Case Studies in Thermal Engineering 32 (2022) 101866

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Case Studies in Thermal Engineering

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A new microchannel heat exchanger configuration using

CNT-nanofluid and allowing uniform temperature on the
active wall
Mohamed Omri a, Hichem Smaoui b, Luc Frechette c, Lioua Kolsi d, e, *
a
Deanship of Scientific Research, King Abdulaziz University, Jeddah, Saudi Arabia
b
Civil Eng. Dpt., King Abdulaziz University, Jeddah, Saudi Arabia
c
Sherbrooke University, J1K 2R1, Qc, Canada
d
Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City, 81451, Saudi Arabia
e
Laboratory of Metrology and Energy Systems, University of Monastir, Monastir City, 5000, Tunisia

A R T I C L E I N F O A B S T R A C T

Keywords: The present study presents a three-dimensional numerical analysis using the finite element
Heat transfer method of nanofluid enhanced heat transfer in micro heat exchanger equipped with triangular
Flow structure fins. The new configuration based on an existent system where a jet impingement supplies a
Micro heat exchanger microchannel structure. A modification of the heat exchanger geometry in the z-direction is added
Triangular fins allowing a uniform wall temperature profile. The micro heat exchanger is assumed to be well
Nanofluid
insulated. The hot fluid (water) flows in the lower channel with a fixed velocity (uw_in = 20 mm/s)
and cold fluid (CNT-water nanofluid) flows in the upper channel which is equipped with trian­
gular fins with a velocity (unf_in) ranged from 5 to 45 mm/s. The nanofluid is considered ho­
mogeneous with temperature-dependent thermophysical properties and the CNT nanoparticles
volume fraction is varied from 0 to 5%. The results are presented in term of thermal and flow
fields, heatlines, overall heat transfer coefficient, thermal effectiveness, and thermal performance
factor (TPF). It was found that the performances of the heat exchanger are significatively
improved using the CNT nanofluid and the triangular fins. But the TPF increase with the CNT
volume fractions and decreases with the fin’s height.

1. Introduction
Due to the trend of miniaturization technologies, the use of micro-sized thermal systems such as micro-heat exchanger becomes a
mandatory necessity. Based on this fact the number of scientific studies related to this subject keeps increasing with a focus on
achieving more efficient and compact micro heat exchangers. The major challenge concerning the enhancement of the heat transfer
between the streaming fluids is the thickness of the separating wall that cannot be very thin due to mechanical considerations. To
oppose this issue, several propositions related the material properties and geometrical design can be found in the literature.
Although micro-channel heat exchangers are known to allow the removal of high heat rates [1–3], along the flow direction the flow
temperature increases leading automatically to an increase in wall temperature. To change the trend of the temperature variation we

* Corresponding author. Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City, 81451, Saudi Arabia.
E-mail addresses: omrimoha2002@yahoo.fr (M. Omri), hismaoui@yahoo.fr (H. Smaoui), luc.frechette@usherbrooke.ca (L. Frechette), l.kolsi@uoh.edu.sa
(L. Kolsi).

https://doi.org/10.1016/j.csite.2022.101866
Received 25 November 2021; Received in revised form 3 February 2022; Accepted 11 February 2022
Available online 14 February 2022
2214-157X/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

can provide cold coolant at different locations across the surface which added more complexity to the distributing the flow with
manifolds. An original approach, adopted in this work, consists of adapting locally the thermal resistance of the heat exchanger to
compensate for the coolant flow-temperature-increase when it travels over the surface. Here, we combine a jet impingement and
variable diameter micro-channels to adapt the thermal resistance. In a work done by Omri et al. [4], they present the temperature
profiles on the active wall: it is clear that the authors succeed decreasing the inlet to outlet temperature but it is not uniform. Along any
microchannel, the temperature increases like in a classic heat exchanger. Here we propose to reduce the outlet of each channel by
reference to its inlet in order to make the temperature profile uniform.
Gerken et al. [5], studied experimentally the heat transfer enhancement in a gas-to-gas micro heat exchanger. They concluded that
the heat transfer and pressure drop can be optimized by considering the adequate combination of partition material and thickness.
Nonino and Savino [6], presented a numerical investigation using the finite element method (FEM) with the aim to evaluate the
performances of a micro heat exchanger. The authors considered various microchannel cross-sectional geometries and various wall
thermal conductivities. They concluded that higher wall conductivity and rectangular cross section provide a maximum heat transfer.
Wajs et al. [7] used a mini-channel heat exchanger for energy recuperation from a microturbine system. The authors concluded that the
apparition of recirculation zone opposes the heat transfer and specific geometry are to be considered when constructing the heat
exchanger to avoid this problem.
Jyothiprakash et al. [8] studied a low temperature three-fluid micro heat exchanger. The governing equations were solved using
the FEM. Huang et al. [9] studied experimentally the heat and fluid flow in micro-channels heat exchanger equipped with cavities, with
a focus on the shape and the expansion and contraction of the cross-section. The addition of cavities was found to improve the thermal
and hydraulic performances. Abuhamdeh et al. [10] investigated the hydrothermal performances of a helical coil micro heat exchanger
with a focus on the effect of the pitch length. The governing equations were solved using the finite volume method (FVM). The increase
of pitch length was found to be unfavourable for the heat transfer and causes a decrease of the overall heat transfer coefficient. Knupp
et al. [11] performed an experimental and numerical analysis on the heat transfer in micro heat exchangers having triangular cross
section micro-channels. The numerical study was based on the FEM despite the experimental measurements were performed via
various non-intrusive techniques. Wu et al. [12] proposed a new model of embedded-clapboard distributor in micro-channels heat
exchanger. The results proved that the use of this new configuration leads to a better distribution of the bubble flow. Kim et al. [13],
studied experimentally a micro pulsating heat exchanger. They visualized the flow via the Laser induced fluorescence technique. The
authors considered two configuration and concluded that the asymmetric heat exchanger with circulating flow provides higher per­
formances compared to the symmetric one with oscillating flow. Yang et al. [14], analysed experimentally the effect of wall conduction
on the performances of a micro heat exchanger. The results show that higher effectiveness occurs during the counter flow configu­
ration. Liou et al. [15] performed an numerical investigation on heat transfer and fluid flow in a serpentine micro heat exchanger and
proposed new correlation for the Nusselt number and friction factor under laminar flow. Nonino et al. [16], used the FEM to study the
heat transfer in a 3D micro heat exchanger. The results show that the increase of the number of the microchannel yields to the
enhancement of the heat transfer and to the increase of the pressure drop. Lowrey et al. [17] studied the hydraulic and thermal
performance in polymer 3D printed micro heat exchanger and in a typical aluminium micro heat exchanger. The authors concluded
that despite the poor thermal properties of the polymer, the performances are relatively reasonable. Omidbakhsh Amiri et al. [18],
performed a numerical study on the flow and temperature fields in a micro-heat exchanger. The studied the effect of the direction of the
inlet velocity and found that horizontal inlet flow has better uniformity of flow and temperature fields.
In addition to the innovative geometrical proposition, due to their enhanced effective thermophysical properties especially the
thermal conductivity, the use of nanofluids becomes an interesting technique allowing the enhancement of the heat transfer in heat
exchangers [19,20].
Tu al al [21]. investigated numerically the heat transfer and fluid flow of TiO2-water nanofluid around micro-ribbed tube in a heat
exchanger. Several geometrical configurations related to the number, height and orientation of the ribs are studied using the finite
volume method with considering a turbulent flow regime. The authors mentioned that the use of nanofluid with a volume fraction of
0.4% leads to a considerable enhancement of the heat transfer but causes an increase of the resistance coefficient due to the increase of
the viscosity. Serour et al. [22], studied experimentally the effect of using a hybrid Gr-TiO2/nanofluid on the thermal and hydraulic
performance of a micro heat exchanger. The authors concluded that for a mixture of 50% Gr and 50% TiO2, the dispersion is stable, and
the overall heat transfer is reduced by only 2% compared to the case of 100% Gr. Thus, due to the high cost of Graphene nanoparticles
and to make the process profitable it is recommended to use a fifty-fifty mixture. Mohammed et al. [23] studied numerically, the
performances of a circular micro heat-exchanger working with various types of nanofluid. Al2O3-water nanofluid was found to provide
the highest overall heat transfer coefficient. Concerning hydrodynamic performances, the Ag-water nanofluid has the lowest pumping
power.
Bahiraei et al. [24] considered the viscous dissipation and evaluated numerically the entropy generation and exergy destruction
during the flow of Graphene/silver hybrid nanofluid in a micro heat exchanger. They mentioned that the exergy destruction is mostly
due to the viscous effect compared to thermal one and that the entropy generation is more important for higher nanoparticles con­
centrations. Li et al. [25] evaluated experimentally the cooling performances of a micro heat exchanger working with carbon-acetone
nanofluid. After the characterization of the nanoparticles, the authors studied the effects of Reynolds number and the nanoparticles
volume fraction and found that both enhances the heat transfer. Alnaqi et al. [26], performed a numerical investigation of the entropy
generation and thermal and hydraulic performances of a zigzag microchannel working with a hybrid non-Newtonian CNT-SiO2/E­
G-H2O nanofluid. The authors mentioned that the increase of zigzags and of nanoparticles volume faction enhances the heat transfer
but also increase the pumping power. Ghachem et al. [27], used the FEM to study the effect hybrid nanofluid on the performances of a
cross flow micro heat exchanger with wavy channels. The effects of number of waves, flow velocity and nanoparticles volume fraction

2
M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 1. Details of the studied configuration.

were studied. The optimal performances were found for a velocity of 50 mm/s, a volume fraction of 5% and a number of waves equal to
8. Bahiraei and Monavari [28] presented a numerical investigation on the thermal and hydraulic performances of a micro plate heat
exchange with a focus on the effect of nanoparticles shape. The authors proved that the platelet-shaped nanoparticles provide the
highest overall heat transfer coefficient. Khan et al. [29] studied the effect of using Al2O3 nanofluid in a wavy and double wavy
micro-heat exchanger. It was concluded that both, the use of waving walls and nanoparticles enhance the heat transfer and a value of
TPF = 2.2 is reached. Recently, Tu et al. [30] studied numerically, the heat transfer around micro-ribbed heat exchanger. The authors
mentioned that the height of ribs, transverse pitch and the use of nanoparticles improve significatively the heat transfer. Ajeeb et al.
[31], considered the non-Newtonian MWCNTs nanofluid flow in a microchannel and concluded that the use of nanoparticles can
improve the heat transfer rate by 33%. Arshi Banu et al. [32], investigated numerically a micro-pin-fin heat exchanger working with
Al2O3 or CuO nanofluids. It was proved that CuO-nanofluid leads to a better heat transfer rate compared to Al2O3-nanofluid and pure

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

water. Other interesting papers related to the subject can be found in the literature [33–36].
Based on the above presented literature, it is noticed that the main issue opposing the enhancement of heat exchange is the layer
separating the fluids streams. The solutions to increase the heat transfer are mainly related to new geometrical configurations and the
use of enhanced fluid thermophysical properties. Based in this fact the present study deals with the use of triangular fins and CNT-
nanofluid in a rectangular cross section counter flow micro heat exchanger.

2. Problem statement, mathematical modeling and numerical method

The studied configuration of the 3D cross micro heat exchanger equipped with triangular fins is presented in Fig. 1. The Heat
exchanger is considered as well insulated, and no heat is exchanged with the surrounding. The hot fluid flowing in the lower channel is
pure water and cold CNT-water nanofluid is flowing in the upper compartment equipped with 5 triangular fins having different
lengths. The inlets temperatures are fixed at Tw_in = 333 K and Tnf_in = 293 K. The average inlet velocity is varied from 5 mm/s to 45
mm/s for the cold nanofluid (unf_in) and is fixed at 20 mm/s for the hot water (uw_in). It is also to be noted that the properties of the
working fluids are considered as temperature dependent. It is to be mentioned that the triangle shape of the fins is chosen to move the
stagnation induced by the fins which make the section-change smooth in the flow-direction.
The continuity, momentum, and energy equations (Eqs (1)–(8)) governing the heat transfer and fluid flow in the considered heat
exchanger are developed for a 3D incompressible laminar flow [27].
∂U1 ∂U2 ∂U3
+ + =0 (1)
∂x ∂y ∂z
[ ] [ ]
∂U1 ∂U1 ∂U1 ∂P ∂2 U1 ∂2 U1 ∂2 U1
ρnf U1 + U2 + U3 =− + μnf + 2 + 2 (2)
∂x ∂y ∂z ∂x ∂x2 ∂y ∂z
[ ] [ ]
∂U2 ∂U2 ∂U2 ∂P ∂2 U2 ∂2 U2 ∂2 U2
ρnf U2 + U2 + U3 =− + μnf + 2 + 2 (3)
∂x ∂y ∂z ∂y ∂x2 ∂y ∂z
[ ] [ ]
∂U3 ∂U3 ∂U3 ∂P ∂2 U3 ∂2 U3 ∂2 U3
ρnf U1 + U2 + U3 =− + μnf + 2 + 2 (4)
∂x ∂y ∂z ∂z ∂x2 ∂y ∂z
[ ] [ ]
∂T ∂T ∂T ∂2 T ∂2 T ∂2 T
ρnf .Cpnf U1 + U2 + U3 = knf + + in the fluid domain (5)
∂x ∂y ∂z ∂x2 ∂y2 ∂z2

∂2 T ∂2 T ∂2 T
+ + = 0 in the solid domain (6)
∂x2 ∂y2 ∂z2
The heatlines are obtained by solving the heatfunction equation:
→
Δ × H = ρnf .Cpnf .U .T − knf .∇T in the fluid domain (7)

Δ × H = − ks .∇T in the solid domain (8)

The subscript ‘’f’’ corresponds to ‘’w’’ for water and to ‘’nf’’ for the CNT-water nanofluid.
Average velocities (uw_in and unf_in) and constant temperatures (Tw_in and Tnf_in) are imposed at the inlets.
The boundary conditions are expressed as follow:
• Hot fluid inlet (water): Ux = − uw in , Uy = Uz = 0 and T = Th
• Hot fluid outlet (water): ∂∂Uxx = Uy = Uz = 0, P = 0 and ∂∂Tx = 0
• Cold fluid inlet (nanofluid): Uz = unf in , Ux = Uz = 0 and T = Tc
∂Uy ∂T
• Cold fluid outlet (nanofluid): ∂y = Ux = Uz = 0, P = 0 and ∂y =0
• Internal walls: Ux = Uy = Uz = 0
• External walls: ∂∂Tn = 0

The following conditions are used to ensure the heat and temperature continuity:
[ ] [ ]
∂T ks ∂T
∂n = knf ∂n nanofluid side
nf s
[ ] [ ]
∂T
∂n = kkws ∂∂Tn water side.
w s
The heat exchanger is built in stainless steel with:
• Thermal conductivity: ks = 15 ​ W.m− 1 .K− 1

• Density: ρs = 7800 ​ kg.m− 3

• Heat capacity: Cps = 420 ​ J.kg− 1 .K− 1

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Table 1
Thermophysical properties of CNT [39].

Property CNT

Cp (J/kg.K) 425
ρ (kg/m3) 2600
k (W/m.K) 6600

Table 2
Grid sensitivity analysis for Hfin = 3 mm, φ = 0.045, and unf_in = 45 mm s-1

Elements Number U [W.m-2. K-1] Percentage increase Incremental increase

M1: 665632 6411.954 – –

M2: 1058144 6558.623 2.287431 –
M3: 1909654 6622.334 3.281054 0.971403
M4: 2307165 6630.121 3.402504 0.117592

Fig. 2. Comparison of the results of the present numerical model, with the experimental results of Brandner et al. [40] and numerical results of Nonino and Savi­
nov [16].

The computational method used to solve the conservation equations in the present study is based on the finite element method
[37]. The operator splitting scheme [38] is used to decouple non-linearity from the Navier–Stokes equation and the convergence
criterion is fixed at 10-5 for all the variables.

3. Thermophysical properties
The thermophysical properties of the used fluid are considered as temperature-dependent.
The thermophysical properties of water are expressed as [27]:

μw = 1.3799566804 − 0.021224019151.T + 1.3604562827.10− 4 .T 2 − 4.6454090319.10− 7 .T 3

10 (9)
+8.9042735735.10− .T 4 − 9.0790692686.10− 13
.T 5 + 3.8457331488.10− 16
.T 6
for 273.15≤T ≤ 373.15

Cpw = 12010.1471 − 80.4072879.T + 0.309866854.T 2 − 5.38186884.10− 4 .T 3

(10)
+3.62536437.10− 7 .T 4
for 273.15≤T ≤ 373.15

ρw = 0.000010335053319.T 3 − 0.013395065634452.T 2 + 4.969288832655160.T

(11)
+432.257114008512
for 293≤T ≤ 373.15

kw = − 0.869083936 + 0.00894880345.T − 1.58366345.10− 5 .T 2 + 7.97543259.10− 9 .T 3 (12)

for 293≤T ≤ 373.15.
The thermophysical properties of the CNT nanoparticles are presented in Table 1. The thermophysical properties of the CNT

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 3. (a) Temperature field for various fins hights at φ = 0.03 and unf-in = 30 mm/s and Temperature profiles at the wall separating the fluids for Hfin = 300 μm, φ =
0.03 and different x-positions: (b) unf-in = 15 mm/s and (c) unf-in = 45 mm/s.

nanofluid are calculated basing on the properties of the base fluid (water) and the volume fraction of the dispersed CNT:
ρnf = (1 − φ)ρw + φρnp (13)
( ) ( ) ( )
ρC p nf
= (1 − φ) ρCp w + φ ρCp nf (14)

( )
k k +k
1 − φ + 2φ knp −npkw ln np2kw w
knf
= ( ) (15)
kw k k +k
1 − φ + 2φ knp −f kw ln np2kw w

μw
μnf = (16)
(1 − φ)2.5

4. Data analysis
The total heat exchanged, the overall heat transfer coefficient and the heat exchanger effectiveness are expressed as follow:
∫i ∫o
• Q̇ = Q̇h = Q̇c = o ṁh .Cphav .dT = i ṁc .Cpcav .dT
Q̇h
• U = A.LMTD

With: LMTD = ln(ΔT

ΔT1 − ΔT2
1 /ΔT2 )
ΔT1 = Thi,av − Tco,av and. ΔT2 = Tho,av − Tci,av

• ε = Q̇Q̇
max

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 4. Average water outlet temperature versus nanoparticles volume fraction for Hfin = 100 μm (a) and Hfin = 400 μm (b), and versus height of the fins (c).

With Q̇max = (ṁ.Cp)min .(Thi,av − Tci,av ) is the maximum possible heat transfer rate.
The thermal thermal–hydraulic performance factor (TPF) is the ratio of the heat transfer enhancement to a unit increase in pumping
power and is relating the Nusselt number, and the friction factor using the following expression:
/
Nufins+nf Nu0
TPF = ( / )1/3
ffins+nf f0

With
h.Dh
Nu =
k
and
ΔP.Dh
f=
0.5.ρ.u2in .L
The friction factors are raised to the one-third power as the pumping power is proportional to the 1/3 power of the friction factor.
Nu0 and f0 refer to the reference values chosen to be the configuration without fins and without adding nanoparticles.

5. Grid dependency and validation

The grid dependency test is performed for Hfin = 300 μm, φ = 0.045, and unf_in = 45 mm s-1. Tests are performed for 4 different
meshes. The overall heat transfer coefficient is chosen as test parameter. As presented in Table 2, the percentage of increase of U from
M3 to M4 meshes is only 0. 117%. Thus, for time economy and accuracy, the mesh M3 (1909654 elements) is used for all the
simulations.
To validate the used model a comparison is performed with the experimental results of Brandner et al. [40] and numerical results of
Nonino and Savinov [16] (Fig. 2) for the case of a crossflow heat exchanger with straight microchannels. The comparison shows a good
agreement between the results and the maximum deviations compared to the experimental and numerical findings are less than 8%
and 2.5%, respectively.

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 5. Effect of fins height on Heatlines (a) and 3D flow Flow Structures (b) for φ = 0.03 and unf_in = 30 mm/s.

6. Results and discussions

In this paper, the effects of various geometrical and physical variables on the flow structure, temperature field and heat exchange
performance in a counter flow micro-heat exchanger equipped with triangular fins are studied. Fig. 3 a presents the effect of the fin’s
height on the temperature field for φ = 0.03 and unf-in = 30 mm/s. The isotherms are represented in 8 different cross sections normal to
the flow direction. The temperature scale is same for all the sub-figures because the inlet temperatures are fixed respectively at Tw_in =
333 K and Tnf_in = 293 K. It is to be mentioned that in the cross sections that didn’t intersect with the fins the isotherms are almost
regular, while irregularities appear in the when there is an intersection. This is due to the presence of the fins that guide the flow and
leads to the apparition of partial vertical stratifications close to the central zones. In fact, the fins that are mounted on the layer that
separates the hot water to the cold nanofluid, contribute effectively to transferring the heat from the hot region to the cold region. This
highlights the synergy between flow and heat transfer is enhanced as the fin height increases. It is also noticed that the temperature
values are higher close to the longitudinal wall due to the imposed adiabaticity condition. More the fins height is increased, the
temperature range becomes narrower, especially in the left side, what suggests more effective heat transfer.
Fig. 3b and c depict the temperature at the wall separating the fluids for Hain = 300 μm, φ = 0.03 and different x-positions. It is
noticed that at a fixed x-position the temperature is quasi-uniform versus z, especially in the x-positions that intersect with more fins.
This uniformity indicates that the studied configuration has a good effectiveness. It is also to be mentioned that the temperature in­
creases significatively from the inlet of to the outlet of the cold nanofluid.
Fig. 4a and b are plotted to investigate the effect of CNT volume fraction on the average water (hot fluid) outlet temperature. For all
the considered height of fins and flow velocities, the effect of adding nanoparticles is beneficial for heat transfer. In fact, the average
outlet temperature decreases for all the considered cases, this is due to high effective conductivity of the nanofluid that favorize the
heat transfer. In addition, it is to be mentioned that the lower water temperatures are for higher flow velocities. For example, for Hfin =
400 μm and φ = 0.04, the average outlet temperature of the hot water is reduced by about 24 K when the velocity is increased from 5
mm/s to 45 mm/s. This is due to the increase of the overall heat transfer coefficient caused by the increase of the velocity.
Fig. 4 c presents the effect of fins height on the average outlet temperature of the hot fluid for the velocities of 5 and 45 mm/s. For
high velocities, it is observed that the height of the fins has a positive effect on the reduction of the outlet temperature, which indicates
that more heat is extracted from the hot fluid for higher heights of fins. For low velocities the average outlet temperature of the hot
water is quasi-constant versus the height of the fins. Thus, the presence of fins is more effective for higher velocities. It is also noticed

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 6. Effect of fins height and inlet velocity on the flow structure for φ = 0.03 at y = 150 (Bottom) and 200 μm (Top) plans for φ = 0.03.

that in term of percentage the presence of fins is more effective for lower CNT volume fractions.
Fig. 5 a portrays the effects of fins height on the heatlines for φ = 0.03 and unf_in = 30 mm/s. Heatlines are employed in order to
visualize the path-line and identify the heat flow intensity inside the heat exchanger. As it can be seen, these heatlines are sensitive to
the fin’s height. The majority of heatlines are found to emanate from the hot water inlet and end on the cold nanofluid inlet. The
heatlines are affected by the variation of the height of the fins and the heat distribution becomes more complicated and distorted for
shorter fins. As the height of the fins increases, the density of heatlines close the central line of the heat exchanger increases and some
appearing heat paths provide a corridor to transport the heat to cold water inlet.
The velocity field in 3 cross-sections and the 3D streamlines for various fins heights at φ = 0.03 and unf_in = 30 mm/s, are presented
in Fig. 5 b. In the lower channel the velocity field is regular, and the streamlines are quasi-horizontal. In the top channel the flow is
more complex due to the existence of the fins and due to the locations of the inlet and outlet that are normal to the principal flow cross-
section. Due to the 3D behavior and the complexity of the flow, the collision between the fluid and the fins walls increases and leads to
a better heat exchange. In the top channel the maximum values of the velocity magnitude are in the interval between the fins for Hfin =
400 μm and in the in the upper part for the other heights.
The 3D flow structure presented in Fig. 5 b is complex, thus for a better understating the streamlines in constant y-plans (y = 200
μm and y = 150 μm) are plotted (Fig. 6). For y = 200 μm the plan doesn’t cross any fin and for y = 150 μm it crosses the first fin. The
flow structure is globally organized and even the presence of the fins doesn’t lead to the creation secondary flows. This is due to
triangular shape of the fins that leads to a progressive change of the cross-section without having sudden change. Even though the flow
structure is similar for the considered velocities, the increase of the velocity intensifies the flow and causes a better heat transfer.
The effects of all the controlling variables on the overall heat transfer coefficient and Heat exchanger thermal effectiveness are
presented in Fig. 7. For all the considered configurations the effect of CNT volume fraction is found to be enhancing the overall heat
transfer coefficient. Similarly, the increase of the average inlet velocity causes an increase of the temperature gradients and leads to an
important increase of the heat transfer. The most interesting finding is related to the effect of the height of the fins, in fact it has
negative effect at low flow velocities and positive impact for high velocities. Thus, a tradeoff between the flow velocity and the fins
heights is required to optimize the overall heat transfer coefficient. As conclusion, for low flow velocities (5 mm/s) it is better to use
short fins and the contrary for high velocities (30 mm/s and 45 mm/s). The velocity is 15 mm/s, represent a transitional velocity, in
fact the overall heat transfer coefficient is approximatively the same for fins heights (300 and 400 μm) and for (100 and 200 μm).
Concerning the variations of the thermal effectiveness versus CNT volume fraction, the behavior of the variation is very complex. In

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

Fig. 7. Overall heat transfer coefficient (U) and Heat exchanger thermal effectiveness (ϵ) versus nanoparticles volume fraction for various fins heights.

Fig. 8. Thermal performance factor versus nanoparticles volume fraction for various fins heights.

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M. Omri et al. Case Studies in Thermal Engineering 32 (2022) 101866

fact, the thermal effectiveness decreases with the volume fraction for low velocities (5 mm/s). At high velocities (30 and 45 mm/s) it
increases versus φ for Hfin = 100 and 200 μm and decreases for Hfin = 300 and 400 μm. For unf_in = 15 mm/s the variation has an
extremum at φ = 0.03. It is also to be mentioned that the highest values of the effectiveness occur for lower velocities, this is due to the
higher residence time that leads to higher outlet temperature for the cold fluid (nanofluid) and lower outlet temperature for the hot
fluid (water) (Fig. 5).
The results presented in Fig. 7, give an idea only on the thermal performances of the micro-heat exchanger. The addition of
nanoparticles and the use of fins cause higher fluid friction and lead to higher pressure drop and pimping power. Thus, from an en­
gineering point of view it is interesting to evaluate the TPF that combine the heat transfer enhancement and the increase of the fluid
friction. The TPF as function of the CNT volume fraction at various fins heights is present in Fig. 8. Despite that the both the addition of
nanoparticles and the use of fins enhances the heat transfer, it is noticed that the use of the CNT has a positive effect of the TPF, while
the effect of fins is negative due to the augmentation of the contact surface between the fluid and the walls that causes an important
pressure drop. The maximum growth of TPF is at higher inlet velocity and lower fins height, in fact it is more than the double when the
CNT volume fraction is increased to 0.045 for an inlet velocity of 45 mm/s and fins height of 100 μm. Except for φ = 0, the TPF values
are higher than 1, which is beneficial for the performances of the micro-heat exchanger. As above mentioned, the height of the fins has
a negative effect on the TPF despite his beneficial effect on the heat transfer rate. But the decision should be also based on economical
aspect by comparing the prices of gained heat and the loosed electrical energy for the fluid pumping.

7. Conclusions
The fluid flow and heat transfer in 3D counter flow micro-heat exchanger equipped with triangular fins and filled with CNT-water
nanofluid is studied in this paper. Several cases related to height of the fins, the average inlet velocity and the CNT volume fraction are
investigated. The main finding can be summarized as follow:
- Irregularities in the temperature profiles occurs when the cross-section intersect with the fins and leads to the apparition of partial
vertical stratifications.
- Due to the presence of the fins, the temperature range becomes narrower announcing the enhancement of the heat transfer.
- The increase of CNT volume fraction to 4.5%, decreases of the temperature of the hot water by about 3o, and consequently enhances
the heat transfer.
- For fixed x-position and due to the presence of the fins, a quasi-uniform temperature field is encountered at the wall separating the
working fluids.
- The increase of the inlet velocity from 5 mm/s to 45 mm/s causes a decrease of the temperature of the hot water that can reach 24o
and thus increase of the overall heat transfer coefficient by more than 300%.
- heatlines emanate from the hot water inlet and end on the cold nanofluid inlet.
- The presence of the fins leads to a complex distribution of the heatlines.
- The height of the fins has a negative effect on the overall heat transfer for low flow velocities and positive impact for high velocities.
- Under specific conditions, the thermal performance factor can be enhanced by more than 100%.

Author statement
Mohamed Omri: Methodology, Investigation, Writing – review & editing. Hichem Smaoui: Conceptualization, Methodology,
Investigation, Writing – original draft, Writing – review & editing. Luc Frechette: Validation, Investigation, Writing – review & editing.
Lioua Kolsi: Numerical Simulations, Writing – original draft, Investigation, Writing – review & editing.

Declaration of competing interest

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.

Acknowledgment
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, (Grant
no. G:647-305-1439). The authors, therefore, acknowledge with thanks the DSR for the technical and financial support.

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