Influence of perforated triple twisted tape on thermal performance characteristics of a tube heat exchanger

Journal Pre-proofs Influence of perforated triple twisted tape on thermal performance characteristics of a tube heat exchanger Muhammad Mostafa Kamal Bhuiya, Md Mamunur Roshid, Md. Mehdi Masud Talukder, Mohammad Golam Rasul, Prasanjit Das PII: DOI: Reference:

S1359-4311(19)34773-8 https://doi.org/10.1016/j.applthermaleng.2019.114769 ATE 114769

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

11 July 2019 13 November 2019 3 December 2019

Please cite this article as: M. Mostafa Kamal Bhuiya, M. Mamunur Roshid, Md. Mehdi Masud Talukder, M. Golam Rasul, P. Das, Influence of perforated triple twisted tape on thermal performance characteristics of a tube heat exchanger, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114769

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Influence of perforated triple twisted tape on thermal performance characteristics of a tube heat exchanger Muhammad Mostafa Kamal Bhuiya a,*, Md Mamunur Roshid a, Md. Mehdi Masud Talukder a, Mohammad Golam Rasul b, Prasanjit Das a a Department of Mechanical Engineering, Chittagong University of Engineering & Technology (CUET), Chittagong 4349, Bangladesh b School of Engineering and Technology, Central Queensland University (CQUniversity), Rockhampton, QLD 4701, Australia * Corresponding Author: Muhammad Bhuiya, Department of Mechanical Engineering Chittagong University of Engineering & Technology (CUET) Chittagong 4349, Bangladesh E-mail: [email protected], [email protected], Mobile: +8801784353193

Abstract One of the challenging tasks in the development of heat exchangers is to select an appropriate geometry that will consume minimum energy. This could be achieved by designing a suitable enhancing device which will boost the thermal performance characteristics of heat exchangers. Twisted tape swirl generator, a heat transfer enhancement device equipped in a tube heat exchanger would induce turbulence and superimposed vortex motion causing a reduction in the hydrodynamic or thermal boundary layer thickness which results in the improvement of convective heat transfer. In this study, a new design of perforated triple twisted tape (PTTT) insert was applied as a swirl flow device with four different porosities (Rp) of 1.2, 4.6, 10.4 and 18.6% to enhance the convective heat transfer of a tube heat exchanger. The effects of porosity (Rp) of PTTT swirl generators on heat transfer, fluid friction and thermal performance characteristics of a tube heat exchanger were experimentally investigated. The experiments were conducted under constant heat flux condition using air as the working fluid in turbulent flow regime for variation in Reynolds number (Re) from 7,250 – 49,800. The Nusselt number of the tube installed with PTTT inserts for porosity ranging from 1.2-18.6% was found to be 88 – 320% higher, whereas, the friction factor was achieved to be 112 – 355% higher in comparison to the plain tube. The highest heat transfer result of 320% was obtained at a porosity of 4.6% with PTTT insert compared to the smooth tube. Despite the significant enhancement in heat transfer, the friction factor was obtained to be 355% higher in comparison to the plain tube at a porosity of 4.6% with PTTT insert. The experimental results demonstrated that Nusselt number, friction factor, and thermal enhancement efficiency (TEE) were increased with decreasing the porosity of the tape inserts except for 1.2%. The heat transfer performance was evaluated based on constant blower power and the values were found to be 1.13 – 1.5 relative to the plain tube. The maximum TEE of 1.5 was achieved using PTTT insert with a porosity of 4.6%. Based on the experimental data, the empirical correlations of heat transfer, friction factor and TEE were developed in terms of Rp, Re and Prandtl number (Pr) to predict the heat transfer, friction factor and TEE. The optimal design of PTTTs based on the evaluation of thermal performance with suitable porosity could be an excellent heat transfer enhancement device for many industrial applications. Keywords: PTTT, Heat transfer, Friction loss, TEE.

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1. Introduction

Due to the increasing energy demand, cost of energy and material, significant attention has been given by the researchers and scientists to build up the efficient heat exchanger devices. Nowadays, the heat transfer enhancement techniques are utilized to improve the thermal performance characteristics of heat exchangers. The heat transfer enhancement techniques are widely applied in several engineering applications; for instance, refrigeration systems, chemical industries, power generation, oil and gas, heating, ventilating, and air conditioning (HVAC), and food and beverage processing, etc. [1]. The heat transfer augmentation devices can create one or more of the following conditions to enhance the heat transfer rate significantly in heat exchanger systems with an undesirable increase in pressure drop: (i) interruption in the development of hydrodynamic and thermal boundary layer and increase in the turbulence intensity, (ii) increase in the area of heat transfer, and (iii) production of swirling/secondary flows [2]. Therefore, the proper selection of heat transfer augmentation devices is a challenging task to fulfil the need for satisfactory enhancement in heat transfer with an acceptable increment in friction. The swirl flow generator could be considered as a promising and effective passive heat transfer enhancement device that has been widely adopted in heat exchanger systems to augment the heat transfer.

There are several swirl generators (SGs), such as helical tape inserts [3, 4], wire-coil inserts [5], winglet vortex generators [6], turbulator and compound turbulators [7-9], delta-wing tape inserts [10], and twisted ring turbulators [11] have been used for enhancement in heat transfer in turbulent flow region. These SGs significantly enhance the heat transfer in heat exchanger systems with a corresponding increase in presser drop which was due to the higher frictional losses as the fluid was flown through the heat exchanger. Besides, the higher pressure drop increased the pumping power required to pump the fluid throughout the system. An experimental study was conducted to investigate the thermo-hydraulic performance characteristics of a circular tube with coiled-wire-inserts for variation in Reynolds number from 3429 – 26,663 Keklikcioglu et al. [5]. The highest TEE of 1.82 was obtained at a pitch-to-diameter ratio of 1.0. Bhuiya et al. [3, 4] experimentally studied the heat transfer, friction factor and thermal performance characteristics of the tube equipped with double and triple helical tape inserts in turbulent flow region under uniform heat flux condition for different helix angles. The results of heat transfer and friction factor were increased 4.05 – 4.5 times and 2.7 –- 3.0 times of the tube with double and triple helical tape inserts compared to the plain tube, respectively. Xu et al. [6] conducted an experimental investigation of thermal performance and flow behaviour characteristics in a circular tube equipped

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with winglet vortex generators under uniform heat flux condition for Reynolds number ranging from 6000 – 34,000. The Nusselt number and friction factor were increased up to 1.82 and 4.88 times in comparison to the smooth tube, respectively, at a condition of pitch ratio of 1.6, attack angle of 45° and blockage ratio of 0.3. In addition, the highest TEE of 1.45 was obtained at a condition of pitch ratio of 2.4, attack angle of 0° and blockage ratio of 0.1. The effects of the wing-width ratio of double-sided delta–wing tapes on heat transfer and fluid friction characteristics of a double pipe heat exchanger in turbulent flow region for variation in Reynolds number from 5300 – 14,500 were investigated by Wijayanta et al. [10]. The results of heat transfer and friction factor were increased up to 2.77 and 11.6 times compared to the plain tube, respectively, for a wing-width ratio of 0.63. In addition, the highest TEE of 1.15 was achieved for the same wing-width ratio. Thianpong et al. [11] investigated the heat transfer, friction factor and thermal performance characteristics in a circular tube installed with twisted ring (TR) turbulators for Reynolds number ranging from 6000 – 20,000 with different width and pitch ratios. The heat transfer and friction factor were increased 2.87 – 3.35 times and 38.6 – 49.7 times compared to the plain tube, respectively, for a width ratio of 0.15 and pitch ratio of 1.0 of the tube equipped with TR turbulators. The highest TEE of 1.24 was obtained of the tube with TR turbulators at width and pitch ratios of 0.05 and 1.0, respectively.

Apart from SGs, twisted tape inserts are widely used as a swirl flow device to enhance the heat transfer in heat exchanger systems. The presence of twisted tape swirl generator induces turbulence and vortex motion, promoting the swirl flow and increases the residence time of the fluid in the flow region. The twisted tape swirl generator caused a reduction in the hydrodynamic or thermal boundary layer thickness which results in the better enhancement in heat transfer through the convection [12]. These devices are used in tube heat exchangers to enhance the fluid-mixing between the wall and core area [13]. Several research studies have been conducted using twisted tapes which include serrated twisted tape [14, 15], multiple twisted tapes [16], double twisted tapes [17, 18], triple twisted tapes [19], selfrotating twisted tapes [20] to investigate the heat transfer and fluid friction characteristics of heat exchanger tube. An experimental investigation of serrated twisted tape on thermal performance characteristics in a circular tube in the turbulent flow region for Reynolds number ranging from 4000 – 20,000 under constant heat flux condition was conducted by Eiamsa-ard and Promvonge [14]. The results of heat transfer and friction factor were achieved to be 72.2 and 233% higher compared to the smooth tube, respectively, at a depth ratio of 0.3. The highest TEE of 1.17 was achieved at a depth ratio of 0.1 at constant pumping power. Piriyarungrod et al. [16] experimentally investigated the thermohydraulic performance characteristics of multiple twisted tapes (M-TTs) fitted in a heat exchanger tube under constant heat flux condition and Reynolds number ranging from 6000 – 20,000. The highest TEE 3

of 1.2 was achieved using (M-TT) when six small twisted tapes were used at a twist ratio of 2.5. Bhuiya et al. [17, 19] conducted an experimental investigation to determine the effect of twist ratio on thermohydraulic characteristics of the tube installed with double counter twisted tapes (DCTTs) and TTTs in turbulent flow region under constant heat flux condition. The results of heat transfer and friction factor were obtained to be 60 – 240 and 73 – 285%, and 91 – 286 and 91 – 320% higher of the tube with DCTT and TTT compared to the plain tube for twist ratios of 1.95 and 1.92, respectively. The highest TEEs of 1.34 and 1.44 were achieved of the tube equipped with DCTT and TTT at twist ratios of 1.95 and 1.92, respectively. Zhang et al. [20] experimentally investigated the heat transfer, friction factor and TEE characteristics of a heat exchanger tube installed with self-rotating twisted tapes (SRTTs) in turbulent flow condition for Reynolds number ranging from 12,000 – 45,000 and at different twist ratios (2.2, 3, 4 and 6). The highest TEE of 1.03 was obtained at a twist ratio of 2.2 of the tube with SRTT.

Numerous research studies have been conducted using modified twisted tapes with several geometries in order to enhance their thermo-hydraulic performance characteristics compared to the typical one. Twisted tapes are used concurrently with other heat transfer augmenting devices so-called compound devices, such as delta-wing/winglet twisted tapes [2, 21], alternate clockwise and counter-clockwise twisted tapes [22] and twisted tapes with alternate-axes and wings [23] for further improvement in heat transfer enhancement. The higher enhancement in heat transfer using modified twisted tapes is obtained by extra turbulence which causes the better mixing of the fluid in the flow region. However, an additional pumping power is required to achieve the higher enhancement in heat transfer. The influence of twisted tapes with twin delta-winged on heat transfer, friction factor and thermal performance characteristics of a heat exchanger tube under uniform heat flux condition for variation in Reynolds number from 5000 – 15,000 and at a twist ratio of 3.0 was conducted by Eiamsa-ard et al. [2]. The results showed that the twin delta-winged twisted tape in counterflow arrangement provided the maximum TEE of 1.26 along with the heat transfer and friction factor of 2.57 and 8.55 times higher compared to the plain tube, respectively. Eiamsa-ard et al. [21] conducted an experimental study using delta-winglet twisted tapes (DWTs) to investigate the heat transfer, friction factor and TEE characteristics in a circular tube in turbulent flow region under uniform heat flux condition for varieties of twist ratios (3, 4 and 5) and depth of wing cut ratios (0.11, 0.21 and 0.31). The heat transfer and friction factor of the tube with DWT were found to be 1.1 – 2.55 and 2.50 – 7.02 times higher compared to the plain tube, respectively. The maximum TEE of 1.24 was achieved using O-DWT (oblique delta-winglet twisted tapes) at constant pumping power relative to the plain tube. An experimental study of alternate clockwise and counterclockwise twisted tape inserts (CC-CC twisted tape) was conducted to evaluate the heat transfer and thermal performance characteristics of a circular tube under constant heat flux condition for a wide range 4

of Reynolds number 3000 – 27,000 and for different twist ratios [22]. The heat transfer of the tube with (CC-CC twisted tape) was obtained to be 27.3 – 90.5% higher compared to the plain tube at a twist ratio of 3.0. The highest TEE of 1.4 was obtained of the tube with (CC-CC twisted tape) at a twist ratio of 3.0. The influence of twisted tapes with alternate-axes and wings on heat transfer, friction factor and TEE characteristics in a circular tube with different wing-chord ratios was conducted by Wongcharee and Eiamsa-ard [23]. The results of heat transfer and friction factor were increased up to 2.84 and 8.02 times in comparison to the smooth tube, respectively, of the tube with alternate-axes and trapezoidal wings for a wing-chord ratio of 0.3. The highest TEE of 1.42 was achieved of the tube with alternateaxes and trapezoidal wings at constant pumping power.

Some attempts have been made to improve the heat transfer enhancement performance using perforated tapes with reasonable increment in pressure drop. Several research studies, such as perforated selfrotating twisted tapes [24], perforated helical twisted tapes [25], multiple square perforated twisted tapes [26], perforated twisted tapes [1, 27, 28] and perforated double counter twisted tapes [12] have been conducted to investigate the thermo-hydraulic performance characteristics of a heat exchanger tube. Zhang et al. [24] conducted an experimental investigation of perforated self-rotating twisted tapes on thermal performance characteristics of a double pipe heat exchanger with different perforation ratios. The results indicated that the Nusselt number and pressure drop increased with increase in perforation ratio. Also, the maximum TEE of 1.101 was achieved for a perforation ratio of 6.46% with perforated self-rotating twisted tapes. Nanan et al. [25] experimentally investigated the effect of perforation pitch ratio of perforated helical twisted-tapes (P-HTTs) on heat transfer, friction factor and thermal performance characteristics in a circular tube under constant heat flux condition. The experimental results demonstrated that the heat transfer, fluid friction and TEE increased with increase in perforation pitch ratio. Moreover, the maximum TEE of 1.28 was achieved using the P-HTT insert for a perforation pitch ratio of 2.0 at constant pumping power. An experimental study was conducted to investigate the effect of multiple square perforated twisted tapes (MSPTTs) on heat transfer and friction factor of a heat exchanger tube for different perforation width and twist ratios, and for a wide range in Reynolds number from 5000 - 27,000 [26]. The heat transfer and friction factor of the tube with MSPTTs were found to be 5.92 and 7.89 times higher compared to the smooth tube for perforated twist ratios of 2.5 and 2.0, respectively, and a width ratio of 0.25. An experimental study was conducted to investigate the effects of the PTTs on heat transfer, pressure drop and thermal performance characteristics of a heat exchanger tube under constant heat flux condition with different twist, diameter and pitch ratios [28]. The highest heat transfer and friction factor results of 86.7 and 425% were achieved in comparison to the plain tube, respectively, at a twist ratio of 3.0, pitch ratio of 0.4 and diameter ratio of 0.17. The highest TEE of 1.07 5

was obtained with a twist, pitch and diameter ratios of 3, 0.4 and 0.11, respectively. An experimental investigation of PTTs on heat transfer and pressure drop characteristics in turbulent flow region under constant heat flux condition for a wide range in Reynolds number (13,000 – 52, 000) in a circular tube was conducted by Ahamed et al. [29]. The heat transfer and pumping power of the tube equipped with PTT were found to be 5.5 and 1.8 times higher compared to the plain tube, respectively, at a porosity of 4.6%. Bhuiya et al. [1, 12] experimentally studied the effect of porosity (Rp) on heat transfer and friction factor characteristics of the tube fitted with PTTs and perforated double counter twisted tapes (PDCTTs) in turbulent flow region under uniform heat flux condition. The results of the tube installed with PTT and PDCTT indicated that the maximum heat transfer, friction factor and TEE were obtained at porosities of 4.5 and 4.6%, respectively. The results of heat transfer and friction factor were found to be 110 – 340 and 80 – 290%, 110 – 360 and 111 – 335% higher of the tube fitted with PTT and PDCTT for porosities of 4.5 and 4.6% with compared to the plain tube, respectively. In addition, the highest TEEs of 1.70 and 1.44 were achieved of the tube with PTT and PDCTT for the porosities of 4.5 and 4.6%, respectively. Apparently, it can be noted that the heat transfer enhancement devices improved the thermal performance of heat exchanger systems, where the friction also unavoidably increased which resulted in higher pumping cost. It is a difficult job for the researchers to select a twisted tape with proper geometric configuration for obtaining a higher enhancement in heat transfer with reasonable pressure loss penalty.

Although lot of studies have been conducted on heat transfer and fluid friction characteristics in a circular tube using different types of inserts by several researchers; however, there was no study concerning the effects of porosity (Rp) of PTTT swirl generator (SW) on thermo-hydraulic performance characteristics of a tube heat exchanger in turbulent flow region. In this study, a new geometric configuration of PTTT swirl generators with four different porosities (1.2, 4.6, 10.4 and 18.6%) was employed as a swirl flow device to investigate the effects of porosity (Rp) on heat transfer as well as fluid friction characteristics of a tube heat exchanger. It is predicted that PTTT swirl generator can generate the intense swirl and vortex flow inside the tube, enhance the turbulence intensity near the tube wall and increase the residence time of the fluid in the tube which results in improvement of the heat transfer rate significantly. Therefore, the aim of this study is to investigate the effects of porosity (Rp) on heat transfer as well as fluid friction characteristics of a tube heat exchanger fitted with PTTT swirl generators for Reynolds number ranging from 7,250 – 49,800 under uniform heat flux condition. The results of heat transfer and friction factor were also compared with those obtained for a plain tube. The second objective of this study is to evaluate the thermal enhancement efficiency (TEE) of the tube equipped with PTTT swirl generators based on constant blower power for determining the practical 6

applicability of PTTT swirl generators. Finally, to establish the empirical correlations of heat transfer, friction factor and TEE using the data obtained from the experiment for predicting the heat transfer, friction factor and TEE, respectively.

During the investigation, some assumptions were considered for making the experiments simple, and also for easy data analysis and comparison. These were:  The non-dimensional parameters, such as Reynolds number, Nusselt number and friction factor were calculated considering the inner diameter Di  rather the hydraulic diameter (Dh) of the tube.  At atmospheric pressure, the local bulk fluid temperature (Tbx) was considered to calculate the fluid properties.  The transaction of heat from the wall of the tube to the fluid was considered solely by forced convection, though there were contact points between the insert and the inner surface of the tube. Therefore, there was a possibility of occurring conduction heat transfer by the inserts. It was impossible during the experimental data analysis to quantify this and there was also heat conduction happened from the tip of the test segment to the nearby portions.

2. Data acquisition The heat transfer and friction loss were calculated from the experimental data that were measured during the experiment for both the tube with inserts and without the insert. In a condition of uniform heat flux around the test segment the experiment was performed and the data were measured at a steady state condition. The velocity of the fluid in the test section was estimated as

V

m ρ b Ax

(1)

The heat supplied by electrical heating was determined as

Qt  Vv I

(2)

The heat received by the fluid was 3% lesser than the heat supplied by the electrical winding which was because of the loss of heat ( Qloss ) from the wall of the tube. The heat loss ( Qloss ) through the insulation was estimated by measuring the average wall and ambient temperature and determined as 1 _ 3% of the entire heat provided.

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So, the actual supplied heat was

Q1  Qt  Qloss

(3)

The rate of heat transfer of the fluid when flowing into the test tube was

Q2  m C p T0  Ti 

(4)

The heat flux was estimated as

q

Q Di L

(5)

where Q is the average rate of heat transfer The heat transfer coefficient was obtained as

h

q Tw  Tb 

(6)

The mean Nusselt number was obtained as

Nu 

hDi k

(7)

The friction factor was calculated as

f

P  L  V 2    b 2  Di 

  

(8)

The porosity of the tape was obtained from

 2 ds 4 Rp  Lt Wd N

(9)

3. Experimental facility

In the experimental arrangement, there were four parts which include the inlet part, test segment, air supply system, and heating system. The details of the experimental arrangement are exhibited in Fig. 1 [1, 17]. The inlet part which was 533 mm long was built up as an undivided segment of the test tube in the experimental facility to avert any flow disruptions in the upstream side, separation, stratification and to obtain a fully developed flow regime in the test segment according to the suggestions of Owner and Pankhurst [30]. The photographic view of the experimental setup is shown in Fig. 2. The details explanation of the experimental apparatus were previously demonstrated by Bhuiya et al. [1, 12, 19].

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Fig. 1. Schematic diagram of the experimental facility

The details explanation of the experimental apparatus were previously demonstrated by Bhuiya et al. . Fig. 3(a) and (b) illustrates the geometric configuration of the test tube with the PTTT insert and the geometry of the PTTT, respectively. The test segment was made of brass with an inner diameter (Di), outer diameter (Do), and length (L) of 70 and 90, and 1500 mm, respectively. PTTTs were made of mild steel with geometric dimensions of length (Lt) 1500, width (Wd) 32.5, and thickness (t) 1 mm. The tapes were fabricated with four different porosities (Rp) which include 1.2, 4.6, 10.4 and 18.6% with analogous pore diameters (ds) of 2, 4, 6 and 8 mm, respectively. In each of the tape, total no of rows in lengthwise was considered 3 and each row contains 60 pores, hence the total no of pores in each tape was considered 180 in calculating the porosity. For both axially and transversely, the distance between two continuous holes of each of the tape was kept 25 and 16.25 mm, respectively. The twist ratio (y = P/Wd, where, P is the pitch length and Wd is the width of the tape) of 1.92 was selected for all the investigated samples as this provided the greater heat transfer performance [1, 12, 19]. Then the test tube was heated in such a way so that it maintained the constant heat flux boundary condition. The variable voltage transformer was applied to control the power and to sustain an identical heat flux boundary condition through the total length of the test tube.

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Fig. 2. The photographic view of the experimental setup

To minimize the convective heat loss an adequate insulation system was maintained on the outer surface of the test tube. Three measurement systems were performed which were temperature, pressure drop and flow rate to evaluate the heat transfer, friction loss and TEE features of the test segment during the experiment. The local surface temperatures of the test tube at sixteen different points were measured with the aid of sixteen K-type thermocouples which were tapped along the test section. The resistance temperature detectors (RTDs) were applied to measure the bulk fluid temperatures.

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Fig. 3. (a) Geometry of the test section fitted with PTTT insert; (b) Geometric parameters of the PTTT insert. Prior to conduct the experiment, the thermocouples were calibrated first, then these were employed to measure the temperatures along the test segment. The wall and bulk fluid temperatures were recorded with the aid of a data logger. An inclined U-shape manometer tube was applied to measure the pressure drop of the test segment for evaluating the fluid friction features. To ascertain the precise measurement of the pressure drop especially, for the low-pressure drop a manometric fluid with a high specific gravity (0.855) was used in the manometer. The data (heat transfer and pressure drop) of the test tube were measured in identical heat flux and an isothermal flow condition during the experiment, respectively. The air flow rate through the test segment was measured with the assistance of an orifice meter which was manufactured on the basis of the ASTM standard [31]. Prior to performing the investigation, the orifice meter was calibrated first with the help of a hot-wire anemometer. The investigations were performed in a fully developed regime of the turbulent flow for Reynolds number ranging from 7,250 – 49,800. During the experiments, all the data (temperature, pressure drop and flow rate) were taken at steady state condition.

To check the accuracy of the apparatus that was applied to perform the experiment and its operation, the uncertainty of the data achieved from the experiment especially, for non-dimensional parameters, such as Reynolds number, Nusselt number and friction factor were calculated. A more precise method in

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estimating uncertainty for experimental results is demonstrated by Kline and McClintock [32]. The uncertainties of the experimentally measured quantities were estimated as per suggestions of Kline and McClintock [32]. The uncertainties of ± 1.6, ± 2.8 and ± 2.4% were achieved for Reynolds number, Nusselt number, and friction factor, respectively. The uncertainty analysis is presented in Appendix A.

4. Results and discussion

The current study investigated the effect of PTTTs on heat transfer, friction loss and TEE with different porosities (Rp) (1.2 –18.6%) for variation in Reynolds number (7,250 – 49,800). The correlations of Gnielinski [33] and Petukhov [34] were applied to verify the data of Nusselt number and friction factor of the smooth tube, in order to check the accuracy of the data of the experiment. The smooth tube’s data were considered as a reference simultaneously with the test tube’s data with inserts to calculate the heat transfer, friction factor, and TEE.

4.1. Verification of results of the smooth tube

The heat transfer results were termed as Nusselt number, whereas, the pressure loss results were considered as friction factor in this investigation. Prior to conduct the experiment, the value of heat transfer and friction loss of the smooth tube were evaluated to confirm the credibility of the experimental facility as well as measurement techniques in the range of interest [2]. Gnielinski [33] and Petukhov [34] correlations were used to compare and validate the data of the smooth tube as illustrated in Fig. 4(a) and (b) [1]. The figure shows that the data of the smooth tube for both the heat transfer and friction factor are well aligned with those obtained from the above-mentioned correlations within data limit of ± 5% and ± 4%, which certify the exactitude of the experimental setup as well as the measurement techniques.

The correlations of heat transfer and friction factor of the smooth tube data obtained from the experiment are pointed out below, respectively:

Nu  0.0137 Re 0.843 Pr 0.33

(10)

f  0.431Re 0.292

(11)

12

(a)

(b) Fig. 4. Verification of the plain tube: (a) Nusselt number and (b) friction factor. 13

4.2. Effect of PTTT insert

The effect of PTTTs and TTTs on heat transfer features is given in Fig. 5(a) in terms of Nusselt number. In the general case, the Nusselt number and Reynolds number are linearly proportional. The reason behind the linear proportional relationship between them could be due to the increment in turbulent intensity, which also amplified the convective heat transfer. The use of PTTT swirl generator significantly enhanced the heat transfer with variation in Reynolds number. Compared to the plain tube, the Nusselt number of the tape when inserted into the tube was found significantly higher.

The fact behind this could be the generation of a secondary or swirl flow with a relatively large flowing path through the tube with intensive mixing of the fluid as well as the creation of the pressure gradient along the radial direction. Moreover, a significant heat transfer augmentation has occurred for the mixing of fluid persuaded by the produced centrifugal force between the core area and wall [1]. The residence time, as well as the mixing of the flow between the core area and tube surface, was amplified with the insertion of twisted tape which played as an incessant swirl flow device across the full extent of the test segment [35]. This swirling was generated due to the destruction in the hydrodynamic and thermal boundary layer as well as an increment in the flow velocity [36]. The swirl flow initiated by the tape inserts and the components of velocity in the radial direction of the flow created the boundary layer separation as well as enhanced the flow turbulence intensity. This caused the augmentation in heat transfer of the smooth tube in comparison to the axial flow.

Fig. 5(b) represents the effectiveness of augmentation in heat transfer of the tube with PTTTs and TTTs in comparison to the smooth tube which is termed as (Nup/Nus). The value of (Nup/Nus) for every case was found higher than one which validated the reason for using the PTTT insert over the smooth tube. The value of (Nup/Nus) also tended to decrement with an increment in Reynolds number which could be because of the less influence of PTTT insert. In addition, this was due to the fact that the influence of tape inserts with rising turbulence intensity was more dominant at lower Reynolds number compared to the higher ones. The heat transfer results of PTTTs were compared with other previously published results to comprehend the effects of PTTTs on heat transfer which are shown in Fig. 6.

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320 280

Nusselt Number, Nu

240

Rp = 1.2% Rp = 10.4% y = 1.92 y = 4.81 Plain tube

Rp = 4.6% Rp = 18.6% y = 2.88 y = 6.79

200 160 120 80 40 0 5000

15000

25000 35000 45000 Reynolds number, Re

55000

(a)

4.5 4

Nup/Nus

3.5

Rp = 1.2%

Rp = 4.6%

Rp = 10.4%

Rp = 18.6%

y = 1.92

y = 2.88

y = 4.81

y = 6.79

3 2.5 2 1.5 5000

15000

25000 35000 45000 Reynolds number, Re

55000

(b) Fig. 5. The relationship between the Nusselt number and Reynolds number: (a) Nu and (b) Nup/Nus 15

440 380

Rp = 4.6% (PTTE) a/Wd = 2.5 (MSPTT) y = 3.0 (DTT) y = 2.5 (TCoTT)

Rp = 4.6% (PDCTT) y = 1.95 (DCTT) y = 2.5 (TCTT)

Nusselt Number, Nu

320 260 200

140 80 20 5000

10000

15000 20000 Reynolds number, Re

25000

30000

Fig. 6. Comparison of Nusselt number with Reynolds number for different previous studies

The variation in pressure drop with Reynolds number for both PTTTs and TTTs is presented in Fig. 7. The pressure drop was increased with increase in Reynolds number. The similar trend was also found for the plain tube. As expected, the higher pressure drop was observed of the tube with PTTTs in comparison to the plain tube. This is due to the intense swirl flow, high loss of viscosity and blockage of the flow inside the tube of the tube with inserts. Moreover, the high loss of pressure inside the tube could be due to the interaction between the pressure forces and inertial forces at the boundary layer. The pressure drop was found to be 107 - 353% higher compared to the smooth tube of the tube equipped with PTTTs.

Fig. 8(a) exhibits the friction loss features of the tube with PTTTs and TTTs. This depicts the variation in friction loss with Reynolds number ranging from 7,250 – 49,800 for different porosities (1.2 – 18.6%). As shown in Fig. 8(a), the trend of the curve for both the tube with insert and the plain tube is similar. In general, the friction factor is progressively decremented with increment in the Reynolds number.

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Pressure Drop, ΔP (N/m2)

320 280

Rp = 1.2% Rp = 10.4% y = 1.92 y = 4.81 Plain tube

Rp = 4.6% Rp = 18.6% y = 2.88 y = 6.79

240 200 160 120 80 40 0 5000

15000

25000 35000 45000 Reynolds number, Re

55000

Fig. 7. Variation in pressure drop with Reynolds number for both PTTTs and TTTs

The explanation behind this phenomena could be the occurrence of vortices backward of the tape due to the high friction forces created by air passing around the tape at low Reynolds number. As expected, the tube with tape inserts showed a higher friction factor compared to the plain tube. There were several vital factors behind the higher friction loss in the tube with inserts, such as, increased in heat transfer surface area, increased in swirl intensity and the loss of high viscosity near the surface of the tube that also caused the blockage of the flow [37].

The variation in friction factor ratio (fp/fs) with Reynolds number for different porosities of the tube with PTTTs and TTTs is illustrated in Fig. 8(b). The value of (fp/fs) gradually decremented with increment in Reynolds number for both cases (with and without insert) as shown in the figure. However, the decrement in friction loss has become relatively small as the flow rate of the heated air mass was increased [35]. The friction factor results were compared with the previous studies which is presented in Fig 9.

17

0.16

Rp = 1.2% Rp = 10.4% y = 1.92 y = 4.81 Plain tube

Friction factor, f

0.13

Rp = 4.6% Rp = 18.6% y = 2.88 y = 6.79

0.10

0.07

0.04

0.01 5000

15000

25000 35000 45000 Reynolds number, Re

55000

(a)

5.00 Rp = 1.2% Rp = 10.4% y = 1.92 y = 4.81

4.50 4.00

Rp = 4.6% Rp = 18.6% y = 2.88 y = 6.79

fp/fs

3.50 3.00 2.50 2.00 1.50 5000

15000

25000 35000 45000 Reynolds number, Re

55000

(b) Fig. 8. The relationship between the friction factor and Reynolds number: (a) f and (b) fp/fs. 18

0.35

Rp = 4.6% (PTTE) Rp = 4.6% (PDCTT) Rp = 4.5% (PTT) a/Wd = 2.5 (MSPTT) y = 1.95 (DCTT) y = 3.0 (DTT) y = 2.5 (TCT) y = 2.5 (TCoT)

0.31

Friction factor, f

0.27 0.23 0.19 0.15 0.11 0.07 0.03 5000

10000

15000 20000 25000 Reynolds number, Re

30000

Fig. 9. Comparison of friction factor with Reynolds number for different previous studies

4.3. Effect of porosity (Rp)

Fig. 5(a) and (b) exhibits the effect of porosity on heat transfer performance characteristic of the tube with PTTTs and TTTs. This figure depicted the enhancement in heat transfer with decreasing porosity of the tube with insert except for 1.2%. The reason behind this could be the less swirling effect was produced due to the higher perforation, whereas, the low perturbation in the flow field was produced due to the lower perforation the of the tape [29]. Thianpong et al. [38] reported that the heat transfer result increased with decreasing diameter ratio (ratio of hole diameter to the width of the tape). The reason behind this was at the larger hole diameter, the flow has been considered to be more analogous to the axial flow directing to the loss of swirl intensity delivered to the flow between the tape and tube wall. However, the stronger swirl intensity was generated at a porosity of 4.6%. This led to the more effective breakdown of the boundary layer to the path of the flow, which could transfer the heat expeditiously over a thin boundary layer [1].

Moreover, the heat transfer duration between the working fluid and the tube surface was extended due to the increase in residence time of the flow with the increase in the intensity of swirl flow. Over the 19

range of investigated porosities (1.2 – 18.6%), the value of heat transfer with PTTT inserts was obtained 88 – 320% higher compared to the value of the plain tube. Among the range of studied porosities, the highest result of heat transfer (Nusselt number) which was 320% higher was provided by the tape with a porosity (Rp) of 4.6% and the result was found to be 132 – 320% higher compared to the smooth tube. The heat transfer of the tube with PTTT inserts was achieved to be 28 - 54% higher in comparison to TTT inserts [19] at comparable Reynolds number as shown in Fig. 5 (a) and (b). The higher heat transfer could be attributed to the higher intensity of swirl flow or vortex strength generated by PTTT. The higher interaction between the swirl flows directed to produce better mixing of fluid, resulting in uniform fluid temperature in the tube, and therefore, provided a more efficient heat transfer. Chang et al. [39] showed that the tube fitted with twin twisted tapes provided 19 – 33% higher heat transfer enhancement in comparison to the single twisted tapes for a specific range of Reynolds number (3000 ≤ Re ≤ 14,000).

The results of the present work were compared with PDCTT insert [12], DCTT insert [17], dual twisted tape (DTT) insert [37], MSPTT insert [26], twin counter twisted tape (TCTT) insert [36], twin cotwisted tape (TCoTT) insert [36]. The results of heat transfer with PTTT insert at a porosity of 4.6%, were found to be 10, 23 and 160% higher in comparison to PDCTT [12] at a porosity of 4.6%, DCTT [17] at a twist ratio of 1.95, and DTT [37] at a twist ratio of 3.0, respectively, at comparable Reynolds number as presented in Fig. 6. However, the results of PTTT insert (Rp = 4.6%) were 84, 87 and 41% lower compared to MSPTT [26] at a perforation width ratio of 2.5, TCTT [36] at a twist ratio of 2.5, and TCoTT [36] at a twist ratio of 2.5, respectively, at comparable Reynolds number (Fig. 6).

The higher pressure drop was observed with the tube with PTTTs compared to TTTs as shown in Fig. 7. This could be due to the effect of stronger swirl and the turbulence flow inside the tube. The highest pressure drop was occurred for the tape with a porosity of 4.6%. The pressure drop of the tube with PTTT was achieved to be 42 – 62% higher compared to TTT.

The influence of porosity on friction factor characteristics of the tube with PTTTs and TTTs for a wide range in Reynolds number is demonstrated in Fig. 8(a) and (b). The trend of curves shown in Fig. 8(a) and (b) is similar and inversely proportional to the porosity except for 1.2%. This provided a strong motivation to use the PTTT as an insert which created strong turbulence or swirl flow inside the tube. At porosity of 4.6%, the friction factor was found maximum than the other porosities. Compared to the smooth tube, the friction factor of the tube with PTTTs was obtained to be 112 – 355% higher over the range studied. The friction loss of the tube using tape with a porosity of 4.6% was obtained 175 – 355% 20

higher than the values of the smooth tube over the specific range of data. Thus, it is obvious that the PTTT insert has a clear effect on friction factor and this could be illustrated comparing to the previous results. The friction factor values of the tube with PTTT inserts were found to be 41 –50% higher in comparison to TTT inserts [19] at comparable Reynolds number as presented in Fig. 8 (a) and (b). This is a consequence of the repeated actions of the intense intensity of swirl or vortex in the tube with PTTTs. The friction factor with twin twisted tapes was obtained to be 120 – 135% higher compared to the single twisted tape within the turbulent flow region [39].

The results of friction factor with PTTT insert were compared with PDCTT insert [12], DCTT insert [17], DTT insert [37], MSPTT insert [26], TCTT insert [36], TCoTT insert [36]. The results indicated that the friction factor of PTTT insert (Rp = 4.6%) was 188, 97 and 45% lower compared to MSPTT [26] at a perforation width ratio of 2.5, TCTT [36] at a twist ratio of 2.5, and ToCTT [36] at a twist ratio of 2.5, respectively, at comparable Reynolds number as presented in Fig. 9. Whereas, the friction factors of the tube with PTTT insert at a porosity of 4.6% were 10, 5, 18 and 22% higher in comparison to PDCTT [12] at a porosity of 4.6%, PTT [1] at a porosity of 4.5%, DCTT [17] at a twist ratio of 1.95, and DTT [37] at a twist ratio of 3.0, respectively, at comparable Reynolds number (Fig. 9).

5. Performance evaluation The enhancement in heat transfer in terms of TEE was evaluated at equal blower power in order to judge the practical benefits of using the PTTTs into the tube heat exchanger. The mathematical relationship in terms of the pressure loss and the volumetric flow rate between the smooth tube and tube with tape insert [40] at constant blower power may be expressed as:

V P s  V P p

(12)

Further, it may be considered as:

 f Re    f Re  3

3

s

(13)

p

1

 f p 3   Re s  Re p    fs 

(14)

where Res is the equivalent Reynolds number of the smooth tube and Rep is the equivalent Reynolds number of the tube with insert The TEE (η) can be defined as the ratio of heat transfer (Nu) (with and without insert) to the ratio of friction factor (with and without the insert) at constant blower power. TEE was estimated at an identical

21

blower power of the tube fitted with PTTTs relative to the smooth tube [1, 17, 19, 21, 36, 41-45] according to the following equation (Eq. (15)): Nu p Nu s



(15)

1 f p 3

    f   s 

From Eqs. (11), (14) and (21), the Res may be stated as a function of Rep which is expressed below:





Re s  1.364515. 0.0032 R p  0.0942 R p  0.272 R p  19.849 Re p

0.0000110782R

3 p

3

2



0.369273

.

 0.0003323R p 2  0.002917R p  0.896042

(16)

The thermal performance factor or TEE which demonstrates the practical applications and benefits of using the tape inserts. TEE was evaluated to assess the net energy gain for all the cases (tube with inserts) using Eq. (15) at constant blower power. Fig.10. indicates the variation in TEE with the Reynolds number of the tube with PTTTs and TTTs for several porosities (Rp) of 1.2, 4.6, 10.4 and 18.6%. With increasing porosity (Rp) and Reynolds number, the TEE was decreased except for 1.2% as shown in Fig. 10. For all the investigated porosities (Rp), the TEE was found more than one which indicated the advantages of the tapes in terms of energy savings [23]. Moreover, it could be attributed to the effect of increasing friction compared to the augmentation in heat transfer was less dominant and vice versa due to the presence of swirl generator [21]. With increasing Reynolds number the TEE was decreased for all the investigated cases. Over the range investigated, the TEE with tape inserts was observed from 1.13 – 1.5 relative to the plain tube. Throughout the studied, PTTT insert at a porosity of 4.6% offered the maximum TEE in comparison to others (Rp = 1.2, 10.4 and 18.6%). The maximum TEE of 1.5 was achieved of the tube with PTTT insert at a porosity of 4.6%. The TEE of the tube with PTTT inserts was found to be 3 – 13% higher compared to TTT inserts [19] at comparable Reynolds number as shown in Fig. 10. Although the use of PTTT provided a reasonable increase in friction factor in comparison to the use of TTT, a considerable increase in heat transfer results in higher TEE compared to TTT. TEE results of the present investigation were compared with the previous studies which are shown in Fig. 11.

The results of TEE with PTTT insert (Rp = 4.6%) were found to be 5, 12, 39, 10 and 37% higher in comparison to the PDCTT [12] at a porosity of 4.6%, DCTT [17] at a twist ratio of 1.95, DTT [37] at a twist ratio of 3.0, TCTT at atwist ratio of 2.5, [36] and TCoTT [36] at atwist ratio of 2.5, respectively, at comparable Reynolds number as shown in Fig. 11. Whereas, the TEE with PTTT insert at a porosity of 4.6% was 10% lower compared to MSPTT [26] at a perforation width ratio of 2.5 and comparable Reynolds number (Fig. 11). 22

Thermal enhancement efficiency, η

1.6

Rp = 1.2% Rp = 10.4% y = 1.92 y = 4.81

1.5

Rp = 4.6% Rp = 18.6% y = 2.88 y = 6.79

1.4 1.3 1.2 1.1 1.0 5000

15000

25000 35000 45000 Reynolds number, Re

55000

Fig. 10. The relationship between the thermal enhancement efficiency and Reynolds number

Thermal enhancement efficiency, η

5.5

4.5

3.5

Rp = 4.6% (PTTE) Rp = 4.6% (PDCTT) a/Wd = 2.5 (MSPTT) y = 1.95 (DCTT) y = 3.0 (DTT) y = 2.5 (TCT) y = 2.5 (TCoT)

2.5

1.5

0.5 5000

10000

15000

20000

25000

30000

Reynolds number, Re Fig. 11. Comparison of thermal enhancement efficiency with Reynolds number for different studies

23

6. Correlations In this study, the tests were conducted under a condition of identical heat flux with PTTTs using the air as an operational fluid. The correlation of Nusselt number (Nu) was developed based on the following Colburn (Dittus-Boelter correlation [46]) equation: Nu = C Rem Prn

(17)

The correlation of friction factor (f) was developed based on the following Colburn (Blasius relation [46]) equation: f = C Rem

(18)

and the correlation of TEE was developed according to Webb [44] and Gee and Webb [45] following correlation at constant pumping power:

Nu Performance evaluation criteria (PEC) 

Nus

(19)

1

 f 3    fs  The correlations of Nusselt number (Nu), friction factor (f) and TEE (η) as shown in Eqs. (20) – (22), respectively, were established for variation in Reynolds number (7,250 – 49,800) and porosity (1.2 – 18.6%). Using the data obtained from the experiment, these correlations were proposed as a function of Rp, Re and Pr.





Nu  0.0003R p  0.0093R p  0.0523R p  0.8087 . Re 3

2

 0.000002R

3 p

 . Pr 0.33

0.00002R p 2 0.0013R p 0.525

(20)





f  0.0032R p  0.0942R p  0.272R p  19.849 . Re 3

2

0.00003R

3 p



0.0009R p 2  0.0079R p 0.5735

(21)

Applying Eqs. (10), (15), (16) and (20), the TEE can be expressed as:

  41.176.C.C10.6802. Re p 0.000018406R



3 p



0.00063218R p 2 0.00407R p 0.12652

(22)



where C  0.0003R p  0.0093R p  0.0523R p  0.8087



3

2



and C1  0.0032 R p  0.0942 R p  0.272 R p  19.849 3

2

The predicted vs. experimental relationships of heat transfer, friction factor and TEE are shown in Figs. 12 – 14, respectively, at which the predicted data were obtained from the above-mentioned correlations (Eqs. (20), (21) and (22)) and the experimental results were obtained from the available experimental data. As shown in Figs. 12 – 14, the predicted data are well aligned with those obtained from the

24

experiment for heat transfer, friction factor and TEE within data range of + 6 to – 5%, +4 to – 6%, and +6 to – 3%, respectively.

Fig. 12. Comparison between the predicted and experimental Nusselt number.

25

Fig. 13. Comparison between the predicted and experimental friction factor.

26

Fig. 14. Comparison between the predicted and experimental thermal enhancement efficiency.

7. Conclusions In this study, the effects of porosity (Rp) of a new design PTTT swirl generator on heat transfer, fluid friction and thermal performance characteristics of a tube heat exchanger were investigated experimentally. The experiments were conducted with four different porosities (1.2, 4.6, 10.4 and 18.6%) of PTTT swirl generators in turbulent flow regime for a specific range of Reynolds number (Re = 7,250 – 49,800) under uniform heat flux condition using air as the working fluid. The results of PTTT swirl generators were compared with those obtained for a smooth tube. The results indicated that a substantial enhancement in heat transfer was achieved with a reasonable increment in friction factor using PTTTs than those of the smooth tube. A significant enhancement in heat transfer performance was obtained with PTTT insert at constant blower power relative to the plain tube. The key outcomes of this study could be concluded based on the experimental results which are as

27

follows:  As expected, with increment in Reynolds number the heat transfer characteristic was increased, whereas, the reverse aptitude was observed for the friction factor and TEE.  In terms of porosity (Rp), the characteristic results of heat transfer (Nusselt number), friction factor and TEE were increased with a decrease in porosity of the tape inserts except for 1.2%.  The Nusselt number of the tube installed with PTTT inserts for porosity ranging from 1.2 – 18.6% was found to be 88 – 320% higher compared to those of the smooth tube.  PTTT insert with a porosity of 4.6%, provided the highest heat transfer enhancement which is 320% higher in comparison to those of the smooth tube and it was achieved to be 132 - 320% higher than those of the smooth tube for this porosity.  The friction factor of the tube with PTTT inserts for porosity ranging from 1.2 – 18.6% was obtained to be 112 – 355% higher in comparison to those of the smooth tube.  PTTT insert with a porosity of 4.6%, resulting in the highest friction factor which is 355% higher and the range of friction factor for this porosity was found to be 175 – 355% higher compared to those of the smooth tube.  The TEE was evaluated based on constant blower power and the value of TEE was achieved to be 1.13 to 1.5 relative to the plain tube.  It could also be noted that the TEE at a porosity (Rp) of 4.6% was more dominant than other porosities (Rp = 1.2, 10.4, and 18.6%) and the maximum TEE of 1.5 was obtained using PTTT insert relative to the plain tube.  For all the experiments, the TEE was found above one which designated the augmentation in heat transfer was more dominant using the swirl flow enhancement device of PTTT with compared to the influence of increasing friction and contrariwise.  The correlations of heat transfer, friction factor, and TEE were established using the experimental data. It was observed that all the data (Nusselt number, friction factor and TEE) are well aligned with the experiment data that were obtained within data range of + 6 – 5%, + 4 – 6%, and + 6 – 3%, respectively.

This study indicated that insertion of a new geometric configuration of PTTT insert into the test tube is significant as this improved the thermal performance of tube heat exchanger significantly in comparison to the plain tube with an acceptable increase in energy consumption. The outcomes of this study can provide the optimal design of PTTT’s geometry for useful applications of PTTT’s in a tube heat exchanger. This study can also provide useful information to the researchers for further investigations of PTTT. For example, a flow visualization high-speed camera and smoke generator could be adopted 28

to visualize the 3D flow structure and flow behaviour inside the tube for a better understanding of the heat transfer mechanism.

Acknowledgement

The authors would like to gratefully acknowledge the Chittagong University of Engineering & Technology (CUET) for continuous assistance in this research.

29

Appendix A

According to Kline and McClintock [47], the uncertainty equation of a result R computed from the m number of measurements (X1, X2, X3, ----------, Xm) having an absolute uncertainty of WR is given by the following equation: 1

2 2 2  R  R  2   R  WR   wx1    wx 2          wxm    X 1   X 2   X m  

(23)

Where, wx1, wx2, wx3, -------- and wxn are the uncertainties of the individual variable X1, X2, X3, -----and Xm.

1. Reynolds number (Re): The uncertainty in the calculation of Reynolds number can be written as:

WRe

2 2   Re      Re   wm    wDi      Di  m  

1/ 2

= ± 119.6

Percentage uncertainty (%) of Reynolds number 

WRe 119.6  = ±1.6% Re 7475

2. Nusselt number (Nu): The uncertainty in the calculation of Nusselt number can be written as: 1/ 2

2 2 2 2  Nu   Nu   Nu   Nu   WNu   wQ    wL    wTw    wTb   = ±2.2526   Tb    Q   L   Tw W 2.2526 Percentage uncertainty (%) of Nusselt number  Nu   = ±2.8% Nu 80.45

3. Friction factor (f): The uncertainty in the calculation of friction factor can be written as: 2 2 2 2  f   f   f   f   W f   wP    wV    wL    wDi     V   L   Di    P

Percentage uncertainty (%) of friction factor 

30

Wf f



1/ 2

= ±0.002887

0.002887 = ±2.4% 0.120302

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Nomenclature a

perforated width

TR

twisted ring

Ax

RTD

resistance temperature detector

SW

swirl generator

DCTT Di Dh Do

the cross-sectional area of the test section [m2] specific heat at constant pressure [J/(kg K)] double counter twisted tape tube’s inside diameter [m] hydraulic diameter tube’s outer diameter [m]

t TCTT TCoTT

Tb

tape thickness twin counter twisted tape twin co-twisted tape mean bulk temperature [K]

ds

pore diameter of the tape [m]

Tw

mean wall temperature [K]

dual twisted tape friction factor, dimensionless convective heat transfer coefficient [W/(m2 K)] I current [ampere] k thermal conductivity [W/(m K)] L tube length [m] Lt tape length [m] mass flow rate [kg/s]  m MSPTT multiple square perforated twisted tape

Tbx V

local bulk fluid temperature [K] mean velocity in the test section [m/s] Mass velocity [kg/m2]

Cp

DTT f h

V

Vv voltage supplied [volt] Wd tape width [m] y twist ratio Rp porosity, dimensionless Greek symbols η thermal enhancement efficiency, dimensionless N no of pores ρ density [kg/m3] PDCTT perforated double counter twisted tape Subscripts PTT perforated twisted tape b bulk PTTT perforated triple twisted tape i inlet ΔP pressure drop along the length of the o outlet 2 tube [N/m ] Q average heat transfer rate [W] p tape inserts 2 q heat flux [W/m ] s plain Qloss heat loss [W] w wall Qt supplied total heat [W] Dimensionless numbers Q1 actual heat supplied [W] Nu Nusselt number, dimensionless SRTT self-rotating twisted tape Pr Prandtl number, dimensionless TEE thermal enhancement efficiency Re Reynolds number, dimensionless Ti inlet temperature [K] Rep equivalent Reynolds number for the tube with tape inserts, dimensionless To outlet temperature [K] Res equivalent Reynolds number for the plain tube, dimensionless

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 The effect of PTTT insert on thermal performance characteristics was investigated.  The heat transfer rate was increased from 88 – 320% compared to the plain tube.  The friction factor was increased from 112 – 355% in comparison to the smooth tube.  The maximum TEE of 1.5 was achieved using the PTTT insert at constant blower power.  The correlations of heat transfer, friction loss and TEE with PTTT were developed.

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Declaration of interests ☒ 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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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