Numerical study on the heat transfer enhancement and pressure drop inside deep dimpled tubes

International Journal of Heat and Mass Transfer 147 (2020) 118845

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Numerical study on the heat transfer enhancement and pressure drop inside deep dimpled tubes Mohammad Hassan Cheraghi, Mohammad Ameri ⇑, Mohammad Shahabadi Energy Conversion Department, Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 16 April 2019 Received in revised form 8 September 2019 Accepted 5 October 2019

a b s t r a c t Heat transfer enhancement is important from the industry point of view. In this study, a new configuration of enhanced tubes has been investigated numerically. The geometry of this new type of tube was provided by exerting deep dimples on the conventional plain tube. Flow-field and heat transfer characteristics of deep dimpled tubes have been studied, and the effects of the various configuration of dimples comprising three different pitches, diameters, and depths of dimples resulting in twenty-seven configurations have been investigated. Performance Evaluation Criteria (PEC), which is commonly used in heat transfer enhancement subjects, has been studied for all geometries. Local temperature, velocity, streamline, and Nusselt number of the deep dimpled tube have been depicted in comparison to the plain tube to study thermo-fluid characteristics. The investigation for each configuration has been done in three different Reynolds numbers: Re = 500, 1000 and 2000, and k-e turbulent model has been utilized in numerical studies. The higher heat transfer rate of deep dimpled tubes has been seen in higher depth and diameter and lower pitch up to 600%, while this lead to the intense growth of friction factor. It has been observed that PEC of the deep dimpled tubes generally varies from PEC = 1.15–3.3 in different cases. Furthermore, increase in the diameter, pitch and Reynolds number, and decrease in the depth, lead to augmentation of PEC of deep dimpled tubes which escalates up to PEC = 3.3 at Re = 2000 when Diameter = 18 mm, depth = 2 mm, and pitch = 4D. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The application of heat exchangers has increased these days. They are widely used in cooling and heating systems such as air conditions, refrigerators, and microturbines [1]. To improve the efficiency of heat exchangers, passive methods have been used widely due to lower costs and needless to the external power supply. The passive method applies special geometry to improve heat transfer performances. Using tube-side artificial roughness on the tube surface is a new passive enhancement technique which significantly increases the rate of heat transfer in comparison to plain tubes, and it comprises two methods: - Two-dimensional roughness such as spirally corrugated, transverse and spirally fins and wire coils spins. - Three-dimensional roughness such as sand-grain roughness, spoon type spirally corrugated, and dimples [2]. The main reason for increment of heat transfer within the dimpled tube is the inhibition of thermal boundary layer formation ⇑ Corresponding author. E-mail address: [email protected] (M. Ameri). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118845 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

and the excessed heat transfer for extended surface of dimples. It has been seen that conventional dimpled tubes would cause lowpressure drop which is desirable in industrial applications, so the research on this area has rapidly extended during past years. Also, for the same heat transfer rate, this type of tube reduces the space of which the heat exchanger occupies, and decreases the weight and amount of initial material in the manufacturing process of heat exchangers. Therefore, it would be cost-efficient from an industrial point of view. Vicente et al. [3] studied experimentally low Reynolds turbulent flow (2000 < Re < 10,000) in helically dimpled tubes by using water and ethylene glycol as the test fluid and ten different configurations of tubes with various depths and pitches of dimples. The result of this study showed that as the depth of dimples increased, the performance of the tube improved. Vicente et al. [4] investigated heat transfer and friction factor in corrugated tubes. Barba et al. [5] experimented heat transfer and pressure drop of a corrugated tube in a laminar flow ranging 100 < Re < 800 and demonstrated that both heat transfer and pressure drop of the corrugated tube were around twice the plain one. Fan et al. [6] numerically studied the effects of geometrical parameters on heat transfer and pressure loss inside a dimpled tube. The results showed that the reduction in the pitch of dimples and increase in their depth contributed to the heat transfer

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Nomenclature A Cp D Dh D F K P Q Pr _ m DP P Nu Re T

heat transfer area special heat, J kg
1 K
1 dimple depth, mm equivalent diameter, mm dimple diameter, mm friction factor thermal conductivity, Wm
1 K
1 dimple pitch, mm heat transfer Prandtl number mass flow rate, kg s
1 pressure drop, Pa pressure, Pa Nusselt number Reynolds number temperature, K

enhancement. However, these variations increased the pressure loss of the enhanced tube. Wang et al. [2] experimentally investigated the heat transfer enhancement and friction factor of ellipsoidal, spherical, and conventional smooth tubes. Experimental data demonstrated that tubes with ellipsoidal dimples simultaneously had higher Nusselt number and lower friction factor in comparison to the tubes with spherical dimples, and ellipsoidal dimples roughness accelerated the transition to critical Reynolds number down to less than 1000. Li et al. [7] carried out experimental and numerical studies to determine the Nusselt number and friction factor in a pipe-in-pipe heat exchanger. The range of Reynolds number for water as the working fluid was 500 < Re < 8000, while for water/glycol fluid was 150 < Re < 2000. They proposed correlations to estimate the Nusselt number and friction factor. The best performance (PEC = 1.55) was obtained at Reynolds number 3500–4500 for water, while Glycol/water solution showed higher PEC in Reynolds number range 150–2000. Kumar et al. [8] experimentally studied the impact of inserted protruded shape shit metal attached to the internal surface of the tube on the heat transfer enhancement. The investigation was done in Reynolds range of (6000 < Re < 35,000). The results indicated the heat transfer rate was around 3.5 times more than the plain tube. Also, the statistical correlations for Nusselt number and friction factor as a function of flow and roughness parameters were developed by experimental data. Shafaee et al. [9–11] in three distinguished papers, experimentally investigated heat transfer and pressure drop of hydrocarbon refrigerant R-600a in two-phase mode inside a helically dimpled tube and a smooth tube. Their experimental results showed that the heat transfer coefficient of the dimpled tube was 1.29–2 times more than a smooth tube, and the pressure-loss ranging 7–103% of a smooth tube. Also, they found out that dimples had considerable effects on the two-phase flow pattern. Liang et al. [12] numerically investigated flow field and heat transfer characteristics of an ellipsoidal protruded tube. The effects of changes in the configuration of protrusions such as depth, pitch, number, and angle on the thermal-hydraulic performance were survived. The results showed that the minimum local pressure was at the center of the protrusion surface, and the maximum Nusselt number was at its leading edge. Rezaei et al. [13] numerically investigated the effects of the semi-attached ribs and Al2O3 nanoparticles on the heat transfer and the flow field inside a microchannel with triangular section. The results indicated that the increase of Reynolds number led to the increment of Nusselt number. Also, adding the nanoparticles increased the heat transfer,

V T V u yþ

q

m e i s max o p ref t w

velocity, m s
3 temperature, K velocity, m s
3 friction velocity mesh resolution indicator fluid density, kg m
3 dynamic viscosity, Pa s enhanced tube tube inlet internal surface maximum tube outlet plain tube reference turbulent water

and it was more influential for higher Reynolds numbers. Pourfattah and et al. [14] numerically studied the impact of the attacking angel of ribs and nanoparticles on the heat transfer and flow characteristics of the turbulent flow. The results showed that the best fluid-thermal performance was applied when the rib attack angel was 60°. Mashayekhi et al. [15] conducted numerical studies to investigate the application of twisted conical strip inserts in two staggered and non-staggered alignments to improve the efficiency of water-Ag nanofluid. Their results revealed that the heat transfer rate in non-staggered alignment was higher than the staggered one. Also, the velocity distribution and temperature were more uniform for the non-staggered alignment. A few studies have been done to investigate the heat transfer characteristics of nanofluids for various conditions [16–20]. The impacts of the surface roughness on the boiling behavior of Argon inside different microchannels utilizing molecular dynamic methods were surveyed by Zarringhalam et al. [21]. Toghraie et al. [22] studied numerically the thermo-fluid characteristics of three different microchannel configurations: smooth, sinusoidal, and zigzag-shaped, including and not including nanofluid. They found that the decrease in the sinusoidal and zigzag-shaped microchannel wavelength led to the increment of the Nusselt number. Also, it was deduced that the zigzag-shaped microchannel was better than the sinusoidal one. Moraveji and Toghraie [23] performed numerical investigations to survey the effects of different numbers of the inlet, tube lengths, and cold outlet on the volumetric flow rate and temperature of a vortex tube. Rao and et al. [24] performed the experimental and numerical studies to investigate the impacts of dimple shapes on the thermofluid characteristics of turbulent flows. Four different shapes of dimples: spherical, teardrop, elliptical, and inclined elliptical were studied. They stated that the teardrop dimples had the highest heat transfer rate, around 18% higher than conventional spherical dimples, while elliptical dimples had the lowest heat transfer rate, around 10% lower than spherical. All the experiments showed that dimpled channels had a significant heat transfer enhancement compared to conventional channels. Rao et al. [25] carried out experiments to survey the effects of dimple depth on the pressure loss and the heat transfer of the pin-fin dimpled channel. They presented that the pin-fin dimpled channel improved convective heat transfer up to 19% compared with pinfin channel, and this channel with deeper dimples showed higher Nusselt number. Also, they found out that the fin pin-dimple channels with shallower dimples had lower friction factors up to 17.6%. Finally, the three-dimensional numerical simulations were

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conducted based on experimental conditions. Aroonrat and Wongwise [26–28] experimentally studied the condensation heat transfer and pressure loss of R-134a within dimpled tubes in three different research. Various configurations of dimples, the effects of heat and mass flux and saturation temperature on the heat transfer coefficient and the pressure drop were examined. Results of these studies revealed that: firstly, dimpled tubes experienced the higher frictional pressure drop and heat transfer rate compared with smooth tubes; secondly, the lowest helical and dimpled pitches had the maximum pressure drop and heat transfer rate and finally, the increase of dimple depth led to reduction of the efficiency index in dimpled tubes. Balcilar et al. [29,30] in two different studies, proposed correlations for the Nusselt number and the pressure drop during boiling and condensation of R134 flowing inside smooth and corrugated tubes. The empirical correlations were obtained by using dimensionless numbers from experimental data of convective condensation and boiling experiments and utilizing a closed-form of multi-layer perceptron (MLP) method of artificial neural network (ANN). Kukulka and Smith [31] experimentally investigated the thermal-hydraulic performance of an enhanced tube (Vipertex 1EHT) for cooling and heating conditions of the internal flow. The enhanced tube could increase the heat transfer rate by more than 500% compared with the smooth tube for constant flow rates. They reported the maximum local Nusselt number at Re = 750 among the laminar Reynolds numbers (Re < 2300). Also, they found that the heat transfer rate in the cooling process was higher than the heating one, and the transition to the turbulent condition occurred at lower Reynolds number in the cooling process in comparison to the heating. Liang et al. [32] proposed a new method of the manufacturing process of enhanced tubes with dimples and protrusions. The effects of the main extruding parameters, such as extrusion depth, extrusion spacing, teeth radius, and tube wall thickness were also studied numerically. Xie et al. [33] conducted numerical simulations to study the flow field characteristic and heat transfer mechanism in turbulent flow (5000 < Re < 30,000) of a new tube with dimples and protrusions. The working fluid used in the simulation was air, and constant temperature assumption was applied through the surface of the tube. The results indicated that the effects of protrusion’s depth, pitch, and diameter on thermal-hydraulic performance were considerable and any changes in each of them either increased or decreased the PEC of the enhanced tube. Application of enhanced tubes is growing significantly, and more endeavor is required to enhance the thermal efficiency of them. The purpose of the present study is to investigate a deepdimpled type of enhanced tube numerically. Although several investigations have been carried out through dimpled tubes numerically and experimentally, few numbers of research such as [24,25] have been conducted to study tubes equipped with deep dimples. In this study, a laminar pattern of flow (500 < Re < 2000) at the inlet, a uniform heat flux exerted over the external surface of enhanced tube and water as the working fluid, are considered. Simulations cover a wide range of configurations of deep dimples on the surface of the tube. None of these conditions has been investigated by others before. The novelty of this study is the geometrical configuration of the studied enhanced tubes, which includes deep dimples against the conventional dimpled tubes. These deep dimpled tubes increase the heat transfer through the tube by increasing the fluid turbulence, disruption of the thermal boundary layer, and expansion of heat transfer surface area. They cause three mechanisms of fluid flow, i.e., increment of local flow velocity, the formation of vortexes behind the dimples and axial swirling of the flow through the tube; which cause higher PEC rather than previously studied dimpled tubes. Also, the laminar flow heat transfer enhancement has been the aim of utilizing and development of

3

deep dimpled series of enhanced tubes. The use of these enhance tubes will allow a reduction in the cooling water mass flow rate required to obtain the desired heat transfer rate. 2. Geometry configuration and data reduction 2.1. Geometry configuration The 3d configuration and cross-section (X = 0) of the deep dimpled tube are depicted in Fig. 1(a). The length, internal diameter and, the wall thickness of the plain tubes are 1000, 18 and 0.5 mm respectively. Also, the inlet entrance length and the outlet length of dimpled tubes are equal and are considered approximate to the diameter of the deep dimples which are insignificant compared with the length of the tube. The geometry of the deep dimpled tube was acquired by exerting deep dimples on the surface of the plain tube. Three geometric parameters have been varied through the simulations: depth, diameter, and pitch of dimples. The centers of dimples are located 120° apart from each other over the peripheral of the tube. The diameter of dimples was provided by three different angles of their center point (60°, 90°, 120°) resulting in three specific diameters (9, 13.5 and 18 mm) as shown in Fig. 1(b). Depths of dimples were considered 2, 4, and 6 mm, respectively. Finally, pitches are considered as equal, twofold, and fourfold to the diameter of the deep dimples (1D, 2D, and 4D). Fig. 1(c), depicts the arrangement of dimples at longitude section of the enhanced tube. These geometrical sizes have been chosen to adopt the deep dimpled tubes with conventional heat exchangers and cover a wide range of geometrical configurations. Table 1 shows all 27 cases and the geometric parameters of deep dimpled tubes. 2.2. Data reduction The following correlations are used to determine important hydrodynamic and thermal parameters. The thermal energy of water through the tube is obtained by:

_ p ðT 0
T i Þ Q w ¼ mC

ð1Þ

_ is the mass flow rate, T i and T o are where Q w is the external heat, m the temperatures of inlet and outlet of tubes respectively. The heating due to the convection mechanism is calculated as follow

Q conv ¼ hAs ðT s
T b Þ

ð2Þ

where As is the area of the internal surface of the deep dimpled tube, Tb = 0.5(Ti + To) is the bulk temperature, and T s is the temperature of the internal surface of the enhanced tube. Heat transfer coefficient (h) is defined by:

h¼

Q conv As ðT s
T b Þ

ð3Þ

The mass flow rate can be obtained by:

_ ¼ Re  l m

pDh 4

ð4Þ

The Reynolds number, non-dimensional parameter, stands for the ratio of inertial to viscous force. Various Reynolds numbers were obtained by various mass flow rates. It is expressed as:

Re ¼

V i Dh q

l

ð5Þ

where l denotes the kinematic viscosity and Dh is hydraulic diameter which is estimated based on the cross-sectional area and circumference of the deep dimpled tubes. Now, Nusselt number is

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Fig. 1. The geometry of deep dimpled tube, (a) 3D view of cross sections, (b) angles of dimples, (c) longitude cross-section.

Table 1 Different configurations of deep dimpled tubes.

f ¼n

Configurations

Diameter (mm)

Depth (mm)

Pitch (mm)

Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case

9 9 9 9 9 9 9 9 9 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5 18 18 18 18 18 18 18 18 18

2 2 2 4 4 4 6 6 6 2 2 2 4 4 4 6 6 6 2 2 2 4 4 4 6 6 6

1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D 1D 2D 4D

Nu ¼

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

hDh kf

DP
o ðL=Dh Þ qV 2 =2

ð7Þ

where V is the mean velocity over the cross-section andDP is the pressure drop between the inlet and outlet of the enhanced tube. A performance evaluation criteria (PEC) comprising both heat transfer enhancement and friction factor is defined as [34]:

Nue =Nup PEC ¼  1=3 f e =f p

ð8Þ

where e and p indexes refer to enhanced and plain tube respectively. 3. Numerical analysis 3.1. Overview

ð6Þ

where kf is the fluid thermal conductivity at the bulk temperature. The friction factor (f), which is defined by Fanning friction factor and is depended to the pressure drop across the tube is:

In this paper, numerical simulations have been carried out to solve the thermo-hydrodynamic performance of the deep dimpled tube. The governing equations are solved based on the finite volume method. A second-order upwind scheme is employed to solve terms of N-S equation accurately. The SIMPLE method is used to solve and handle the coupling of pressure and velocity in the momentum equation. The iterations are continued up to residual target for continuity, momentum and energy equations at 10
6, which is appropriate to provide accurate results in engineering simulations [35]. It is necessary to employ an applicable turbulent model for the simulation to achieve accurate answers. The flow pattern at the entrance of the tube is authentically laminar; however, due to the high gradient of velocity and pressure, separations and induced vortexes along the tube because of deep dimples, the flow would become turbulent in the studied Reynolds numbers, so an appropriate turbulent model is essential. Three different

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turbulent models: k-e model, SST k–x model, and the Reynolds stress model have been used to compute the Nusselt number as a flow specification. The agreement of the calculated Nusselt number for all three models was so close, yet k-e model took the minimum time of the convergence, so it has been chosen as the turbulent model for simulations. 3.2. Governing equations The basic conservation equations, momentum, and energy, are defined as:

including

q

@ui ¼0 @xi

q

    @ui @uj @  @p @  ui uj ¼
þ l þ lt þ @xj @xi @xj @xj @xi

continuity,

ð9Þ

@ @ ðui T Þ ¼ @xi @xi





l

þ

Pr

lt @T Prt @xi

ð10Þ 3.4. Validation

ð11Þ

where q is the fluid density, u is velocity, l is dynamic viscosity, p is pressure, and T is temperature. Prt is the turbulent Prandtl number and lt is the turbulent viscosity. It should be noted that viscous dissipation is overlooked in simulations. Equation for turbulence kinetic energy K and turbulence dissipation rate e:

q q

@   @ Kuj ¼ @xj @xj @   @ euj ¼ @xj @xj



lþ



lþ





lt @K þ C
qe rk @xj 

lt ¼ q C l



lt @ e e2 pffiffiffiffiffi þ C 1 Ce
C 2 re @xj K þ em

  @ui lt @ui @uj @ui ¼ þ @xj q @xj @xi @xj

ð13Þ

ð14Þ

K2

ð15Þ

e

The constants can be expressed as:

C l ¼ 0:09;

 C 1 ¼ max 0:43;

lt

lt þ 5

;

C 2 ¼ 1:0;

  u

m

ð16Þ

where yis the height of wall-adjacent cell to the wall, and the friction velocity u is defined as:

s ffiffiffiffiffiffiffiffiffiffiffiffi ffi u ¼

sw q

8 3:302x
1=3
1:00 > > <
1=3
0:50 Nux ¼ 1:302x

0:506 > > : 4:364 þ 8:68 103 x e
41x

x 6 0:00005 0:00005 6 x 6 0:0015 x P 0:001 ð18Þ

Ten different sections along the plain tube were chosen to calculate the Nusselt number, and these amounts were validated by Shah’s correlation. Fig. 3 demonstrates the numerical and the Shah’s amounts of Nusselt number, and it has a different range of 0.5% To 2% at Re = 2000, so it shows an acceptable validation of numerical studies to theory. The results obtained from Re = 500 and 1000 has shown the same agreement. The mechanism of the fluid flow behavior inside these new enhanced tubes is totally different with the ones that have been studied experimentally yet; however, according to the results of this study discussed at Section 4, variations in thermofluid characteristics by geometrical modifications of the deep dimpled tube shows a good agreement with Ref. [25]. 3.5. Boundary condition and physical parameters

rk ¼ 1:0

yþ , which is the indicator of near-wall mesh quality and is a nondimensional parameter, can be expressed as:

yþ ¼ y

To be assured about the simulation accuracy, the friction factor was validated by empirical equations, and the Nusselt number of the plain tube at Re = 500, 1000 and 2000 was validated by proposed correlation provided by Shah [36] as follows:

ð12Þ

Cis the rate of production of kinetic energy (K) and can be expressed as:

C ¼
ui uj

and pressure were taken place as it is depicted in Fig. 2. At the near-wall region, to achieve wall-adjacent cell height based on Eqs. (16) and (17), the near-wall mesh resolution y+  1 was assumed, so the first layer height was obtained y = 0.15 mm. It is necessary to refine meshes until the results show the minimum differences and achieve mesh validation and independence. The enhanced tube with the most geometrical modification (Case 25) was chosen to be examined with different grid numbers. Two factors, Nusselt number and friction factor, were considered in five various number of elements, 512831, 1028628, 1513091, 2090697, 4109230 at Re = 2000, for checking the differences. According to Table 2 indicating the results, the factors change around 2% from total elements of 2090697–4109230 and this difference is much lower than the others, so to decrease the computational costs and time, 2090697 cells have been chosen.

ð17Þ

3.3. Meshing To achieve accurate simulations, the quality of the mesh is vital, especially for this complicated form of the enhanced tube, including several deep dimples and consequently variations in the flow pattern. A non-structural mesh was provided for all the deepdimpled and plain tubes. A dense mesh with prism layers was provided at the near-wall regions especially at the leading, trailing edges and centers of dimples where the most gradients in velocity

The wall of the tube is considered a non-slip wall. Water is chosen as the working fluid for simulations. The density of water is q ¼ 998:2 kg=m3 , the dynamic viscosity of it is l ¼ 0:001003 kg=ðm  sÞ, the specific heat of it is C ¼ 4:18 J=kg  K, and the water thermal conductivity is k ¼ 0:6 W=kg  K. The Prandtl number of water is considered to be Pr = 7, the temperature of the inlet water is T in = 298.15 k. A fully-developed pattern for the inlet flow and the uniform inlet velocity correspond with Re = 500, 1000 and 2000 were considered as the assumptions. A constant heat flux (q00 = 10000 W/m2) was exerted on the outer surface of the tubes. Fig. 4 shows the boundary conditions exerted on the deepdimpled tube. The boundary conditions set as constant velocity and temperature for the inlet and zero static relative pressure for the outlet and the tube surface. 4. Results 4.1. Deep-dimpled tube characteristic study In this section, the flow and heat transfer characteristics within the plain and deep dimpled tubes are studied.

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Fig. 2. The grid generation of deep dimpled tube: (a) on the outer surface; (b) outlet section.

Table 2 Mesh study for case 14 at Re = 2000. Element No. Friction Factor Nusselt Number

512831 0.195 46.2

1028628 0.285 51.4

Fig. 3. Nusselt numbers of numerical simulation and Shah’s correlation.

1513091 0.349 57.3

2090697 0.405 61.8

4109230 0.413 62.9

4.1.1. Flow field and thermal characteristic Fig. 5(a) and (b) show the velocity distribution at longitude section of deep dimpled (case 23) and plain tubes. It can be seen that the flow channel contracts at deep dimpled sections, so the flow velocity increases considerably; nevertheless, the velocity reduces at the sections without dimples. This increase and decrease in the velocity lead to a periodic trend of velocity along the deep dimpled tube. Also, the velocity has a constant trend through the plain tube. Fig. 5(c) illustrates the velocity contours of fluid flow at different Xsections of Case 23. The maximum velocity can be seen at X = 700 mm, where the flow channel cross-section area has the minimum amount among the other sections. Moreover, the velocity experiences a downward trend by the channel area increment, e.g., X = 900 mm. Fig. 5 (d) depicts the streamline inside the deep dimpled tube (case 23). It is obvious that because of the positive pressure gradient at the trailing edge of the dimples, vortexes are formed contributing to the reduction of the flow velocity. Also, as the fluid flow faces the deep dimples, it desires to change its path. This phenomenon repeats in the following dimple sections with a rotation of 60°, which causes the axial swirling and mixing of the

Fig. 4. Boundary conditions of enhanced tube.

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(a)

X=100

(b)

X=300

X=500 (c)

X=700

X=900

(d) Fig. 5. Velocity: (a) distribution along the enhanced tube (case 23); (b) distribution along the plain tube; (c) distribution at different longitude sections of the enhanced tube (case 23); (d) streamline along the enhanced tube (case 23).

Fig. 6. Temperature distribution along the (a) enhanced tube (case 23); (b) plain tube.

entire flow through the tube. These three mechanisms: The local flow velocity increment, the vortexes formed at the behind of the dimples and the axial swirling of the flow through the tube, are the main differences between the new deep dimpled tubes and previously investigated dimpled and plain ones. Fig. 6(a) and (b) show the temperature distribution along the plain and deep dimpled tube. It can be seen that the temperature of the fluid at the wall-adjacent of the plain tube is high while the fluid passing through the center of the tube has a lower temperature, so there is no significant heat transfer along the tube. On the other hand, along the deep dimpled tubes, most volume of the working fluid plays a considerable role in the heat transfer mechanism due to the swirling and vortexes formed. Fig. 7(a) and (b) depict the temperature distribution at different Xsections of the plain and deep-dimpled tube. Because of the mixing of the hot water next to the wall and the cold water at the subsequent layers made by deep-dimples showed in Fig. 5(d), the temperature distribution is more homogenous at cross-sections compared with a plain tube. Thus, this trend helps the cooling mechanism of the tube surface significantly, and the maximum temperature of the surface of the deep dimpled tube is 35° lower than the plain tube. Also, these lead to significant augmentation of heat transfer inside deep dimpled tubes in comparison to the plain ones.

4.1.2. Comparison of heat transfer coefficient in the plain and enhanced tubes The heat transfer coefficient of the deep-dimpled (case23) and plain tubes are shown in Fig. 8(a) and (b). A downward trend can be seen in both plain and deep dimpled tubes due to the increase

in the temperature gradient between the tube and the working fluid along the tube while the tube is exposed to the constant heat flux. Fig. 8(b) demonstrates a periodic behavior of the heat transfer coefficient (h) across the length of the deep dimpled tube. As the fluid flow passes the deep dimpled sections, its velocity rises due to the channel area shrinkage. This leads to the increment of the local heat transfer coefficient at these areas results in peak points of Fig. 8(b). After passing these regions, vortexes are made at the behind of the dimples, causing a reduction in the flow velocity and the ocal heat transfer coefficient leading to the bottom points of Fig. 8(b). Finally, when the fluid flow passes through the sections without dimples, its velocity is equal to the fluid flowing inside the plain tube ends in linear parts of the Fig. 8(b). Consequently, due to these phenomena and also the axial swirling depicted in Fig. 5(d), there is an enhancement of overall heat transfer coefficient up to six times within the deep dimpled tubes. Fig. 9 shows the contour of Nusselt number distribution along the deep dimpled tube and confirms the behavior of the wall heat transfer coefficient (h). It is clear that the local Nusselt number reduces along the deep dimpled tube, and its peak points are located at the bottom of the dimples where the velocity reaches its highest range. Conversely, the local Nusselt number reduces at trailing edge of the dimples where the fluid leaves the dimpled section.

4.2. Effects of different geometrical parameters on the Nusselt, Fanning friction factor and PEC In this section, the variations in the flow characteristic and tube parameters are surveyed. The simulations of this paper have been performed for all cases of Table 2 in three Reynolds numbers.

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a

X=100 mm

X=300 mm

X=500 mm

X=700 mm

X=900 mm

b

h (w/m2.k)

h (w/m2.k)

Fig. 7. Temprature distribution at different x-sections of the: (a) plain tube, (b) deep dimpled tube (case 23).

X (a)

X (b)

Fig. 8. Wall heat transfer coefficient (h) distribution along the: (a) deep dimpled tube (case 23); (b) plain tube.

Fig. 9. Nusselt number distribution along the deep-dimpled tube (case 23): (a) primarily section, (b) middle section, (c) ending section.

However, to avoid a massive amount of data and more quality explanations for each case, three different cases have been considered in each geometrical parameter variations. It is worth mentioning that the trend of other cases is the same as the chosen ones. In each case, two factors remain constant, and the effects of the third one on the parameters are studied by three amounts in three different Reynolds numbers: 500, 1000, 2000. 4.2.1. Pitch variation Fig. 10(a)–(c) present the variation of friction factor, Nusselt number, and PEC for different pitches. The diameter and depth of tubes are 13.5 mm and 4 mm respectively, and the pitches are considered 1D, 2D, and 4D (cases 13, 14 and 15). As opposed to plain tubes where the friction factor decreases with the augmentation of Reynolds number, the friction factor experiences an upward trend

in the deep-dimpled tube, Fig. 10(a). The reason is the high pressure-drop caused by vortexes formed at the behind of dimples, which would be boosted by the rising of Reynolds number. By increasing the pitch, less number of deep dimples cover the surface of the enhanced tube, so that it would reduce the number of induced vortexes along the tube leading to lower friction factor in a particular Reynolds number. Fig. 10(b) demonstrates that increment in pitch, leading to a slight decrease in the Nusselt number, which is consistent with the observations from Xie et al. [25]. By increasing the pitch, lower number of deep dimples covers the surface of the tube, so the regions where the velocity and local heat transfer rises would reduce. Also, the swirling of the fluid flow along the tube reduces relatively. In general, by increasing the pitch, the considerable friction factor reduction is evident from 15 to 7.6 in comparison to the slight heat transfer decrease, so it

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7

Re=2000 Re=1000 Re=500

15

6

Nue/Nup

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30

50

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Fig. 10. Effects of different pitches on: (a) friction factor; (b) Nusselt number; (c) PEC.

causes PEC enhancement from PEC = 2.29 to PEC = 2.8 at Re = 2000, Fig. 10(c). Fig. 11 demonstrates pressure distribution at longitude section of the deep dimpled tube when d = 4 mm, D = 13.5 and for three different pitch sizes. It can be seen the deep dimpled tube with a lower pitch (higher number of dimples along the tube) has a higher pressure gradient along with it. Also, it is obvious that there is a decrease in the local pressure at the dimpled sections due to the increment of velocity caused by the channel area shrinkage, and then, a positive pressure gradient after these sections at the expanded flow areas can be seen. 4.2.2. Diameter variation Fig. 12(a)–(c) show the variation of friction factor, Nusselt number, and PEC in different diameters of the deep-dimpled tube in three different Reynolds numbers. The tube pitch and depth are 2D and 4 mm, respectively, and the diameters are considered 9 mm, 13.5 mm and 18 mm (cases 5, 14, and 23). It presents a slight rise in the Nusselt number and Fanning friction factor by diameter increase. The increment in the diameter of the dimples increases the heat transfer surface of the enhanced tube and reduces the channel area of the flowing fluid at dimpled sections which contribute to the enhancement of the fluid swirling. These lead to the increment of the Nusselt number of deep dimpled tubes. Also, augmentation of the diameter of the dimple causes higher pressure gradient along the tube, so the friction factor enhances. These variations in heat transfer and friction factor are in a good agreement with Xie et al. results [25]. Finally, the PEC will increase from 8% to 11% by the diameter increment in different Reynolds numbers because heat transfer growth is predominant in comparison to pressure-drop. Fig. 13(a)–(c) depict streamline of the working fluid within the deep dimpled tube at three various dimple diameters at Re = 2000 (cases 5, 14 and 23). It can be seen that the increase in the diameter

of the dimples; streamlines are denser at the behind of them, which shows more water volume flow rate participating in the formation of vortexes. These contribute to the slight increment of pressure drop and Nusselt number along the deep dimpled tube, which is proved by Fig. 12.

4.2.3. Depth variation Fig. 14(a)–(c) demonstrate the impacts of different depths of dimples (d = 2 mm, 4 mm, and 6 mm) on flow characteristic parameters in three different Reynolds numbers when D = 13.5 and P = 2D (cases 11, 14 and 17). It can be seen in Fig. 14(a) that the friction factor has an upward trend when the depth of dimples increases in a constant Reynolds number. Dimples act as an impediment along the flow direction, so deep dimples contribute to higher pressure drop along with the tube result in augmentation of friction factor. These phenomena intensify dramatically for deeper dimples. The friction factor ratio of the enhanced tube to the plain tube is around 44 for case 17 at Re = 2000, which is two times more than its ratio at Re = 1000 approximately. Fig. 14(b) demonstrates the ratio of the Nusselt number of the dimpled tube to the plain tube for different depths of dimples. As shown, the Nusselt number rises by the depth increase. Deeper dimples decrease the flow direction surface area leading to increment of flow velocity at dimpled sections which causes the augmentation of local convective heat transfer coefficient at these areas. Also, more vigorous axial swirling and vortexes are made by deeper dimples along the fluid flow direction. These lead to the increment of the Nusselt number at a particular Reynolds number. Finally, according to Fig. 14(c), the increment in friction factor overcomes the augmentation of heat transfer, and the PEC would decrease by the increase in the depth of dimples. This reduction of PEC by the increase in depth was also reported by Xie et al. [25]. It can be seen that among all the geometrical configurations, the minimum PEC

Fig. 11. The pressure distribution at longitude section of the deep dimpled tube when d = 4 mm, D = 13.5 and pitches: a = 13.5 mm, b = 27 mm, c = 54 mm.

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12.4

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(c)

Fig. 12. Effects of different diameters on: (a) friction factor; (b) Nusselt number; (c) PEC.

Fig. 13. The streamline of the working fluid inside the enhanced tube at various dimple diameters: (a) D = 9 mm; (b) D = 13.5 mm; (c) D = 18 mm, when d = 4 mm, p = 2D and Re = 2000.

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0

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(b)

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Fig. 14. Effects of different depths on: (a) friction factor; (b) Nusselt number; (c) PEC.

of deep dimpled tubes occurs for the depth of d = 6 mm at Re = 2000, PEC = 1.15. Fig. 15 presents the pressure distribution along the deep dimpled tubes at three different depths when D = 13.5 mm, P = 2D, and Re = 2000. As it is clear, the pressure drop of the flow inside the deep dimpled tube with d = 6 mm is maximum compared with other depths. It proves the friction factor augmentation depicted in Fig. 14(a). Fig. 16 depicts the contours of heat transfer coefficient at different dimples depths: (a) d = 2 mm, (b) d = 4 mm, (c) d = 6 mm when D = 13.5, P = 2D, and Re = 2000. It is obvious that the heat transfer coefficient reduces along the deep dimpled tubes, and its reason is the increasing temperature gradient between the fluid flow and the surface of the deep dimpled tube. Also, it can be seen that higher local heat transfer coefficient attributes to the bottom of the dimples, where the flow velocity enhances significantly. Therefore, the deeper dimples contribute to increment of overall heat transfer coefficient along the deep dimpled tube.

Fig. 17 illustrates streamline contours for different depths: (a) d = 2 mm, (b) d = 4 mm and (c) d = 6 mm when D = 13.5 and P = 2D and Re = 2000. As shown, flow velocity has a higher amount at deeper dimpled sections because of the shrinkage of the flow direction surface area. By comparing Fig. 17(a)–(c), it is seen that the increment of dimples depth contributes to the enforcement of vortexes formed behind them. Also, based on the figures, higher velocity gradient can be seen at deeper dimpled sections, which causes more pressure drop along the enhanced tubes with deeper dimples. 4.3. Effects of Reynolds number variations on the fluid characteristics Fig. 18(a)–(c) show streamline contours and Fig. 19 depicts pressure distribution at longitude section of case 17 at three different Reynolds numbers: (a) Re = 500, (b) Re = 1000 and (c) Re = 2000. First, vortexes can be seen at the behind of the deep dimples in all three Reynolds numbers which prove the turbulent

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Fig. 15. The pressure distribution along the deep dimpled tube for different depths: (a) d = 6 mm; (b) d = 4 mm and (c) d = 2 mm when D = 13.5, P = 2D and Re = 2000.

Fig. 16. The heat transfer coefficient at different dimples depths: (a) d = 6 mm, (b) d = 4 mm, (c) d = 2 mm when D = 13.5, P = 2D and Re = 2000.

Fig. 17. The streamlines at different dimples depths: (a) d = 2 mm, (b) d = 4 mm, (c) d = 6 mm when D = 13.5, P = 2D and Re = 2000.

characteristics of flow inside the deep dimpled tubes. This is in contrast to the behavior of the laminar flow inside the plain tube in theses Reynolds numbers. Second, by increasing in Reynolds number, the average velocity of the working fluid inside the deep dimpled tube would ascend. This contributes to the higher heat transfer along with the deep dimpled tubes and consequently higher Nusselt number, which is evident in Figs. 10(b), 12(b) and 14(b). Finally, a superior-velocity gradient can be seen at higher Reynolds numbers leading to higher pressure drop along the deep dimpled tubes up to 464 (pa) for Re = 2000 in case 17, which is shown in Fig. 19. 5. Conclusion In this study, a new configuration of an enhanced tube (deep dimpled tube) has been studied by the computational fluid dynamics (CFD). Investigations have been conducted in three different

depths, diameters and pitches of dimples result in twenty-seven different geometrical configurations. Numerical studies have been done in three different Reynolds numbers (Re = 500, 1000, 2000). Finally, thermofluid characteristics of the deep dimpled tubes have been compared with the plain tube and the performance evaluation criteria (PEC) for different cases. The main results are presented as follows:  Modification in the conventional tubes by deep dimples, three major differences in the fluid flow behavior are observed: First, the flow velocity increases at the bottom of the dimples; second, the vortexes are formed at the behind of the dimples, and finally, there would be axially swirling along the flow direction. All these contribute to the change of the flow pattern and characteristics from laminar to turbulent at studied Reynolds numbers inside the deep dimpled tubes.

Fig. 18. The streamlines at logtiude section of case 17 at three different Reynolds numbers: (a) Re = 500, (b) Re = 1000, (c) Re = 2000.

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Fig. 19. The pressure distribution along the deep dimpled tube for case 17 at three different Reynolds numbers: (a) Re = 2000, (b) Re = 1000, (c) Re = 500.

 The flow velocity rises by passing throw the dimpled sections because of decrease in the flowing surface area; after that, it would decrease at the behind of them causing a periodic trend in heat transfer coefficient diagram of deep-dimpled tubes against its non-periodic trend in plain ones. Also, vortexes and axial swirling along the tube prevent the formation of the thermal boundary layer and cause more homogenous temperature distribution in deep dimpled tubes where the swirling and vortexes transfer hot volume of water at wall-adjacent to the cold center section. These lead to higher Nusselt number of these new types of tubes in comparison to the plain ones.  The overall Nusselt number will increase with higher dimple diameters and depths, and lower pitches. It grows up to 6 times more compared with the plain tube at constant heat flux when pitch = 18, diameter = 18, and depth = 6 (case 25) in Re = 2000.  Periodic velocity trend and vortexes formed at the behind of the dimples would increase the pressure drop of the fluid flow inside the deep dimpled tubes compared with plain tubes, accordingly the friction factor increases by the increment of depth and diameter and reduction of the pitch. However, the depth of dimples has the highest impact on the friction factor. The friction factor ratio of the deep dimpled tube on the plain tube reaches to f/f0 = 44 when pitch = 18, diameter = 18, and depth = 6 (case 25) in Re = 2000.  By increasing the pitch of the dimples, the number of dimples reduces, so it contributes to a reduction in Nusselt number and friction factor, while PEC rises. Rising of the diameter of dimples causes more flow swirling and heat transfer surface area, which leads to the increment of the Nusselt number, friction factor, and PEC simultaneously. The depth of dimples inhibits the fluid flow along the tube and causes high pressure-loss. Also, depth increment leads to more heat transfer and Nusselt number, yet it cannot overcome the friction factor jump, so the PEC reduces by the increase in depth of dimples. Among the studied Reynolds numbers, higher Nusselt number, friction factor, and PEC have been observed for higher Reynolds numbers.  Finally, after conducting 27 simulations of enhanced tubes for three different Reynolds numbers, the deep dimpled tube with geometric parameters of depth = 2 mm, diameter = 18 mm and pitch = 4D results in maximum PEC = 3.3 at Re = 2000. Finally, this new type of tubes fabricated by modifications of the plain tube will minimize the energy consumption and the cost of industrial heat exchangers by decreasing their size and increasing their PEC. Future research, including the study of the cooling process, and also two-phase flow passing through deep dimpled tubes could be investigated. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118845.

References [1] M.R. Salimpour, A.T. Al-Sammarraie, A. Forouzandeh, M. Farzaneh, Constructal design of circular multilayer microchannel heat sinks, J. Therm. Sci. Eng. Appl. 11 (1) (2019) 011001. [2] Y. Wang, Y.-L. He, Y.-G. Lei, J. Zhang, Heat transfer and hydrodynamics analysis of a novel dimpled tube, Exp. Therm Fluid Sci. 34 (8) (2010) 1273–1281. ´ a, A. Viedma, Heat transfer and pressure drop for low [3] P.G. Vicente, A. Garcı Reynolds turbulent flow in helically dimpled tubes, Int. J. Heat Mass Transf. 45 (3) (2002) 543–553. [4] P.G. Vicente, A. Garcıa, A. Viedma, Experimental investigation on heat transfer and frictional characteristics of spirally corrugated tubes in turbulent flow at different Prandtl numbers, Int. J. Heat Mass Transf. 47 (4) (2004) 671–681. [5] A. Barba, S. Rainieri, M. Spiga, Heat transfer enhancement in a corrugated tube, Int. Commun. Heat Mass Transfer 29 (3) (2002) 313–322. [6] Q. Fan, X. Yin, 3-D numerical study on the effect of geometrical parameters on thermal behavior of dimple jacket in thin-film evaporator, Appl. Therm. Eng. 28 (14–15) (2008) 1875–1881. [7] M. Li, T.S. Khan, E. Al-Hajri, Z.H. Ayub, Single phase heat transfer and pressure drop analysis of a dimpled enhanced tube, Appl. Therm. Eng. 101 (2016) 38– 46. [8] P. Kumar, A. Kumar, S. Chamoli, M. Kumar, Experimental investigation of heat transfer enhancement and fluid flow characteristics in a protruded surface heat exchanger tube, Exp. Therm. Fluid Sci. 71 (2016) 42–51. [9] M. Shafaee, H. Mashouf, A. Sarmadian, S. Mohseni, Evaporation heat transfer and pressure drop characteristics of R-600a in horizontal smooth and helically dimpled tubes, Appl. Therm. Eng. 107 (2016) 28–36. [10] A. Sarmadian, M. Shafaee, H. Mashouf, S. Mohseni, Condensation heat transfer and pressure drop characteristics of R-600a in horizontal smooth and helically dimpled tubes, Exp. Therm. Fluid Sci. 86 (2017) 54–62. [11] H. Mashouf, M. Shafaee, A. Sarmadian, S. Mohseni, Visual study of flow patterns during evaporation and condensation of R-600a inside horizontal smooth and helically dimpled tubes, Appl. Therm. Eng. 124 (2017) 1392–1400. [12] Z. Liang, S. Xie, L. Zhang, J. Zhang, Y. Wang, Y. Yin, Influence of geometric parameters on the thermal hydraulic performance of an ellipsoidal protruded enhanced tube, Numeric. Heat Transfer, Part A: Appl. 72 (2) (2017) 153–170. [13] O. Rezaei, O.A. Akbari, A. Marzban, D. Toghraie, F. Pourfattah, R. Mashayekhi, The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel, Physica E 93 (2017) 179–189. [14] F. Pourfattah, M. Motamedian, G. Sheikhzadeh, D. Toghraie, O.A. Akbari, The numerical investigation of angle of attack of inclined rectangular rib on the turbulent heat transfer of Water-Al2O3 nanofluid in a tube, Int. J. Mech. Sci. 131 (2017) 1106–1116. [15] R. Mashayekhi, E. Khodabandeh, M. Bahiraei, L. Bahrami, D. Toghraie, O.A. Akbari, Application of a novel conical strip insert to improve the efficacy of water–Ag nanofluid for utilization in thermal systems: a two-phase simulation, Energy Convers. Manage. 151 (2017) 573–586. [16] A.R. Rahmati, O.A. Akbari, A. Marzban, D. Toghraie, R. Karimi, F. Pourfattah, Simultaneous investigations the effects of non-Newtonian nanofluid flow in different volume fractions of solid nanoparticles with slip and no-slip boundary conditions, Therm. Sci. Eng. Prog. 5 (2018) 263–277. [17] M.H. Esfe, H. Hajmohammad, D. Toghraie, H. Rostamian, O. Mahian, S. Wongwises, Multi-objective optimization of nanofluid flow in double tube heat exchangers for applications in energy systems, Energy 137 (2017) 160– 171. [18] B. Karbasifar, M. Akbari, D. Toghraie, Mixed convection of Water-Aluminum oxide nanofluid in an inclined lid-driven cavity containing a hot elliptical centric cylinder, Int. J. Heat Mass Transf. 116 (2018) 1237–1249. [19] M. Parsaiemehr, F. Pourfattah, O.A. Akbari, D. Toghraie, G. Sheikhzadeh, Turbulent flow and heat transfer of Water/Al2O3 nanofluid inside a rectangular ribbed channel, Physica E 96 (2018) 73–84. [20] A. Arabpour, A. Karimipour, D. Toghraie, The study of heat transfer and laminar flow of kerosene/multi-walled carbon nanotubes (MWCNTs) nanofluid in the microchannel heat sink with slip boundary condition, J. Therm. Anal. Calorim. 131 (2) (2018) 1553–1566. [21] M. Zarringhalam, H. Ahmadi-Danesh-Ashtiani, D. Toghraie, R. Fazaeli, Molecular dynamic simulation to study the effects of roughness elements with cone geometry on the boiling flow inside a microchannel, Int. J. Heat Mass Transf. 141 (2019) 1–8.

M.H. Cheraghi et al. / International Journal of Heat and Mass Transfer 147 (2020) 118845 [22] D. Toghraie, M.M.D. Abdollah, F. Pourfattah, O.A. Akbari, B. Ruhani, Numerical investigation of flow and heat transfer characteristics in smooth, sinusoidal and zigzag-shaped microchannel with and without nanofluid, J. Therm. Anal. Calorim. 131 (2) (2018) 1757–1766. [23] A. Moraveji, D. Toghraie, Computational fluid dynamics simulation of heat transfer and fluid flow characteristics in a vortex tube by considering the various parameters, Int. J. Heat Mass Transf. 113 (2017) 432–443. [24] Y. Rao, Y. Feng, B. Li, B. Weigand, Experimental and numerical study of heat transfer and flow friction in channels with dimples of different shapes, J. Heat Transfer 137 (3) (2015) 031901. [25] Y. Rao, C. Wan, Y. Xu, An experimental study of pressure loss and heat transfer in the pin fin-dimple channels with various dimple depths, Int. J. Heat Mass Transf. 55 (23–24) (2012) 6723–6733. [26] K. Aroonrat, S. Wongwises, Experimental study on two-phase condensation heat transfer and pressure drop of R-134a flowing in a dimpled tube, Int. J. Heat Mass Transf. 106 (2017) 437–448. [27] K. Aroonrat, S. Wongwises, Condensation heat transfer and pressure drop characteristics of R-134a flowing through dimpled tubes with different helical and dimpled pitches, Int. J. Heat Mass Transf. 121 (2018) 620–631. [28] K. Aroonrat, S. Wongwises, Experimental investigation of condensation heat transfer and pressure drop of R-134a flowing inside dimpled tubes with different dimpled depths, Int. J. Heat Mass Transf. 128 (2019) 783–793. [29] M. Balcilar, K. Aroonrat, A. Dalkilic, S. Wongwises, A generalized numerical correlation study for the determination of pressure drop during condensation

[30]

[31]

[32]

[33]

[34] [35]

[36]

13

and boiling of R134a inside smooth and corrugated tubes, Int. Commun. Heat Mass Transfer 49 (2013) 78–85. M. Balcilar, K. Aroonrat, A. Dalkilic, S. Wongwises, A numerical correlation development study for the determination of Nusselt numbers during boiling and condensation of R134a inside smooth and corrugated tubes, Int. Commun. Heat Mass Transfer 48 (2013) 141–148. D.J. Kukulka, R. Smith, Thermal-hydraulic performance of Vipertex 1EHT enhanced heat transfer tubes, Appl. Therm. Eng. 61 (1) (2013) 60–66, 2013/10/ 15/. Z. Liang, S. Xie, J. Zhang, L. Zhang, Y. Wang, H. Ding, Numerical investigation on plastic forming for heat transfer tube consisting of both dimples and protrusions, Int. J. Adv. Manuf. Technol. (2019) 1–16. S. Xie, Z. Liang, L. Zhang, Y. Wang, H. Ding, J. Zhang, Numerical investigation on heat transfer performance and flow characteristics in enhanced tube with dimples and protrusions, Int. J. Heat Mass Transf. 122 (2018) 602–613. R. Webb, E. Eckert, Application of rough surfaces to heat exchanger design, Int. J. Heat Mass Transf. 15 (9) (1972) 1647–1658. A. Shadlaghani, M. Farzaneh, M. Shahabadi, M.R. Tavakoli, M.R. Safaei, I. Mazinani, Numerical investigation of serrated fins on natural convection from concentric and eccentric annuli with different cross sections, J. Therm. Anal. Calorim. 135 (2) (2019) 1429–1442. A. Bejan, A.D. Kraus, Heat Transfer Handbook, John Wiley & Sons, 2003.