International Journal of Heat and Fluid Flow 105 (2024) 109258
Contents lists available at ScienceDirect
International Journal of Heat and Fluid Flow
journal homepage: www.elsevier.com/locate/ijhff
Empirical investigation of nanofluid performance in a microchannel heat
sink for various attributes in low Reynolds number range
Sandeep Gupta *, P.M.V. Subbarao
Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
A R T I C L E I N F O
A B S T R A C T
Keywords:
Alumina nanofluids
Microchannel heat sink
Thermo-hydraulic performance
Low Reynolds number
Axial conduction
Conjugate heat transfer
Efficient cooling techniques are imperative and present a significant challenge in the electronics industry due to
the increasing miniaturization of devices. Elevated temperatures on the surface of components pose a particular
concern within the low Reynolds numbers range due to back axial conduction. The current research endeavours
to provide an experimental assessment of cooling efficacy, heat transfer coefficient, thermohydraulic perfor­
mance and loss in concentration utilizing alumina nanofluids with 1–4 % (w/w) concentration in a microchannel
heat sink at low Reynolds numbers (10 ≤ Re ≤ 50). The findings indicate notably, the introduction of nanofluids
resulted in a 51.54 % reduction in back axial conduction in the microchannel heat sink compared to base fluid,
consequently yielding surface temperatures up to 29 % lower in the microchannel heat sink and a substantial
enhancement in heat transfer coefficient and Nusselt number up to 43.34 % and 35.85 %, respectively at Reynold
number 50. The optimal thermohydraulic performance was noted to be 1.17 at a 3 % (w/w) nanoparticles
concentration and Reynold number 50. Correlations have been devised to predict the Nusselt number and friction
factor for the microchannel heat sink based on the corresponding nanofluid concentration. The increase in heat
transfer coefficient was elucidated by considering thermophoresis and Brownian motion of nanoparticles in the
base fluid. In conclusion, this study affirms the potential of nanofluids in efficiently cooling electronic devices,
showcasing superior heat transfer performance at low Reynolds number.
1. Introduction
The escalating demand for energy-efficient, sustainable, and
portable electro-mechanical machines has brought about a revolution in
the automation sector. The fundamental driving force behind cuttingedge advancements in various sectors like space exploration, defense,
and quantum computing lies in the miniaturization of electronic devices.
Consequently, effective heat transfer management in microelectronic
devices to uphold optimal operating temperatures has emerged as a
paramount area of research focus in recent decades (Tuckerman and
Pease, 1981; Weisberg et al., 1992; Goodling, 1993). Microelectronics,
as evident, has undergone a remarkable reduction in dimensional scales,
reaching micrometer regions. This reduction translates to reduced
power requirements for components, decreased weight, and smaller
machine dimensions—attributes that hold significant value for defense,
aviation, space exploration, and automation industries. However, it’s
crucial to note that the power flux density in microelectronics (power
consumption per unit volume) is notably higher compared to macrodevices operating under similar boundary conditions. This is primarily
due to the substantial reduction in the surface area available for heat
dissipation (Kandlikar, 2012; Premachandran and Balaji, 2011). Given
the high heat transfer demand per unit area and the size limitations of
micro devices, utilizing conventional heat transfer equipment to
enhance heat dissipation is impractical. Advanced cooling technologies
are imperative to effectively manage the temperature within the safe
threshold for such micro devices (Lee and Choi, 1996; Gamrat et al.,
2005; Kim, 2004; Sidik, 2017).
Microchannels comprise parallel arrays of channel or tunnel-like
structures meticulously engineered into the heat transfer substrate to
augment device cooling. The intervening walls of these microstructures
amplify the surface area available for efficient heat transfer. Within
these microchannels, a cooling fluid, typically water, circulates, facili­
tating the transfer of heat energy from the intermediate walls through
conduction and convection processes (Zhou, 2020; Ghani et al., 2017;
Thakre et al., 2014). Microchannel heat sinks (MCHSs) are distinguished
by their high heat transfer rates and minimal pressure drops, rendering
them exceptionally suitable for cooling high-power-density electronics
and microelectromechanical systems (MEMS).
Enhancing heat transfer in microchannels can be achieved through
* Corresponding author.
E-mail address: sandeep2114@gmail.com (S. Gupta).
https://doi.org/10.1016/j.ijheatfluidflow.2023.109258
Received 13 October 2023; Received in revised form 28 November 2023; Accepted 28 November 2023
0142-727X/© 2023 Elsevier Inc. All rights reserved.
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Nomenclature
A
Cp
d
I
k
l
M
m˙
n
Nu
Δp
Q
q¨
Re
T
v
V
z
nf
np
Out
p
s
Th
W
x
Surface area, m 2
Specific heat, kJ/kg.K
Diameter of the microchannel, m
Current supplied to the heater, A
Thermal conductivity, W/m.K
Length of the microchannel, m
Maranzana number
Coolant mass flow rate, kg/ s
Number of microchannels in heat sink
Nusselt number
Pressure difference across microchannel, N/m 2
Heat, W
Surface heat flux, kW/m2
Reynolds number
Temperature, ◦ C
Velocity, m/s
Voltage, V
Distance between thermocouple and microchannel, m
Nanofluid
Nanoparticle
Outlet
Particle
surface
Thermocouple
Wall
Axial position
Greek symbols
ρ
Density, kg/m 3
φ
Nanoparticle concentration, v/v
μ
Viscosity, Pa.s
λ
Density ratio
Acronyms
DI
Deionized
DLS
Dynamic light scattering
FF
Friction factor
HTC
Heat transfer coefficient
MCHS
Microchannel heat sink
NF
Nanofluid
NP
Nanoparticle
PD
Pressure drop
PDS
Particle diameter size
RPM
Revolutions per minute
SEM
Scanning electron microscopy
THP
Thermo-hydraulic performance
Wt.%
Weight Percentage
w/w
Weight by weight percentage
Subscripts
Avg
Average
bc
Backward conduction
bf
Base fluid
conv.
Convected
eff
Effective
f
Fluid
In
Inlet
L
Loss
either active methods involving external power application for heat
removal, such as channel flow boiling, induction of surface vibrations,
boundary layer injection, or boundary layer removal, or through passive
methods that typically involve the alteration of microchannel geometry
and the modification of the working fluid. Surface alterations, including
slits, roughness, and protuberances, have undergone extensive research
and find practical applications in contemporary microchannels (Dewan
and Srivastava, 2015; Li, 2019; Sadique and Murtaza, 2022; Jabin et al.,
2019). On the other hand, modifications involving the working fluid,
such as the utilization of nanofluids (NFs) with high thermal conduc­
tivity, pseudoplastic fluids, and viscoelastic fluids, are still in the early
stages of research due to the challenges associated with producing,
stabilizing, and effectively circulating these specialized fluids (Li, 2019;
Habibishandiz and Saghir, 2022).
The fluid flowing within the microchannel is pivotal for facilitating
heat transfer from the intermediate walls of the microchannel, which
subsequently extract heat from the heat source. As a result, the working
fluid plays a fundamental role in the heat transfer mechanism of
microchannels, and its characteristics significantly influence the effi­
ciency of the cooling process. Nanofluids (NFs) represent an innovative
category of fluids wherein nanosized particles are suspended within the
base fluid (BF). Due to their distinctive properties, particularly higher
thermal conductivity, NFs have been extensively studied across various
applications, notably in microchannel heat sinks (Sidik, 2017; Godson,
2010; Kumar, 2018; Japar, 2020; Ganvir et al., 2017). The utilization of
NFs and nanoparticles (NPs) is also under extensive investigation in the
realm of renewable energy resources, photovoltaic systems, solar stills,
and the preparation of biodiesels (Gupta and Sharma, 2023; Maadi,
2021).
In the realm of Microchannel Heat Sinks (MCHS), Nano Fluids (NFs)
have emerged as promising coolants owing to their enhanced heat
transfer properties and reduced entropy generation and irreversibility
(Bahiraei, 2020). Existing research in the MCHS domain has predomi­
nantly focused on high Reynolds numbers. However, there is a notable
gap in research concerning the utilization of NFs to investigate their heat
transfer properties and evaluate the impact of back conduction at low
Reynolds numbers. It is crucial not to overlook axial back conduction
within the low Reynolds number range, as it tends to elevate surface
temperatures. One of the initial studies in the field of nanofluids usage
was conducted by Choi and Eastman (Choi and Eastman, 1995), who
explored the enhancement of thermal conductivity in NFs. They docu­
mented a notable improvement in the thermal conductivity of NFs by
incorporating trace amounts of NPs into the BF.
Following this research, many subsequent studies focused on inves­
tigating the heat transfer performance of NFs in MCHS. Among these
studies, Keblinski et al. (Keblinski, 2002) examined the impact of NP size
on the heat transfer performance of NFs within microchannels. Their
findings indicated that adding smaller NPs to the BF resulted in an
increased thermal conductivity of the NFs. However, they also observed
a rise in pressure drop in the NFs. Moreover, they noted that heat
transfer enhancement was more significant in smaller channels. Wen
and Ding (Wen and Ding, 2004) conducted experiments (Reynolds
number range: 500–2100) and concluded that using alumina NFs could
significantly enhance heat transfer in the microchannel. They attributed
this enhancement to the longer entrance length of the boundary layer in
NFs, which had a major influence on their results. Yang et al. (Yang,
2005) utilized graphite NPs to prepare NFs and found that the experi­
mental values of heat transfer coefficient (HTC) increased less than
predicted by theoretical correlations. Furthermore, Lee et al. (Lee and
Mudawar, 2007) evaluated the heat transfer performance of Al2O3 and
water NFs in an MCHS. They discovered that HTC increased with the
NPs concentration, albeit at the expense of increased pressure drop.
Heidarshenas et al. (Heidarshenas, 2020) conducted an experimental
study explaining the effect of NP size and concentration on the heat
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S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
transfer performance of NFs containing water and Al2O3 in an MCHS.
They observed an increase in HTC with an increase in NP concentration
but a decrease with an increase in NP size. Additionally, they found that
the pressure drop increased with higher NP concentration and size.
Researchers (Bahiraei et al., 2022) studied the effect of nanoparticles
with different shapes on thermo-hydraulic performance and concluded
that particles with an O shape had the lowest pressure drop. J. Li and C.
Kleinstreuer (Li and Kleinstreuer, 2008), as well as Chein & Huang
(Chein and Huang, 2005), theoretically proposed a new model based on
Brownian motion. This model better explained the experimental results
and the enhancement in heat transfer using low-concentration NFs
without causing pressure drops. Kumar et al. (Kumar and Sarkar, 2018)
presented a numerical analysis of the thermal performance of an MCHS
using aluminum oxide–water NFs. They found that the use of NFs
increased HTC by up to 15.6 %, with no appreciable rise in the pressure
drop across the heat sink. These results were consistent with the
experimental data. Bahiraei et al. (Bahiraei, 2016) conducted singlephase and two-phase modeling in computational fluid dynamics (CFD)
analysis to investigate the nanofluid bulk temperature along the tube
length. They found that both sets of results were in good agreement.
Several other studies have also investigated the use of NFs in MCHSs and
reported significant improvements in heat transfer performance
compared to traditional working fluids at high Reynolds numbers (Re).
The mechanism underlying heat transfer enhancement in MCHSs using
NFs is still under investigation. Several theories have been proposed,
including Brownian motion of NPs, increased thermal conductivity of
the working fluid, and an increase in surface area due to the presence of
NPs. In conclusion, the utilization of NFs in MCHSs has demonstrated
promising results in enhancing heat transfer performance. Nowadays
artificial neural network, genetic algorithm, artificial intelligence and
machine learning-based methods and algorithms are also being used to
predict the heat transfer characteristics of NFs (Bahiraei, 2020; Aliza­
deh, 2021).
In analysis of MCHS, the linear nature of the axial variation in bulk
fluid temperature occurs only when the constant heat flux applied, is
sensed at the interface of the solid and fluid in the microchannel.
However, this assumption does not hold true in cases where a micro­
channel system is subject to a conjugate condition, wherein the actual
point of application of the boundary condition is at a distance from the
true solid–fluid boundary. Maranzana et al. (Maranzana et al., 2004)
analytically studied the effect of axial wall conduction effect at low Re
number and introduce the Maranzana number and explained that con­
stant heat transfer conditions cannot be applied in MCHS where M >
0.01 (Re 〈1 0 0), where back axial conduction effect is predominant.
Back axial conduction is not a recent discovery; rather, it has been
largely overlooked inadvertently due to its seemingly minor impact on
heat transfer in conventional-sized channels. However, as the hydraulic
diameter of a channel decreases, the correlation between the substrate
and bulk fluid temperatures gains importance due to the proportionate
dimensions of the fluid in relation to the solid wall. A study by Khan­
dekar and Moharana (Khandekar and Moharana, 2015) explained the
effect of back axial conduction in MCHS and reported that effect is
analysed in MCHS operating on liquid coolant. Recent study by Magh­
rabie et al. (Maghrabie, 2022) provided a comprehensive review of heat
transfer analysis in MCHS and reported a lack of studies available at low
Reynolds numbers (<50). The references therein do not delve into the
effect of axial back conduction, particularly prevalent at low Reynolds
numbers in MCHS using NFs. Further research is imperative to thor­
oughly investigate the heat transfer performance of NFs at the lower
Reynolds numbers in MCHS. Bedi and Subbarao (Bedi and Subbarao,
2021), documented occurrence of the back conduction effect at low
Reynolds numbers (<50) in pure fluid. Therefore, for this study, a
Reynolds number range of 10 to 50 was specifically chosen.
Emphasizing the importance of axial back conduction is crucial, as it
reduces convective heat transfer in MCHS. Back conduction leads to an
increase in surface temperature, necessitating control. This study
investigates axial conduction, heat transfer analysis, pressure drop,
thermohydraulic performance and estimation of loss in concentration of
NFs in MCHS when operated at low Reynolds numbers using NFs.
2. Materials and method
2.1. Preparation of alumina nanofluids
The Al2O3 NPs were procured from SRL Pvt Ltd. with particle
diameter of 30 nm. The selection of alumina nanoparticles was delib­
erate, driven by their inherent ability to maintain excellent dispersion
stability in a variety of base fluids, even in the absence of surfactants.
Alumina nanoparticles typically possess a high inherent surface charge
due to the presence of hydroxyl groups on their surface. This charge
helps in electrostatic repulsion, reducing the likelihood of particles
sticking together and forming agglomerates. Alumina nanoparticles
have high thermal conductivity, enhancing the heat transfer properties
of the nanofluid. When dispersed in a base fluid, they can significantly
enhance the thermal conductivity of the nanofluid. The density, specific
heat, and thermal conductivity of these alumina NPs were 3900 kg/m3,
880 J/kg K and 42 W/m K, respectively.
The parameters for preparing NFs with alumina NPs were selected
based on a thorough review of the literature (Noroozi et al., 2015; Ali
and Salam, 2020; Mahbubul, 2014; Shah, et al., 2018). In the prepara­
tion of NFs using alumina NPs and DI water with 18 mho purity, a
measured amount of alumina NPs was introduced into DI water and
stirred using a magnetic stirrer at 500–800 RPM without applying heat,
stirring for 30–45 min until achieving a uniform dispersion of the NPs.
The NP concentration in the solution varied from 1 to 4 % (w/w) to
achieve the desired properties. To ensure even dispersion of the NPs in
the base fluid (BF), the solution was subjected to ultrasonication at 50 %
power and 20 kHz for 10–20 min. This process helped in breaking down
any agglomerates and improving particle dispersion. An ice jacket was
used to maintain the solution temperature below 25 ◦ C. In this study, the
surfactant was not used as the concentration is not high and limited up
to 1.02 % volumetric concentration and stable solution was prepared
using sonication process. Also, the heat sink is made up of stainless steel,
which has less deposition of alumina NPs as it often has a smoother
surface compared to some other materials. Smoother surfaces generally
provide fewer sites for particles to adhere to, resulting in reduced
deposition. Also, it often develops a passive oxide layer (primarily
chromium oxide) that can affect the interaction with nanoparticles. This
oxide layer may act as a barrier, reducing the direct contact between the
nanoparticles and the underlying metal surface. These combined factors
contribute to reduced agglomeration and deposition of NPs on the
surface.
Post the NF preparation, the solution was stored in an appropriate
container and kept in a clean, dry location. It was crucial to shield the
NFs from light, heat, and mechanical agitation, as these factors could
lead to settling or aggregation of the NPs. The prepared samples were
examined for any visible sedimentation after seven days, both with and
without the ultrasonication process (Fig. 1). The observations indicated
no apparent sedimentation in the ultrasonicated samples. Ultra­
sonication played a critical role in minimizing NP agglomeration in the
NFs, a feat that would have been difficult to achieve without this
process.
2.2. Characterization of nanofluids
The prepared NFs underwent characterization through scanning
electron microscope (SEM) imaging to observe the particle morphology.
In the absence of sonication, SEM imaging (Fig. 2a) depicted particle
agglomeration. Conversely, Fig. 2b showcased the improved quality of
the NFs after undergoing the sonication process, with particles being
uniformly dispersed in the base fluid (BF) and devoid of agglomeration.
Particle size and their distribution were analyzed using dynamic light
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S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 1. Nanofluids without ultra-sonication (sample 1–4) and with ultra-sonication (sample 6–9) after seven days of preparation, DI water (sample 5).
Fig. 2. Nanofluids SEM image (a) without sonication and (b) with sonication.
scattering (DLS). The measurements were conducted using a zetasizer.
The prepared samples, with NP concentrations ranging from 1 to 4 %
(w/w), exhibited an average particle diameter size (PDS) between 103.5
and 197.2 nm. In Fig. 3a and Fig. 3b, the Particle Diameter Size (PDS)
and their intensity percentage are illustrated respectively for 4 % NP
concentration. Without utilizing sonication, the PDS was notably high,
measuring approximately 1100 nm (Fig. 3a). This significant size was a
result of particle agglomeration within the nanofluids (NFs), leading to
visible settling. Conversely, in Fig. 3b, the impact of the ultrasonication
process is evident. Following ultrasonication, the PDS was drastically
reduced to 197.2 nm, highlighting the effectiveness of sonication in
mitigating particle agglomeration, and enhancing dispersion within the
NFs.
applicable to uniformly scaled, non-interacting, and randomly dispersed
spherical particles, particularly in cases of statistically homogeneous
and low-volume fraction of solid suspensions in liquid. According to the
Maxwell model, the effective thermal conductivity is expressed as
follows:
keff =
μnf
= exp(6.599ϕ/(0.288 − ϕ), for ϕ = 0 to 4.0% vol.
μbf
2.4. Experimental setup and method
(1)
The specific heat of the NFs was described by Zhou and Ni (Zhou and
Ni, 2008), employing a model that aligns well with experimental results.
This model is rooted in statistical and classical mechanisms, assuming
that the NPs are in thermal equilibrium with the BF.
(ρCp )bf (1 − φ) + φ(ρ(Cp )np )
ρnf
(4)
Table 1 represents the thermophysical properties of NFs calculated at
20 ◦ C.
The thermophysical properties of the NFs were calculated using
available equations. Density, for instance, was determined using mixing
theory (Pak and Cho, 1998):
(Cp )nf =
(3)
The viscosity of nanofluids (NFs) is influenced by a range of pa­
rameters, including properties of the BF, volume fraction of NPs, their
size, shape, and temperature. A high predictive accuracy, with R2 = 0.99
for ϕ ranging from 0 to 4.0 %, was achieved as per the findings of
reference (Alkasmoul, 2018).
2.3. Properties of nanofluids
ρnf = ρbf (1 − φ) + ρnp φ
kp + 2kbf + 2(kp − kbf )ϕ
kbf
kp + 2kbf − (kp − kbf )ϕ
The experimental apparatus for heat transfer analysis in MCHS is
depicted in Figs. 4a,b. The MCHS substrate material is stainless steel,
featuring 18 cylindrical channels with a diameter of 400 µm and a length
of 40 mm. A stainless-steel cylindrical tank serves as a reservoir and is
connected to a peristaltic pump (Make-Acuflo with Master Flex tubing
96400–16). The pump was calibrated to provide mass flow rates at
various RPMs, capable of supplying a flow rate ranging from 0.25 g/min.
to 24 g/min. at different RPMs. MCHS is connected to an inlet and outlet
header to ensure uniform flow throughout all the channels.
A plate-type heater with a capacity of 50 W was utilized to generate a
uniform heat flux of 3750 W/m2 and 6875 W/m2 respectively on the top
surface of the MCHS. Power was supplied through a variable transformer
connected to the heater. The supplied current and voltage values were
(2)
Given that thermal conductivity is a crucial property influencing
enhanced heat transfer, numerous experimental studies have been
conducted in this domain. Utomo et al. (Utomo, 2012) conducted ex­
periments demonstrating that the addition of NPs improves thermal
conductivity. To evaluate the thermal conductivity of base liquid-NPs
solid suspensions, the Maxwell model was employed. This model is
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S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 3. Nanofluids particle diameter size intensity a) without sonication b) with sonication.
Table 1
Thermophysical properties of NFs calculated at 20 ◦ C.
Mass concentration
of NP (%)
Density
(kg/
m3 )
Heat
capacity
(J/kg.K)
Thermal
conductivity
(W/m.K)
Viscosity
(Pa.s)
0
1
2
3
4
998.2
1005.64
1013.08
1020.52
1027.96
4182
4149.17
4116.81
4084.93
4053.51
0.597
0.605
0.613
0.621
0.629
0.00099
0.00105
0.00112
0.00119
0.00127
measured using a multimeter. A differential pressure transducer was
employed to measure the pressure drop across the MCHS. To control the
coolant’s outlet temperature, a radiator with a fan was utilized to
maintain a constant tank temperature. A closed loop was formed using
silicon piping. Tank temperature, coolant inlet and outlet temperature,
MCHS surface temperatures, etc., were measured using T-type thermo­
couples and a data acquisition system. T-type thermocouples were
chosen to match the temperature range of the experiment and were duly
calibrated prior to their utilization. To minimize heat loss from the
system, asbestos insulation ropes and bakelite casing were utilized. The
heat loss through MCHS to the surroundings was quantified under noflow conditions to calculate the net heat flux to the MCHS. Initially,
the setup was operated using DI water by adjusting the flow rate with the
pump RPM at a desired Reynolds number. The steady-state condition is
achieved in a two-hour period. Temperature readings at different loca­
tions (shown in Fig. 4c), voltage, and current were recorded.
Fig. 4a. Schematic of the experimental setup.
5
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 4b. Test rig for experimental work.
Fig. 4c. Schematic of axial temperature measurement system of MCHS.
All experiments were repeated to ensure repeatability, and the mean
values were used for calculation purposes (Fig. 5a). The experimental
setup was validated using previously published data (Tiselj, 2004) at a
mass flow rate of approximately 0.07 g/s and a constant heat flux of
about 6 W. This validation was based on comparing the non-dimensional
axial surface temperature variation with the non-dimensional length of
the microchannel heat sink. The trend of the axial temperature is nearly
identical (Fig. 5b). However, there is an approximate difference of 7–19
% between these values due to variations in channel length, heat sink
material, and flow parameters.
supplied to the channel surface was:
The convective heat transfer by the fluid Qconv. was calculated by the
following equation:
Qconv. = ṁCp (Tout −
Tin )
(7)
As axially back conduction of heat was observed, to calculate the
axially backward conducted heat (Qbc) the following heat balance
equation was used (Bedi and Subbarao, 2021):
Q = Qconv. + Qbc + Qloss
2.5. Equations used and parameters calculations
(8a)
Thus, the net back axially conducted heat was calculated as follow:
The joules equation was used calculate the total heat given to the
MCHS:
Q = V.I
(6)
Qnet = Q − QL
Qbc = Q − Qconv. − Qloss
(8b)
The heat flux can be calculated by:
(5)
q̈ =
The heat loss QL was estimated by calculating the temperature dif­
ference between the surrounding and channel surface. Thus, the net heat
6
Qconv.
Qconv.
=
Area of heating surface n × l × πd
(9)
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
f =()
l
d
Δp
( )
2
× ρ2v
(13)
To determine the thermo-hydraulic performance following equation
was used (Li, 2020):
( )
Nunf
Nubf
THP = (
(14a)
)1/3
Δpnf
Δpbf
In order to consider the variation in Pr, the thermo-hydraulic perfor­
mance can also be formulated in terms of Stanton Number and FF
(Wang, 2022):
( )
Stnf
Stbf
(14b)
THP = ( )1/3
Fig. 5a. Variation in axial temperature of MCHS measured by thermocouples.
fnf
fbf
2.6. Uncertainty analysis
In the experiment, several sources of error were identified, including
systematic error, variations in environmental conditions, and potential
human errors. The uncertainties associated with both the measured and
calculated parameters were documented in Table 2 and Table 3,
respectively. The uncertainty analysis followed the procedure outlined
by Selvam et al. (Selvam, 2016), equation (15) was used to calculate the
uncertainty in the Nu number.
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
]
[
(
) √
√ (Δq̈)2 (Δ(ΔT))2 (ΔD)2
ΔNu
√
(15)
=
+
+
q̈
Nu
ΔT
D
2.7. Computational methodology
For simulation purposes, a rectangular piece of aluminum was cho­
sen as the heat sink, with dimensions 40 mm x 6 mm x 9 mm as depicted
in Fig. 6. Circular microchannels with a radius of 400 µm were cut into
this structure. After validation using experimental results, this reduced
model was utilized for simulations across all cases. Fig. 7 a illustrates the
contours of static temperatures for this reduced model. The measured
values of inlet coolant temperature at a steady state were employed to
set the temperature conditions at the inlet. Notably, there’s a noticeable
increase in fluid temperature from the inlet to the outlet within the
microchannels. The coolant temperature at different locations was uti­
lized to calculate the local Heat Transfer Coefficient (HTC). Addition­
ally, the heat flux at the channel surface, depicted in Fig. 7b, varied
along the length due to back conduction of heat on the heat sink surface.
This variation in heat flux was considered in the calculation of local
HTC.
Fig. 5b. Comparison of present and Tiselj (Tiselj, 2004) non dimensional
temperature profile.
However, it’s important to note that due to back conduction of heat,
the heat flux on the channel surface is not constant. This variation was
computed using results from ANSYS Fluent.
The local heat transfer coefficient was computed as follows:
hx =
q̈
(Tsx − Tfx )
(10)
Here Tsx and Tfx are the channel surface temperature, and the bulk
fluid mean temperature at location x in channel axial direction. Tsx was
calculated by the thermocouple temperature as follows:
Tsx = Tthx −
q̈z
k
(11)
Table 2
Uncertainty associated with various measured parameters.
Here Tthx is the temperature measured by the thermocouple at
location x and z is the distance between the channel surface and ther­
mocouple location.
The mean heat transfer coefficient was computed by using:
havg =
1
L
∫L
hx • dx
(12)
0
The following equation was used to calculate the FF:
7
Parameter
Uncertainty (%)
Channel diameter
Length
Temperature
Voltage
Current
Mass flow rate
Pressure drop
±1.52
±0.12
±0.85
±1
±1.5
±0.008
±1
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
concentration in the BF. As the concentration of NPs increases in NFs,
the fraction of conduction decreases (Fig. 11), and the convection part of
heat increases (Fig. 12). Fig. 13 shows the MCHS surface temperature
rise (T-Tambient), when operated at Re = 10, showing the lesser increase
in surface temperatures when driven on NFs compared to BF. Also, this
increase is lowered as the NPs concentration rises in the BF. Thus, NFs
could help to limit the surface temperature rise due to their increased
thermal conductivity, which can act as thermal bridges between the
microchannel and the substrate, reducing the temperature gradient and
the magnitude of back conduction. Correspondingly, for the same sur­
face temperatures of MCHS using BF and NFs, slightly lesser mass flow
rate is required for the NFs, which in turn could reduce the pumping
power saving the external energy input.
Table 3
Uncertainty associated with various calculated parameters.
Parameter
Uncertainty (%)
Heat flux
Reynolds number
Heat transfer coefficient
Nusselt number
Friction factor
THP
±1.81
±1.52
±2.17
±2.65
±3.54
±3.84
3.2. Heat transfer characteristics
The effect of increasing Re on HTC at different NP concentrations is
depicted in Fig. 14. The HTC value increases with an increase in Re and
NP concentration in DI water. The maximum HTC value is obtained at
Re = 50, and θ = 4 %, reaching 8351 W/m2K. This value is 43.34 %
higher than the HTC value for DI water at the same Re. In Fig. 15, the
increase in Nu with the concentration of NP in NF at different Re is
shown. The NFs exhibit the maximum increase in Nu, approximately
35.85 %, at a concentration of 4 % alumina NPs and Re = 50.
There are several mechanisms that contribute to the increase in HTC
observed in NFs, including increased thermal conductivity, surface area
and enhanced convection. The addition of NPs to a BF increases its
thermal conductivity, enhancing its ability to transfer heat. This is
because the NPs have a much higher thermal conductivity than the BFs.
NPs have a higher surface area to volume ratio, meaning they can
interact with a larger surface area of the fluid. This increases the inter­
facial area between the fluid and the heat source, which in turn, in­
creases the heat transfer coefficient. Adding NPs to a liquid can alter the
flow patterns of the fluid, leading to enhanced convection. This can
increase the heat transfer coefficient by promoting better mixing of the
fluid and reducing the thickness of the thermal boundary layer. In NFs,
the NPs undergo Brownian motion, which results in increased collision
frequency with the fluid molecules. This, in turn, leads to enhanced
thermal energy transfer between the particles and the BF, resulting in an
increased HTC (Godson, 2010; Kim, 2019; Siricharoenpanich et al.,
2021; Huminic and Huminic, 2011; Pinto and Fiorelli, 2016; Moham­
med, 2011).
As the NPs weight is more than the BF molecules and the NPs size is
larger than the base liquid molecule, so in one collision, the NP collides
with many BF molecules, so the impulsive energy is higher than the
collision of liquid molecules among themselves. Thus, the collision be­
tween an NP and a base liquid molecule can transfer more energy.
Consequently, NFs exhibit improved heat transfer characteristics and
higher HTC.
Thermophoresis, conversely, is the migration of particles in a fluid
due to temperature gradients. When a temperature gradient is present in
a NF, the NPs will experience a force called thermophoresis (also known
as thermodiffusion) that drives them towards the hotter regions of the
fluid. This results in an accumulation of NPs in the hotter regions,
further enhancing the HTC (Habibishandiz and Saghir, 2022; Maghra­
bie, 2022; Kim, 2019). Overall, the combination of these mechanisms
results in a higher heat transfer coefficient in NFs compared to their BFs,
making them a promising option where efficient heat transfer is essen­
tial. The percentage increase in Nu is lesser at lower Re and at lower
concentration as thermal entry length is greater for higher Re and
θ(Lt,laminar 0.05RePrD, where 0.05RePrD = Lh,laminar ) because of the
higher thermal gradient in the entry length region (Wen and Ding,
2004).
Thus, it was observed that the HTC of NFs depends on Re, Pr, and NP
concentration (in turn density ratio λ). As Re, Pr, and λ increases, Nu also
increases. Based on the 50 experimental data obtained from the present
Fig. 6. Reduced model of MCHS for computational analysis.
3. Result and discussion
3.1. Axial conduction study
Axial conduction in microchannel heat sinks refers to the mechanism
of heat transfer that occurs in axially in backwards direction in solid part
of the microchannel (Fig. 8). Generally, the wall thickness of MCHS is of
same order as diameter of the channel. Thus, axial heat conduction in
the solid walls cannot be neglected, particularly at low Re range.
Consequently, in microchannel heat sinks, achieving a constant wall
heat flux condition is difficult. Thus, conjugate heat transfer can influ­
ence the heat patterns, especially at low Re and must be taken into
account.
At low Re, the flow is laminar, and the heat transfer coefficient is also
controlled by the conduction. Back conduction becomes more signifi­
cant at lower Re because the fluid velocity is lower, which reduces the
convective heat transfer coefficient and results in higher surface tem­
peratures. To evaluate axial conduction effect, Maranzana et al. (Mar­
anzana et al., 2004) proposed a parameter which is a ratio of the heat
conducted in the solid wall to the heat convected through the coolant.
The axial conduction effects were proved to be significant for Maranzana
number, M > 0.01. Various values of ‘M’ (calculated with equation (16)
exhibited by the present setup, are ranged between 0.02 to 0.25. Fig. 9
shows the variation of heat axially conducted with respect to Maranzana
number. As the value of M increases, the fraction of heat conducted
axially also increases.
( )( )
kw
Aw
1
M=
(16)
.
.
kf
Af RePr
The proposed method for addressing back conduction in micro­
channel heat sinks is to use NFs, which can improve the thermal con­
ductivity of the fluid in the microchannels and reduce the temperature
gradient between the microchannel and the substrate, thereby reducing
back conduction. Fig. 10 shows the rise in inlet fluid temperature with
respect to reservoir temperature for BF and NFs by gaining heat due to
heat flowing axially backwards. Thus, the convection part of the total
heat given is reduced. Using the NFs minimizes the effect of back con­
duction, and the convection part of total heat increases with the NPs
8
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 7. a) Temperature contour of reduced model of MCHS b) heat flux at channel surface for Re 50, 4% concentration and heat flux= 6875 W/m2.
Fig. 8. Back conduction in microchannel heat sink.
experimental study, a correlation for determining the Nu has been
developed:
(
)
Nu = 0.337 Re0.385 Pr0.459 λ6.827
Fig. 9. Fraction of axial heat conducted with Maranzana no. at Re = 10.
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S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 12. Fraction of convection of heat input v/s Re at different mass con­
centrations of NPs.
Fig. 10. MCHS inlet fluid temperature rise with Re at different mass concen­
trations of NPs.
Fig. 13. Surface Temperature rise of MCHS v/s Re at different mass concen­
trations of NPs.
Fig. 11. Fraction of axial conduction of heat input v/s Re at different mass
concentrations of NPs.
increased particle size in NFs. FF value has been indicated in Fig. 18,
showing the FF variation, following the decreasing trend with respect to
Re. FF value increases with an increase in NPs concentration. The similar
non-linear behaviour of PD and FF between BF and NFs shows that the
alumina NPs do not alter fluid behaviour. It increases the PD and FF due
to increase in frictional forces and viscosity (Li, 2020). Designing the
microchannels to minimize pressure drop while maintaining effective
heat transfer is essential for an efficient cooling system. Based on the 50
experimental values, a correlation for the FF in terms of Re and λ has
been proposed:
Above correlation is valid for 10 ≤ Re ≤ 50, 4.04 ≤ Pr ≤ 8.7, 1 ≤ λ ≤
1.1029.
The above correlation was found to be in good agreement with the
experimental result of 5.93 % MAE. Fig. 16 shows the comparison be­
tween the experimental and correlated values of Nu.
3.3. Pressure drop and friction factor
The pressure drop within the microchannels is another critical aspect
of thermohydraulic performance. High pressure drops can negatively
affect the system’s efficiency and the energy needed to pump the
coolant. When the NPs flow through a microchannel, their size and
concentration can have an impact on the pressure drop across the
channel. As the size and concentration of the NPs in the BF increase, the
pressure drop across the channel typically increases as well. Fig. 17
shows the pressure drop value across MCHS using the NFs, which in turn
shows the increase in pumping power. The rise in PD value for Re = 10 is
about 58.75 % and 96.25 % for θ = 3 and 4 %, respectively. The higher
PD for θ = 4 % can be attributed to a higher concentration as well as
FF = 65.1(Re− 0.99 λ1.634 )
Which is Valid for 10 ≤ Re ≤ 50, 1 ≤ λ ≤ 1.1029.
3.4. Thermo-hydraulic performance
The overall thermal performance indicates the performance of
MCHS, considering the hydraulic-thermal performance using different
coolants. THP analysis of a MCHS is central to designing an effective and
efficient cooling system for electronic components. It can be observed in
10
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 14. Variation in HTC with Re for DI water and nanofluids at different mass
concentrations.
Fig. 16. Comparison between experimental and correlated Nusselt number
for NFs.
Fig. 15. Variation in Nu with Re for DI water and nanofluids at different mass
concentrations.
Fig. 17. Variation in pressure drop across MCHS with Re at different NPs mass
concentrations.
Fig. 19 that as the Re increases, the value of THP also increases for all the
concentration of NPs. In Fig. 20, as the NP concentration is increasing in
the BF, the THP is also increasing up to 3 %, after which it shows a slight
decrease in the THP for θ = 4 %. THP based on equation (14b) is rep­
resented in Fig. 21, in which Stanton number and FF were used to
calculate the THP. The difference between the two values of THP is less
than 1 %, allowing for the use of either equation for THP calculation.
The reason for decrease in THP for θ = 4 % can be attributed as larger
particles have a greater tendency to interact with the walls of the
microchannel, creating more friction and resistance to the flow of the
fluid. Consequently, this results in a higher pressure drop across the
microchannel. Additionally, larger particles may also cause clogging in
the microchannel, further increasing the pressure drop. Therefore, it is
important to consider the size and concentration of NPs when designing
microfluidic systems in order to optimize their performance and avoid
potential issues such as clogging or excessive pressure drop. THP allows
to optimize the design parameters such as microchannel geometry and
coolant flow rates to achieve the desired balance between heat transfer
efficiency, pressure drop, and overall thermal performance.
3.5. Loss in concentration
NFs are suspensions of NPs in a BF. The concentration of NPs in the
NF can be lost during flow in a microchannel due to several reasons like
settling, agglomeration, and deposition. The NPs can settle to the bottom
of the channel due to gravity. The NPs can aggregate and form larger
particles, which can then settle to the bottom of the channel. The NPs
can deposit on the walls of the channel due to Brownian motion, van der
Waals forces, or electrostatic attraction. These factors result in an in­
crease in the concentration of NPs near the channel walls, where they
are more likely to be transported by fluid flow and decrease the con­
centration in the NF. The loss in concentration could be visibly seen in
the channel walls and the piping.
The loss of concentration after the experimentation has been esti­
mated using UV–VIS spectrophotometry. Fig. 22 shows the spectrum of
NFs showing the peak absorbance value at 226.5 nm. Fig. 23 shows the
loss in concentration of NFs at different Re. It was observed that per­
centage loss reduced with an increase in Re for all the concentrations.
The maximum loss has been observed at low Re (Re = 10).
11
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 20. Variation in THP of MCHS using NFs with mass concentration of NPs
at different Re.
Fig. 18. Variation in FF in MCHS with Re at different mass concentrations
of NPs.
Fig. 21. Variation in THP of MCHS using NFs with mass concentration of NPs
at different Re using Stanton number and FF.
Fig. 19. Variation in THP of MCHS using NFs with Re at different mass con­
centrations of NPs.
• It was observed that the percentage increase in heat transfer coeffi­
cient increases as the nanoparticles concentration and Reynolds
number increase. Heat transfer coefficient and Nusselt number value
increased by 43.34 % and 35.85 %, respectively for Re = 50 and 4 %
concentration.
• Although the heat transfer coefficient and Nusselt number increased
as the Reynolds number and concentration increased but simulta­
neously pressure drop and friction factor also increased, which was
seen as a penalty to pumping power. At low Reynolds number value,
the pressure drop value was not much higher for the nanofluids. For
the highest concentration of nanofluids (4 %), the pressure drop was
about 2 kPa.
• The thermohydraulic performance of nanofluids increased up to 3 %
concentration, but a decreasing trend was seen for a 4 % concen­
tration for all the Reynolds number values. The maximum thermo­
hydraulic performance value was found to be 1.17 for Reynolds
number = 50 and 3 % concentration.
• The percentage loss in concentration of NFs when flowing in the
system was found to be in inversely proportional to Re due to
Various methods can be used to mitigate the loss of NPs concentra­
tion, such as using a surfactant to stabilize the NPs, controlling the flow
rate to prevent settling and aggregation, and using a more viscous BF to
reduce diffusion.
4. Conclusion
Nanofluids have been extensively researched as a promising alter­
native to conventional coolants in microchannel heat sinks due to their
improved thermal performance. The present study has shown that using
nanofluids can significantly enhance the heat transfer performance of
microchannel heat sink compared to conventional coolants and reduce
the effect of axial conduction. The followings are the key conclusions
made from the above study:
• The back axial conduction and surface temperatures were found to
be lesser for nanofluids when compared to basefluid. Reduction in
back conduction was found to be upto 51.54 %. That results in
reduction of surface temperatures by 29 %.
12
S. Gupta and P.M.V. Subbarao
International Journal of Heat and Fluid Flow 105 (2024) 109258
Fig. 22. Spectrum of nanofluids using UV–Visible Spectrophotometer.
Data availability
No data was used for the research described in the article.
Acknowledgement
The authors would like to thank Indian Institute of Technology Delhi
for providing the facility to carry out this research work.
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CRediT authorship contribution statement
Sandeep Gupta: Writing – review & editing, Writing – original draft,
Validation, Software, Resources, Methodology, Investigation, Concep­
tualization. P.M.V. Subbarao: Conceptualization, Writing – review &
editing, Supervision, Resources.
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.
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