resistance. The maximum relative deviations of the f-factor for air inlet angles 90°, 60°, 45° and 30° between experimental results and simulation results are 6.8%, 5.3%, 5.3%, and 5.4%, respectively.
0
RRR hdv am ¼ RRRV dv V
ð28Þ
ð29Þ
Fig. 18 presents the volume average synergy angle am against Reynolds number under different air inlet angles. When the air inlet flow direction is not orthogonal to the inlet surface of heat exchangers, it induces the volume average synergy angle am less than that for the air inlet angle 90°. Therefore, the heat transfer performance is increased. The overall heat transfer performance is also affected by the uniformity of the air flow distribution. The more uniform the air flow distribution is, the better is the heat transfer performance. From Figs. 14 and 15, it can be seen that the symmetry of the velocity distribution between two adjacent oval tubes for inlet angles 60° and 45° is less worse than that for the inlet angle 90°. However, under these conditions, the effect of decreasing the intersection angle plays the dominant part of the overall heat transfer performance, so the overall heat transfer characteristics for inlet angles 60° and 45° are better than that for the inlet angle 90°. On the other
Fig. 18. am comparisons for different air inlet angles.
4. Heat transfer performance comparison As mentioned above, the air inlet angle 45° provides the best heat transfer performance, and the air inlet angle 90° provides the smallest pressure drop. Attention is now turned to the relative heat transfer performance of the heat exchanger with the same mass flow rate for various air inlet angles. JF factor, which is a dimensionless number of the larger-the-better characteristics, related to the j-factor and f-factor is successfully used to evaluate the thermal hydraulic performance of the heat exchanger. Considering different heat transfer area, the JF factor is defined as follows [29]
JF ¼
j=jref ðf =f ref Þ
1=3
ð30Þ
where jref and fref are the j-factor and f-factor, respectively, of the air inlet angle 90°. The comparison results are shown in Fig. 19, where the Reynolds number is taken as the abscissa. It can be seen clearly that the air inlet angle 45° offers the best overall heat transfer performance, next is the air inlet angle 60°, while the air inlet angle 30° has the worst overall heat transfer performance. Compared
Fig. 19. JF factor comparisons for different air inlet angles.
L. Tang et al. / International Journal of Heat and Mass Transfer 145 (2019) 118702
with the air inlet angle 90° in the range of the studied Reynolds number, the average relative deviations of the JF factor of the air inlet angles 60°, 45° and 30° are 5.2%, 5.8%, and 18.3%, respectively.
[5]
[6]
5. Conclusions [7]
In this study, the influence of various air inlet angles on the heat transfer and flow friction characteristics of a 2-row plain finned oval tube heat exchanger was analyzed by experimental and numerical methods. The overall heat transfer performance was evaluated by the JF factor. The main conclusions are drawn as follows:
[8]
[9]
[10]
1. Air inlet angle 45° provided the best heat transfer performance, air inlet angle 90° provided the smallest pressure drop, while air inlet angle of 30° provided the worst heat transfer performance associated with the largest pressure drop. 2. The effect of air inlet angles on the performance of heat transfer and pressure drop was analyzed by a numerical method. With the decrease of the air inlet angle, the uniformity of the air velocity distribution in the z-direction became worse. The heat transfer characteristics at different air inlet angles were analyzed from the prospective of the field synergy principle and the effect of the air velocity distribution uniformity. 3. The overall heat transfer performance was evaluated by the JF factor for the same mass flow condition. The air inlet angle 45° offered the best overall heat transfer performance, followed by the air inlet angle 60°, while the air inlet angle 30° showed the worst overall heat transfer performance.
[11]
[12] [13]
[14]
[15]
[16]
[17]
[18]
Declaration of Competing Interest
[19]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[20]
Acknowledgment
[22]
This work is supported by National Nature Science Foundation of China (Grant No. 51774237) and The Youth Scientific Research and Innovation Team of Xi’an Shiyou University (No. 2019QNKYCXTD10). References [1] J.S. Leu, M.S. Liu, J.S. Liaw, et al., A numerical investigation of louvered fin-andtube heat exchangers having circular and oval tube configurations, Int. J. Heat Mass Transf. 44 (22) (2001) 4235–4243. [2] H. Han, Y.L. He, Y.S. Li, et al., A numerical study on compact enhanced fin-andtube heat exchangers with oval and circular tube configurations, Int. J. Heat Mass Transf. 65 (2013) 686–695. [3] A. Hasan, K. Siren, Performance investigation of plain circular and oval tube evaporatively cooled heat exchangers, Appl. Therm. Eng. 24 (5–6) (2004) 777– 790. [4] M. Zeeshan, S. Nath, D. Bhanja, Numerical study to predict optimal configuration of fin and tube compact heat exchanger with various tube
[21]
[23] [24] [25]
[26]
[27]
[28]
[29]
11
shapes and spatial arrangements, Energy Convers. Manage. 148 (2017) 737– 752. N. El Gharbi, A. Kheiri, M. El Ganaoui, et al., Numerical optimization of heat exchangers with circular and non-circular shapes, Case Stud. Therm. Eng. 6 (2015) 194–203. A. Gholami, M.A. Wahid, M.A. Mohammed, Thermal–hydraulic performance of fin-and-oval tube compact heat exchangers with innovative design of corrugated fin patterns, Int. J. Heat Mass Transf. 106 (2017) 573–592. B. Lotfi, B. Sundén, Q.W. Wang, An investigation of the thermo-hydraulic performance of the smooth wavy fin-and-elliptical tube heat exchangers utilizing new type vortex generators, Appl. Energy 162 (2016) 1282–1302. X.B. Zhao, G.H. Tang, X.W. Ma, et al., Numerical investigation of heat transfer and erosion characteristics for H-type finned oval tube with longitudinal vortex generators and dimples, Appl. Energy 127 (2014) 93–104. N.H. Kim, K.J. Lee, Y.B. Jeong, Airside performance of oval tube heat exchangers having sine wave fins under wet condition, Appl. Therm. Eng. 66 (1–2) (2014) 580–589. D. Diaz, A. Valencia, Heat transfer in an oval tube heat exchanger with different kinds of longitudinal vortex generators, Heat Transf. Res. 48 (18) (2017) 1707– 1725. X.B. Zhao, G.H. Tang, Y.T. Shi, et al., Experimental study of heat transfer and pressure drop for H-type finned oval tube with longitudinal vortex generators and dimples under flue gas, Heat Transf. Eng. 39 (7–8) (2018) 608–616. D.G. Kröger, Air-cooled Heat Exchangers and Cooling Towers, PennWell Corporation, Tulsa, Oklahoma, 2004. E.H. Ahmad, H.M. Badr, Mixed convection from an elliptic tube at different angles of attack placed in a fluctuating free stream, Heat Transf. Eng. 23 (5) (2002) 45–61. L.Z. Zhang, Flow maldistribution and thermal performance deterioration in a cross-flow air to air heat exchanger with plate-fin cores, Int. J. Heat Mass Transf. 52 (19–20) (2009) 4500–4509. Z.Y. Liu, H. Li, L. Shi, et al., Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers, Appl. Therm. Eng. 89 (2015) 356–364. S. Unger, M. Beyer, M. Arlit, et al., An experimental investigation on the air-side heat transfer and flow resistance of finned short oval tubes at different tube tilt angles, Int. J. Therm. Sci. 140 (2019) 225–237. X.P. Du, M. Zeng, Z.Y. Dong, et al., Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers, Exp. Therm Fluid Sci. 52 (2014) 146–155. X.P. Du, M. Zeng, Q.W. Wang, et al., Experimental investigation of heat transfer and resistance characteristics of a finned oval-tube heat exchanger with different air inlet angles, Heat Transf. Eng. 35 (6–8) (2014) 703–710. X.P. Du, Y.T. Yin, M. Zeng, et al., An experimental investigation on air-side performances of finned tube heat exchangers for indirect air-cooling tower, Therm. Sci. 18 (3) (2014) 863–874. V. Gnielinski, New equations for heat and mass transfer in the turbulent flow in pipes and channels, NASA STI/recon Tech. Rep. A 75 (1975) 8–16. T.E. Schmidt, Heat transfer calculations for extended surfaces, Refrig. Eng.. 57 (1949) 351–357. W.M. Kays, A.L. London, Compact Heat Exchangers, McGraw-Hill, New York, 1984. H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education, 2007. Z.Y. Guo, D.Y. Li, B.X. Wang, A novel concept for convective heat transfer enhancement, Int. J. Heat Mass Transf. 41 (14) (1998) 2221–2225. W.Q. Tao, Z.Y. Guo, B.X. Wang, Field synergy principle for enhancing convective heat transfer-its extension and numerical verifications, Int. J. Heat Mass Transf. 45 (18) (2002) 3849–3856. W.Q. Tao, Y.L. He, Q.W. Wang, et al., A unified analysis on enhancing convective heat transfer with field synergy principle, Int. J. Heat Mass Transf. 45 (24) (2002) 4871–4879. Z.Y. Guo, W.Q. Tao, R.K. Shah, The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer, Int. J. Heat Mass Transf. 48 (9) (2005) 1797–1807. L.H. Tang, W.X. Chu, N. Ahmed, et al., A new configuration of winglet longitudinal vortex generator to enhance heat transfer in a rectangular channel, Appl. Therm. Eng. 104 (2016) 74–84. 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, Int. J. Heat Mass Transf. 43 (14) (2000) 2529–2539.