







































I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

20 

 

 

 

Article 

Advanced passive heat transfer enhancement: 

numerical analysis of TiO₂-water nanofluid flow in 

tubes fitted with twisted tape and conical ring 

inserts 
Itquan Hossen*, Prasanjit Das, Ashraful Zannat Akhi 

Department of Mechanical Engineering, Chittagong University of Engineering and Technology, Chittagong-4349, 

Bangladesh 

A R T I C L E   I N F O 
 

Article history: 
Received 10 September 2025  
Received in revised form 
25 October 2025 
Accepted 09 November 2025 
 
Keywords: 
Twisted tape, TiO2 nanofluid,  
Passive heat transfer enhancement, Friction factor, 
Nusselt number, Thermal performance factor 
 
*Corresponding author 
Email address:  
itquan2013@gmail.com 
   
DOI: 10.55670/fpll.fuen.5.1.3 

A B S T R A C T 
 

The primary objective of this study is to investigate the heat transfer 
enhancement, friction factor, and thermal performance factor of a plain tube 
with single and double twisted tapes, combined with a semicircular cut with 
and without dimples, a perforated V-cut, and conical rings, using a TiO2-water 
nanofluid. Numerical simulations of tube flow and heat transfer were 
conducted. The nanofluid used in the simulations contains TiO2 nanoparticles 
at concentrations of 0.5% and 1.5% by volume. The nanofluid inlet temperature 
was set at 300 K, and boundary conditions were applied. The maximum heat 
transfer coefficient increases from plain tube to 88.2% and 71.42% at double 
twisted tape with perforated V-cut and semi-circular cut, respectively, with 
dimples in 0.5% and 1.5% TiO₂ concentrations. The maximum Nusselt number 
increased by 115.53% and 100.9% at double twisted tape with perforated v-cut 
and semi-circular cut with dimples compared to the plain tube in 0.5% and 
1.5% TiO2 concentrations, respectively. The simple tube with a perforated V-cut 
and a conical ring insert exhibits a 94.44% higher friction factor at a 1.5% TiO2 
concentration. The maximum thermal performance factor was found to be 2.04 
for double twisted tapes at a 0.5% TiO2 concentration. Additionally, this study 
presents contour plots of the velocity distribution, pressure distribution, 
temperature distribution, and turbulent kinetic energy. 

 
1. Introduction  

In thermal engineering, a device used for transferring 

thermal energy between fluids, whether that's between a 

solid surface and a liquid or between solid particles and a gas, 

is called a heat exchanger. Without the exchange of work or 

the application of external heat, these machines are used in 

heating, cooling, evaporation, condensation, and heat 

recovery [1]. Heat exchange performance improvement is of 

special significance, as improved heat transfer performance 

can translate into more compact systems, lower costs, and 

substantial energy savings [2,3]. Heat transfer improvement 

techniques are an effective way to realize these advantages. 

Active, passive, and compound are three significant 

classifications of heat transfer improvement methods. Active 

techniques involve the application of external sources of 

power, such as fluid injections, electric or magnetic fields, 

mechanical assistance, or surface vibration, to enhance heat 

transfer. Passive techniques utilize turbulators, roughened 

surfaces, fine surfaces, coiled tape, dimples, and protrusions 

or nanofluids to enhance the thermal efficiency of the system 

without introducing any supplementary energy. To attain 

greater heat transfer rates than by each method alone, 

composite techniques combine active and passive solutions 

[4,5]. Passive solutions include twisted tape inserts, which 

have received substantial attention due to their ease of 

application, economy, and simplicity of installation [6]. Strips 

of metal are shaped into particular geometries and placed in 

fluid flow conduits to improve heat transfer. These inserts 

create interference with the thermal boundary layer, 

increasing convective heat transfer through swirl flow and 

turbulence. They also lead to a pressure drop, and hence a 

compromise between heat transfer improvement and 

frictional loss is unavoidable. To maximize thermal 

performance and minimize pressure loss, various twisted 

tape geometries have been investigated in recent studies [5].  

 

 

Future Energy 

Open Access Journal 

https://doi.org/10.55670/fpll.fuen.5.1.3 

 

 

 

 

 

 

 

 

February 2026| Volume 05 | Issue 01 | Pages 20-29 

Journal homepage: https://fupubco.com/fuen 

 
ISSN 2832-0328 

mailto:itquan2013@gmail.com
https://doi.org/10.55670/fpll.fuen.5.1.3
https://fupubco.com/fuen


I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

21 

 

The following is an overview of recent studies that 

investigate the thermal performance outcomes of various 

twisted tape designs. Wongcharee et al. [6] examined the 

thermal-hydraulic behavior of U-cut twisted tapes (U-TTs) 

under homogeneous heat flow conditions when inserted into 

a circular tube. Their work focused on twist ratios (y/w = 3.5 

and 4.0) and U-cut ratios (s/t = 0.5 to 3.0). The thermal 

performance factor (TPF) was found to be 1.28 when s/t = 0.5 

and y/w = 3.5, which was better than any other configuration. 

They observed that U-TTs with smaller U-cut ratios (s/t = 0.5 

to 2.0) exhibited a significantly higher Nusselt number 

compared to regular twisted tapes. For U-TTs, however, 

friction losses were regularly larger than for standard tapes 

[6]. Li et al. [7] quantitatively investigated employing hollow 

twisted tapes for heat transfer enhancement in laminar flow. 

Their studies showed that cross-hollow twisted tapes 

enhanced general heat transfer performance by 28.1% over 

ordinary tapes. Reducing the gap between the tube and the 

twisted tape also improved heat transfer, and four unilateral 

twisted tapes at Reynolds numbers above 600 produced ideal 

performance.  

Abed et al. [8] investigated forced convection heat 

transfer in a horizontal pipe with twisted-tape inserts under 

constant heat flow using a numerical method. Their working 

fluid was water; they investigated Reynolds number (4000 ≤ 

Re ≤ 9000), twist ratio (4.0 ≤ TR ≤ 6.0), and heat flow (5000 ≤ 

q ≤ 10000 W/m²). Their results showed that V-cut twisted 

tapes with a twist ratio of 4 offered the highest thermal 

performance factor (TPF = 4.45), surpassing simple twisted 

tapes (TPF = 4.19). Promvonge et al. [9] investigated heat 

transmission in a circular tube combined with conical-ring 

and twisted-tape inserts. Their tests, using air as the working 

fluid, revealed that the combined inserts raised the Nusselt 

number by up to 367%, thanks to the formation of reverse 

and swirl flows, which improved fluid mixing. Abbasian Arani 

and Amani studied the effect of tube diameter on the heat 

transmission ability of TiO₂-water nanofluids [10].  By 

increasing turbulence, they demonstrated that tube size 

increases enhanced heat transfer and led to greater pressure 

drops.  Kumar et al. [11] also demonstrated that double V-cut 

perforated twisted tapes significantly enhanced heat transfer, 

with the optimum result achieved at a twist ratio of 2. 

Nanofluid developments in recent years have also further 

extended the scope for enhancing heat transfer. Dagdevir and 

Ozceyhan [12] conducted a comparison study utilizing plain 

tube, perforated twisted tape, and dimpled twisted tape. 

Working with mixes of ethylene glycol and water, they found 

that the concentration of ethylene glycol in the mixtures 

degraded thermal-hydraulic performance.  

For instance, Eiamsa-ard et al. [13] found that TiO₂-

water nanofluids with a volume concentration of 0.21% 

improved heat transmission by 9.9–11.2%, while Weerapun 

[14] noted that nanofluids displayed a 6–11% greater 

convective heat transfer coefficient than baseline fluids. S. 

Eiamsa-ard [15] investigated the twin-twisted-tape heat 

exchanger tube TiO2-water nanofluid heat transfer 

improvement. Heat transmission improved by 9.9-11.2% and 

thermal performance by 4.5% at 0.21% TiO2 volume 

concentration. According to a review of previous studies, 

various approaches have been employed over the years to 

optimize heat exchange performance. Passive techniques 

have previously been employed, utilizing a variety of inserts 

with different types of cuts, various types of fluids, including 

nanofluids, and surface modifications to reduce the thickness 

of the thermal boundary layer. As a result, the search for a 

suitable insert remains a significant challenge. This study 

focuses on the numerical investigation of heat transfer 

improvement with TiO₂-water nanofluid in a tube fitted with 

conical rings and modified twisted tapes. The combinations of 

twisted tapes used in this study are: single twisted tape with 

perforated v-cut (STPV), single twisted tape with semicircular 

cut (STSC), perforated v-cut twisted tape with conical rings 

(PVTC), double twisted tape with perforated v-cut and 

semicircular cut (DTT-1), double twisted tape with 

perforated v-cut and semicircular cut with dimples (DTT-2), 

and plain tube. As can be seen, these combinations of twisted 

tapes have not been used in previous studies. Therefore, the 

effect of these combinations on heat transfer enhancement 

remains unknown.  

For nanofluids, TiO2 is utilized due to its superior 

performance compared to other nanomaterials. TiO2 

nanoparticles exhibit exceptional capabilities for enhancing 

thermal conductivity in nanofluids. TiO2-water nanofluids 

have been reported to exhibit a thermal conductivity 

enhancement of up to 37% at elevated temperatures. Thermal 

conductivity for TiO2 nanofluids ranges from 4-11.8 W/m·K, 

which is significantly higher than that of most base fluids, and 

hence is extremely suitable for use in heat transfer 

applications [16,17]. The thermal stability of TiO2 is 

particularly noteworthy, as the material maintains its 

structure and function up to 1000-1200°C. This heat 

resistance is superior to that of several other nanomaterials, 

which can break down or become less effective at lower 

temperatures [18,19]. Moreover, TiO2 is non-toxic and safe 

for humans, giving it a significant advantage over other 

nanoparticles that may pose health or environmental risks. 

TiO2 nanoparticles possess fairly good dispersibility in polar 

and nonpolar base fluids, especially with the use of sufficient 

dispersants [20]. In contrast to other commonly used 

nanoparticles, TiO2 exhibits similar or improved 

performance. This study investigates the effects of heat 

transfer enhancement of STSC, STPV, PVTC, DTT-1, and DTT-

2, and assesses the Nusselt number, friction factor, and 

thermal performance factor (TPF) over a range of Reynolds 

numbers (5000–49800) and TiO₂ volume concentrations 

(0.5% and 1.5%). However, optimization of twisted tape 

design and volume concentration percentage of TiO2 in water 

are not done in this study. There is a scope for future study by 

optimizing these combinations of twisted tapes and 

nanofluids. The results of this study seek to shed light on heat 

exchanger designs for refrigeration, power plants, chemical 

processing, and electronic cooling systems. 

2. Numerical modelling 

2.1 Physical modeling 
Three types of twisted tape were used to insert into a 

plain tube. The tapes were semicircular cut, perforated V-cut, 
and semicircular cut with dimples. The working fluid used 
was a TiO2-water nanofluid with varying concentrations. The 
fluid entered the tube at a specific inlet temperature and 
flowed through the 70 mm diameter section, where the 
testing would take place. The investigation was conducted 
within the range of Reynolds numbers of 5000 to 49800. 



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

22 

 

Detailed information on the geometry is given in Table 1. 
Figure 1 shows the physical model of the plain tube, STSC, 
STPV, PVTC, DTT-1, and DTT-2. 

In this study, air will be used as the working fluid in the 

plain tube validation, and TiO2-water will be used as the 

working fluid with different concentrations. The thermo-

physical properties of TiO2 are given in Table 2. The 

properties of air are listed in Table 3, which are used as the 

defaults in ANSYS. 

Table 1. Dimensions of the physical model 

 

 

Figure 1. (a) 3D view of Plain Tube, (b) STSC, (c) STPV, (d) PVTC, (e) 

DTT-1, (f) DTT-2 

 

 

2.2 Mesh generation 
The term "mesh" refers to the abstract mathematical 

space utilized to generate polygons, tetrahedra, or hexahedra 

and other geometrical structures. Different mesh types are 

chosen based on geometric complexity, desired accuracy, and 

computational resources. Inadequate grid development, on 

the other hand, might reveal discrepancies from the intended 

mathematical design [22]. In this study, tetrahedron meshes 

were applied to the fluid domain for all of the geometries. The 

mesh size was 25 mm. A refined mesh was utilized along the 

tube wall to ensure the effect of the viscous sublayer. The first 

layer thickness inflation option was used to ensure that the y+ 

value remained below 1. Edge sizing with a particular number 

of divisions was applied to maintain meshing quality. Meshing 

criteria, such as orthogonal quality, skewness, and element 

quality, will be evaluated to determine mesh quality. Table 4 

shows the meshing elements and summary. Figure 2 

illustrates the meshing for the pipe wall, insert, and rings, 

which include holes and dimples. 

Table 2. Properties of TiO2 [21] 

 

Table 3. Properties of air 

 

Table 4. Meshing details 

 

 

 

 

 

 

 

 

 

 

Plain tube length, L 1500mm 

Tube inner diameter, d 70mm 

Twisted tape length, l 1440mm 

Tape width, w 24mm 

Tape thickness, t 2mm 

Pitch length of insert, y 48mm 

Twist ratio, TR= y/w 2 

V cut width, W 7mm 

Depth of cut 6mm 

Perforated hole diameter  6mm 

Distance Between two holes 12mm 

Radius of Semicircular Cut 6mm 

Opposite Semicircular cut 
distance 

24mm 

Diameter of dimple 2 mm 

Conical ring length, Y 60mm 

Ring inlet diameter, 𝐷1 15mm 

Ring outlet diameter, 𝐷2 25mm 

Pitch length of ring, P 240mm 

Pitch ratio, PR=P/𝐷1 4 

Volume 
Concentration, 

φ (%) 

Density, 
ρ 

(kg/m3) 

Specific 
Heat, Cp 
(J/kg.K) 

Thermal 
Conductivity, 

k (W/m k) 

Viscosity, 
µ 

(kg/m.s) 

0 1055.39 3502.0 0.413 0.00240 

0.5 1071.26 3446.5 0.418 0.00251 

1 1087.14 3392.7 0.418 0.00265 

1.5 1103.01 3392.7 0.441 0.00279 

Dynamic viscosity, μ 1.7894×10-5 kg/m-s 

Specific heat, Cp 1006.43 J/kg-k 

Prandtl number, Pr 0.744 

Air density, ρ 1.225 kg/m3 

Thermal conductivity, k 0.242 W/m k 

Orthogonal 
quality 

0.99 Transition ratio 0.272 

Element size 20 mm Maximum layer 10 

  Edge sizing Number of 
divisions 

Inflation option Smooth 
transition 

Number of 
elements 

12000-19000 node 32096 



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

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Figure 2. (a) Meshing profile for solid tube, (b) Inflation layer for tube 
wall, (c) Meshing profile for perforated v-cut twisted tape, (d) 
Meshing profile for semicircular cut twisted tape, (e) Meshing profile 
for perforated V-cut twisted tape with conical ring, (f) Meshing profile 
for double twisted tape with perforated v-cut and semi-circular cut 
with dimples 

2.3 Governing equations 
Mathematical modeling will be applied to anticipate flow 

and heat transfer characteristics. The finite difference method 

was used to evaluate the partial governing equations for 

boundary layers and swirling flows. Three governing 

equations characterize the properties of a fluid. The 

governing equations are solved by ANSYS Fluent, assuming 

the fluid is steady. The governing equations are used from Xie 

et al. [23]. The governing equations are given below. 

𝜕

𝜕𝑥𝑖
(𝜌𝑢𝑖) = 0             (1) 

where 𝜌 is fluid density, 𝑢𝑖  is the ith-direction of flow velocity. 
Momentum equation: 

𝜕

𝜕𝑥𝑗
(𝜌𝑢𝑖𝑢𝑗) = −

𝜕𝜌

𝜕𝑥𝑖
 +

𝜕

𝜕𝑥𝑗
(µ + µ𝑡)(

𝜕𝑢𝑖

𝜕𝑥𝑗
 + 

𝜕𝑢𝑗

𝜕𝑥𝑖
)         (2) 

where, 𝑢𝑖  is the ith-direction of flow velocity, 𝑢𝑗  is the jth-

direction of flow velocity, µ is dynamic viscosity, µ𝑡 is the eddy 
viscosity.  
Energy equation: 

𝜕

𝜕𝑥𝑖
(𝑢𝑖𝑇) =

𝜕

𝜕𝑥𝑖
[(

µ

𝑃𝑟
+

µ𝑡

𝑃𝑟𝑡
)

𝜕𝑇

𝜕𝑥𝑖
]          (3) 

where 𝑢𝑖  is the ith-direction of flow velocity, T is temperature, 
µ is dynamic viscosity, µ𝑡 is the eddy viscosity, Pr is the 
Prandtl number, and 𝑃𝑟𝑡  is the Prandtl number of the 
turbulent flow. 
Turbulent kinetic (Г) energy equation: 

𝜕

𝜕𝑥𝑗
(𝜌𝑘𝑢𝑗) =

𝜕

𝜕𝑥𝑗
[(μ +

µ𝑡

σ𝑘
)

𝜕𝑘

𝜕𝑥𝑗
] + Г − ρɛ         (4) 

where 𝜌 is fluid density, 𝑢𝑗  is the jth-direction of flow velocity, 

µ is dynamic viscosity, µ𝑡 is the eddy viscosity, Γ is the 
turbulent kinetic energy production rate, and ɛ is the 
dissipation rate of turbulent kinetic energy. 
Specific dissipative rate (ɛ)  equation: 

𝜕

𝜕𝑥𝑗
(𝜌ɛ𝑢𝑗) =

𝜕

𝜕𝑥𝑗
[(𝜇 +

µ𝑡

𝜎ɛ
)

𝜕ɛ

𝜕𝑥𝑗
]+𝐶1Гɛ -𝐶2

ɛ2

𝑘+√ʋɛ
        (5) 

where, σ𝑘 = 1 and σɛ = 1.3  , 𝐶1 = 𝑚[0.43 
µ𝑡

µ𝑡+5 
]  and 𝐶2 = 1 

and  ʋ  is the kinematic viscosity. 

2.4 Simulation Setup 
In this investigation, the energy equation was used in the 

ANSYS setup. When Nakhchi et al. [24] evaluated various 

turbulence models, including the standard k-model, the 

Renormalized Group (RNG) k-model, and the Shear Stress 

Transport (SST) k-model, they discovered that the (RNG) k-

model provides good accuracy. The RNG model of turbulence 

is derived from the instantaneous Navier-Stokes equations 

using a statistical method called "renormalization group" 

(RNG) methods. The RNG model improves accuracy for 

swirling flows by considering the effects of swirling on 

turbulence. The RNG viscous model with enhanced wall 

treatment was applied in this study. The use of y+ with 

enhanced wall treatment gives scalable benefits over 

standard wall functions. For solver parameters in the Fluent 

model setup, the pressure-based and steady-state models 

were used. Then, the RNG k- model for viscosity was chosen. 

The inlet temperature of air was taken to be 300K. The walls 

of STSC, STPV, PVTC, DTT-1, and DTT-2 were set to adiabatic 

walls. The boundary conditions are shown in Table 5. 

Table 5. Boundary conditions 

 

2.5 Numerical procedures 
The pressure-based solver is used in this study to solve 

the steady-state problem. The governing equations are solved 

by the finite volume method. The SIMPLE (Semi-implicit 

Method for the Pressure-Linked Equations) algorithm was 

selected for the numerical study. Twisted tapes fitted with a 

plain tube were utilized with PRESTO (Pressure Staggering 

Option). The Quadratic Upstream Interpolation for 

Convective Kinematics (QUICK) approach employed 

momentum, energy, turbulent kinetic energy, and specific 

dissipation rate to obtain accuracy. When the residuals 

dropped below 10-3 the numerical solutions converged, 

except for the energy equation, which dropped below 10-6. 

3. Results and discussion 

3.1 Validation of simulations 
In order to validate the simulation results for a plain tube 

to calculate heat transfer augmentation, the results are 

compared with the Gneilski correlation for Nusselt number 

comparison and the Petukhov correlation for friction factor 

[25]. A previous experimental work of Promvonge et al. [26] 

using a conical ring and a previous experimental investigation 

by Bhuiya et al. [27] was validated by simulation results. 

Surface Thermal Momentum 

Inlet 300k Velocity inlet 

Outlet - Pressure outlet 

Tube wall 7500 W/𝑚2 No-slip condition 

Walls of all 
twisted tapes and 

conical rings 
0 W/𝑚2             -       



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20000 40000 60000

F
ri

ct
io

n
 f

ac
to

r,
 f

Reynolds number, Re

Petukov

Current Study

(b)

The Gneilnski correlation was used to verify the plain 

tube for the Nusselt number. The Nusselt number deviation 

percentage ranges from 3.78% to 5.18% with an RMS error of 

3.079%. The friction factor for the simple tube was confirmed 

using the Petukhov correlation [25]. The friction factor's 

deviation percentage varied from 6.3778% to 13.405%. with 

an RMS error of 2.837%. Figure 3 illustrates the validation 

results for the Nusselt number and friction factor. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
Figure 3. (a) Nusselt number validation for plain tube, (b) Friction 

factor validation 

To ensure the simulation procedure validated a previous 
experimental work done by Promvonge et al. [28]. The 
working fluid for this experiment was air. The deviation 
percentage of the Nusselt number varied from 16.5% to 
18.01%. The validation of the Nusselt number for a conical 
ring is shown in Figure 4. 

3.2 Heat transfer enhancement characteristics 
Heat transfer coefficient results from ANSYS Fluent were 

gathered. The connection between the Reynolds number and 
the heat transfer coefficient of double and single twisted tape 
inserts at various concentrations of TiO2 is shown in Figure 5, 
which demonstrates that, in all cases, the heat transfer 
coefficient increased as the Reynolds number increased. The 
heat transfer rate increased because the twisted tapes created 
vortices and turbulence in the fluid flow, which ensured 
better fluid mixing and, consequently, increased the heat 
transfer rate [29]. Besides, twisted tapes create a larger 
effective surface area, which improves overall heat transfer 
performance. The Maximum Heat transfer coefficient is 

increased from plain tube to 88.2% and 71.42% at PVTC and 
DTT-2 in 0.5% and 1.5% TiO₂ concentrations, respectively. 

 
Figure 4. Nusselt number validation for a conical ring 

 

 
(a) 

 

(b) 

 

Figure 5. (a) Comparison of the Reynolds number and the heat 

transfer coefficient for 0.5% TiO2, (b) Comparison of the Reynolds 

number and the heat transfer coefficient for 1.5% TiO2 

Figure 6 depicts the relationship between the Nusselt 
number and the Reynolds number. The maximum Nusselt 
number increased by 115.53% and 100.9% for double 
twisted tape with perforated V-cut and semi-circular cut with 
dimples, compared to the plain tube in 0.5% and 1.5% TiO2 
concentrations. Figure 6 illustrates that, in all instances, the 
Nusselt number increased as the Reynolds number increased. 

0

20

40

60

80

100

120

0 20000 40000 60000

N
u

ss
el

 n
u

m
b

er
, 
N

u

Reynolds number, Re

Gneilnski

Current Study

(a)

0

20

40

60

80

100

120

140

160

0 5000 10000 15000 20000 25000 30000

N
u

ss
el

t 
n

u
m

b
er

, 
N

u

Reynolds number, Re

Promvonge et al.

Current Study



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

25 

 

Convective heat transfer was amplified as the intensity of 
turbulent flow increased with the Reynolds number. The 
twisted and double-twisted tapes swirl generators have a 
considerable impact on the heat transfer rate for all Reynolds 
numbers. This may produce secondary or swirl flow, which 
provides a longer channel for the fluid to flow through the 
tube. Intense fluid and pressure gradient mixing might also 
have been formed in the radial direction. 

(a) 

 

(b) 

Figure 6. (a) Comparison of the Reynolds number and Nusselt 

number for 0.5% TiO2, (b) Comparison of the Reynolds number and 

Nusselt number for 1.5% TiO2. 

The friction factor was computed using the Darcy-
Weisbach equation after collecting the pressure drop from 
the inlet to the outlet in the ANSYS Fluent results. Figure 7 
shows the effects of double twisted tape inserts on friction 
factor characteristics. The friction factor of the tape-inserted 
tube steadily decreased as the Reynolds number rose. It is 
shown that the friction factor increased by a vast amount at 
lower Reynolds number values and by a relatively small 
amount at higher Reynolds number values. This might be 
explained by the fact that at lower Reynolds number values, 
which correspond to lower flow rates, air can travel over the 
tape and produce large frictional forces, as tiny vortices are 
present behind the tape. The friction coefficients of PVTC 
were 94.44% greater than those of the plain tube. When 
designing heat exchangers, the thermal performance factor 
(TPF) is very important. The TPF demonstrated the 
usefulness of using twisted tape in heat exchangers [29]. With 
an increase in Reynolds number, the performance 
characteristics for all twisted tapes tended to decline. This 
suggested that the energy-saving devices for usage at lower 
Reynolds numbers were the enhancement devices. Figure 8 
shows the thermal performance factor using double and 

single twisted tapes for 10000 to 55000 Reynolds numbers. 
The maximum thermal performance factor was found at DTT-
2.  The maximum value of TPF is 2.04 and 1.88 at 0.5% and 
1.5% TiO2 concentrations, respectively. 

(a) 

(b) 

Figure 7. (a) Comparison of the Reynolds number and Friction 

factor for 0.5% TiO2, (b) Comparison of the Reynolds number and 

Friction factor for 1.5% TiO2 

3.3 Contour plots 
The velocity contour for the plain tube and STSC, PVTC, 

DTT-1, STPV, DTT-2 are shown in Figure 9. The fluid velocity 
reaches the free stream velocity at the center of the pipe and 
becomes zero adjacent to the pipe wall. Also, velocity 
increases at the tube's inlet region and decreases when the 
insert geometry restricts the passage. 

The temperature distribution contour for the plain tube 
and STSC, STPV, PVTC, DTT-1, and DTT-2 are shown in Figure 
9. For a plain tube, the temperature increases at the boundary 
layer adjacent to a solid surface. Figure 10 illustrates the 
temperature range from high to low at the boundary surface 
fluid. After using the insert on a plain tube, the heat was 
distributed everywhere, enhancing the heat transfer. 

The pressure distribution contour for the plain tube and 
STSC, STPV, PVTC, DTT-1, and DTT-2 are shown in Figure 11. 
At the inlet section, pressure was higher, but a pressure drop 
occurred at the outlet section due to frictional forces. After 
using conical rings, fluid flow creates more disturbance 
because more pressure drop occurs in the outlet section. 

Figure 12 shows the turbulent kinetic energy for various 
sections of plain tubes and tubes equipped with inserts. The 
contour figure shows that TKE is higher where the boundary 
is closest to the tube wall and also where the alternate axis 
dimpled twisted tape is located, indicating high shear stress. 

 
 
 



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

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(a)                                                                                                                                 (b) 

Figure 8. (a) Comparison of the Reynolds number and TPF for 0.5% TiO2, (b) Comparison of the Reynolds number and TPF for 1.5% TiO2 

 

 

Figure 9. (a) Plain Tube, (b) STSC, (c) PVTC, (d) DTT-1, (e) DTT-2, (f) STPV 

 

 

Figure 10. (a) Plain Tube, (b) STSC, (c) STPV, (d) PVTC, (e) DTT-1, (f) DTT-2 



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Velocity increases in the tube's inlet region and 

decreases when the insert geometry restricts the passage. For 

a plain tube, the temperature increases at the boundary layer 

adjacent to a solid surface. After using the insert on a plain 

tube, the heat was distributed everywhere, enhancing the 

heat transfer. At the inlet section, pressure was higher, but a 

pressure drop occurred at the outlet section due to frictional 

forces. After using double-twisted tape inserts, fluid flow 

creates more disturbance because a greater pressure drop 

occurs in the outlet section. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Conclusion 

In the present research, the heat transfer and friction 
factor characteristics of turbulent flow for STSC, STPV, PVTC, 
DTT-1, and DTT-2 at varying TiO2 concentrations were 
investigated numerically. When compared to the plain tube, 
the DTT-2 significantly boosted the heat transmission rate. 
The following are the primary findings of this numerical 
study: 
• The double twisted tapes offered a higher heat transfer 

rate, friction factor, and thermal performance factor as 
compared to the plain tube. As the Reynolds number 
increased, so did the Nusselt number. The Maximum Heat 
transfer coefficient is increased from plain tube to 88.2% 
and 71.42% at DTT-2 in 0.5% and 1.5% TiO₂ 

            

 

Figure 11. (a) Plain Tube, (b) STSC, (c) DTT-1, (d) STPV, (e) DTT-2, (f) PVTC 

 

 

Figure 12. (a) Plain Tube, (b) STSC, (c) STPV, (d) DTT-1, (e) PVTC, (f) DTT-2 



I. Hossen et al. /Future Energy                                                                                                 February 2026| Volume 05 | Issue 01| Pages 20-29 

28 

 

concentrations, respectively. Also, the maximum Nusselt 
number rose by 115.53% and 100.9% at DTT-2 compared 
to the plain tube in 0.5% and 1.5% TiO2 concentrations, 
respectively. The Nusselt number increased because the 
twisted tapes with insertion create vortices and turbulence 
in the fluid flow, which ensured better fluid mixing that 
increased the heat transfer rate. Besides, twisted tapes 
create a larger effective surface area, which improves 
overall heat transfer performance. There were four 
different cases. The Nusselt number was enhanced for 
double twisted tapes, perforated V-cut with and without 
conical ring, semicircular cut tape by 74.52%, 101.2%, 
29.19%, 18.49% respectively for 1.5% of TiO2 nanofluid 
and by 67.7231%, 97.32%, 26.2%, 18.23% respectively for 
0.5% TiO2 nanofluid. 

• The friction factor decreased with the increase of the 
Reynolds number. The friction factor of a tube with a 
double twisted tape insert was higher than that of the plain 
tube. The maximum friction factor increased from that of a 
plain tube to 94.44% with a double twisted tape at a 1.5% 
TiO2 nano-fluid concentration. The friction factor was 
increased for double twisted tapes, perforated V-cut with 
and without conical ring, semicircular cut tape by 75.4%, 
94.44%, 55.32%, 33.3078%, respectively for 1.5% of TiO2 
nano fluid, and by 71.757%, 82.86%, 45.29%, 28.75% 
respectively for 0.5% TiO2 nano fluid. 

• The thermal performance factor was also evaluated. The 
thermal performance factor decreased with increased 
Reynolds number. The maximum thermal performance 
factor was found to be 2.04 at a Reynolds number of 14000 
for DTT-2 at a 0.5% concentration of TiO2. 

For further investigation, the cuts on the twisted tape can be 
modified. Also, the conical rings configuration can be changed 
as well. Since in this study conical rings with V-cut have been 
used, the hexagonal ring with V-cut or rectangular cut can be 
utilized to analyze the heat transfer enhancement. Besides, 
the pressure drop analysis can be done between the V-cut 
with conical ring configuration and the v/rectangular cut with 
hexagonal configuration. 

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the corresponding author. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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