Numerical study on the improvement of the cooling of a microprocessor
by the use of nanofluids
TALOUB DJEDID1, BOURAS ABDELKARIM2, ZIED DRISS3
1,2Department of Physics, Faculty of Sciences, University Mohamed Boudiaf of M'sila, ALGERIA
1Laboratory of Materials Physics and its Applications, University Mohamed Boudiaf of M’sila,
ALGERIA
3Department of Mecanics, Electromechanical Systems Laboratory, University of Sfax, TUNISIA
Abstract: - The numerical study on the improvement of the cooling of a microprocessor by the use of Nanofluids
has been made. Natural convection is analyzed in a box fence with a temperature source encountered at its lower
border and loaded with an Ethylene Glycol-Copper nanoparticle. This article explores the influences of relevant
aspects such as thermal Rayleigh number, solid volume fraction, and enclosure dimensions on the thermal
efficacy of the box fence, which are enhanced with an enlargement in thermal Rayleigh number and solid volume
fraction. The results also illustrate that the change of the warmth transfer rate concerning the box dimensions of
the enclosure is unlike at inferior and elevated thermal Rayleigh numbers. A simile is offered between the upshots
got and the literature. Results were presented in terms of heat transfer rate depending on thermal Rayleigh number
(Rat = 103, and 106), nanoparticle solid volume fraction (0 ≤ φ < 5%), and box dimensions. The results show that
raising the solid volume fraction of the nanoparticles (φ = 5%) drive a rise in the efficient conductivity of the
working fluid and consequently the improvement of the heat transfer rate by approximately ≈ 10% per compared
to the base fluid case.
Key-Words: - Natural convection, box enclosure, thermal Rayleigh numbers, nanofluid, volume fraction.
Received: June 23, 2021. Revised: January 14, 2022. Accepted: February 25, 2022. Published: March 26, 2022.
1 Introduction
In recent years, we continue to witness the
unparalleled development undergone by power
electronics, particularly in terms of miniaturization
technology. However, this development is
handicapped by the limitation of the cooling
necessary to the evacuation of higher and higher heat
fluxes from even smaller surfaces. The first
generation of power electronics components were
cooled by natural convection using air heaters. Then,
and as this became insufficient, fans were integrated
into it allowing air to be blown directly onto the fins
constituting the radiator. Considerable investigations
have been performed on the properties of nanofluids
and their applications in warmth transfer systems. It
is, thus, of basic interest to investigate innovative and
functional techniques that support the natural
convection outflow for different shapes of electronic
constituents. The nanofluids have also been used to
enhance the warmth transfer rate by increasing the
thermal conductivities of the fundamental fluid using
suspended nanoparticles. Among the works that
exist, we quote some experimental and/or numerical
works with/without the use of nanofluid.
Siddiqui et al. [1] performed an empirical
investigation on flat warmth sink utilizing Al2O3 and
CuO nanoparticles. Bahiraei et al. [2-4] optimized
and investigated the efficiency and entropy
generation of a combination nanofluid having
graphene nanoplatelets adorned with silver
nanoparticles in three separate liquid unions for CPU
cooling. Hybrid nanofluids show a promising way to
improve cooling in electronics. Sarafraz et al. [5]
experimentally studied the thermic performance of a
coolant bloc operating with gallium, a nanofluid
(CuO/water), and clean water. The processor utilized
in this investigation is rated at three conditions of
standby, normal, and overload operating methods.
The impacts presented that gallium is the
considerable effective coolant between nanofluid and
water in terms of convective thermic performance. Qi
et al. [6-9] established and examined an empirical
setting for the warmth transfer properties of CPU
refrigerated by nanofluids. The impacts of
nanoparticle mass particles and Reynolds numbers on
warmth transfer and flow characteristics are
discussed. It was also discovered that Al2O3-water
and TiO2-water nanofluids could decrease CPU
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temperature by 23.2% and 14.9% at most useful
likened to water respectively. Sun et al. [10]
experimentally measured in a liquid-cooled central
processing unit (CPU) warmth sink the warmth
transfer coefficient and the flow resistance
coefficient of Cu-water and A12O3-water
nanofluids. The results demonstrate that the cooling
performance of a CPU warmth sink was remarkably
improved by using the Cu-water and A12O3-water
nanofluids and the exterior temperature of the CPU
scrap was reduced by 4-18°C compared with
demineralized water. Snoussi et al. [11] numerically
treated the laminar flow of nanofluids in a 3D copper
microchannel warmth sink (MCHS) with a
rectangular enclosure and invariant warmth flux. The
numerical consequences illustrate that the increase in
warmth flux has a remarkably small influence on the
warmth transfer coefficient for pure water, while an
observable impact for the instance of a nanofluid.
Shoukat et al. [12] investigated the stability of
nanofluids and saw the warmth transfer improvement
compared to water. Chen et al. [13] investigated
numerically and experimentally cooling performance
CPU, used TiO2-water 9% as coolant. The numerical
results agree nicely with the empirical results. The
results demonstrated that nanofluids can effectually
decrease the middle CPU temperature by 4.54 ◦C at
best compared to water underneath similar
operational conditions. Izadi et al. [14] studied the
thermal radiation and the thermogravitational
transfer of a micropolar nano liquid in a permeable
enclosure in the existence of the constant magnetic
effect. Used the Galerkin finite element approach
with the structured non-uniform gid is to estimate the
developed equations. The main factors are Darcy–
Rayleigh number, Darcy number, porosity,
nanoparticle concentration, radiation parameter,
vortex viscosity characteristic rand Hartmann
number. The results demonstrate that the middle
Nusselt number decreases with an increment of the
Hartmann number for increased values of the thermal
Rayleigh number, a small modification in the average
Nusselt number can be located. Elbadawy et al. [15]
numerically studied the effect of the use of nanofluids
on the increase in warmth transfer and the aspects of
fluid flow in a rectangular microchannel warmth
sink. The results reveal that increasing the
concentration of nanoparticles improves the cooling
process. Amiri et al. [16] numerically studied in
parallel micro-channels the design of micro-heat
exchangers, the uniformities of flow and. Used
Carboxy methylcellulose as a coolant. Studied the
structures and effects of collectors on flow and
temperature distributions. Maher et al. [17]
developed, analyzed, and simulated a detailed, non-
isothermal, three-dimensional computational fluid
dynamics (CFD) model for fluid flow and heat
transfer physiognomies. Nanofluids have been
presented as efficient refrigerants to be used in this
type of warmth sink to raise the rate of warmth
dissipation. The results show that analyzing
performance parameters as a function of Reynolds
number is tricky and that utilizing nanofluids in a
microchannel warmth sink is unusable because water
is cheaper and safer. Mohd et al. [18] innovated to
enhance warmth transfer performance in an MCHS
to meet the cooling market of electronic devices
established with high-power integrated circuit
(microchip) boxes. The use of nanotechnology in the
shape of a nanofluid in an MCHS has drawn the
attention of investigators due to the dramatic
improvement in thermal conductivity. The study
showed that the combination MCHS delivers a more
reasonable cooling performance than the MCHS with
the single passive approach. Mokrane et al. [19]
conducted numerical and empirical research to
examine the elements of laminar flowing and
compelled convection warmth transfer in micro-
channels. Studied various cooling techniques to
improve the warmth transfer methodology in
electronic components. The results demonstrated that
the micro warmth exchanger was competent to
disperse about 70-78% of the warmth given off by the
electronic element. Souby et al. [20] numerically
evaluated the performance of the first and second
laws of MCHS employing the novel cost-efficient
binary/ternary combination nanofluids. The
influences of hybrid nanofluid volume concentration
and Reynolds number on the warmth transfer,
pressure decrease combined thermal-hydraulic
elements, and entropy generation elements of MCHS
were examined. The results show that the
CuO/MgO/TiO2-water ternary combination
nanofluid showed sounder warmth transfer efficacy
than the MgO/TiO2-water binary combination
nanofluid. Ramadhan et al. [21] experimentally
explored the stability of the tri-hybrid nanofluid for a
volume concentration of 0.5 to 3.0% and temperature
conditions of 30 to 70 °C to measure the thermal
conductivity employing a heat analyzer. KD2 Pro
thermal effects. The results illustrate that the tri-
hybrid nanofluids with a concentration of 0.5%
offered the lower sufficient thermal conductivity of
13.4% at 70°C. Payal et al. [22] presented detailed
research of nanotechnology, its process to
nanoelectronics, classing and kinds of nanomaterials
employed in nanoelectronics, application regions of
nanoelectronics, and calculating instruments with
nanoscale characterization. Sanpui et al. [23]
investigated the use of a Cu-water nanofluid
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numerically for the simulation of warmth transfer
performance due to transient laminar natural
convection inside a square enclosure with a
protruding isothermal heating element. Mirzaei et al.
[24] studied the flowing and warmth transfer of a
second-order viscoelastic fluid in an axisymmetric
porous-walled canal for turbine cooling applications
are investigated. Çakmak et al. [25] numerically
investigated the improvement of warmth transfer in
an enclosure using the nanofluid Al2O3-EG. Revealed
the effects generated by delays in the viscosity and
thermal conductivity of the nanofluid on the laminar
natural convection warmth transfer happening in a
square fence. Discovered that nanofluid viscosity
was the considerable effective aspect for warmth
transfer rate. Abdulkadhim et al. [26] numerically
used natural convection in complicated fence shapes
such as trapezoidal, parallelogrammic, elliptic, and
wavy geometries, considering different approaches.
Examined the effect of the position of the inside of
the body and its size. Roy et al. [27] numerically
investigated the electrohydrodynamic enhancement
of the laminar flow of nanofluids with natural
convection in a shut cavity. The consequences show
that the electric field induced by the charged particles
significantly influences the flow field inside the
cavity.Taloub et al. [28, 29] numerically investigated
natural convection of steady-state laminar heat
transfer in a ring between two hexagonal cylinders
and a horizontal ring within a heated inner elliptical
surface and a cold outer square surface. A Cu-water
nanofluid passes through this annular space. Studied
the impacts of various thermal Rayleigh numbers,
nanoparticle volume fraction, and the effect of inner
cylinder eccentricity on natural convection.
Aminossadati et al. [30] examined the influences of
relevant parameters such as thermal Rayleigh
number, solid volume fraction, warmth source place,
and fence vertex angle on thermal implementation in
an isosceles triangular fence with warmth source
found at its lower wall and refilled with an Ethylene
Glycol-Copper nanofluid. These effects show that the
variation of the heat transfer rate for the enclosure
apex angle and the placement and measurements of
the warmth source is various at inferior and increased
thermal Rayleigh numbers. Haq et al. [31] presented
a study on the thermal management of water-based
single-walled carbon nanotubes (SWCNTs) interior
the partially warmed triangular cavity with a warmed
cylindrical block. The thermal conductivity of the
liquid is completely enhanced by presenting the
SWCNT and detailed conditions are presented at the
internal circular cylinder. The numerical resolution is
desired utilizing the finite element approach (FEM).
Simulation is affected by the effects of cylindrical
blocks, heated lengths, Rayleigh number, the volume
fraction of nanoparticles, and magnetic parameters
on warmth transfer rate, flowing speed areas, and
temperature diffusion. The analysis concludes that at
the hectic length, the warmth transfer rate for the
warm cylinder is lower than that for the cool cylinder.
Sojoudi et al. [32] realized a mathematical model to
simulate the mixed convection of the Al2O3-water
nanofluid in a triangular space driven per the lid
utilizing the Lattice Boltzmann approach (LBM).
Different thermal conductivities and viscosities of the
working nanofluid were taken into account. For
different Richardson numbers, aspect ratios, solid
volume fractions of nanoparticles, and different
frequencies and amplitudes of wall cover sinusoidal
thermal forcing. The grid sensitivity test was
performed and the results were validated against the
experimental study. Thangavelu et al. [33]
numerically investigated the warmth transfer per
natural convection interior a fence with central
heating employing a nanofluid. The effect of
different central heater lengths on the flowing and
temperature domains is analyzed for various thermal
Rayleigh numbers. The numerical results illustrate
that the warmth transfer raises with the increase in the
length of the heating element at the perpendicular and
horizontal positions for rising values of the thermal
Rayleigh numbers. In certain, a more heightened
accumulation in warmth transfer is received with a
heater found in a perpendicular place of maximum
height. Oudina [34] numerically studied the
hydrodynamic and thermic aspects of Titania
nanofluids loading a cylindrical ring. Ethylene
glycol, motor oil, and water are utilized as basic
fluids. Maxwell's prototype for warmth transfer in
nanofluids is observed to count for the impacts of
nanoparticle volume particle diffusion on the various
equations, in that a formed computer code is utilized
established on the finite volume approach associated
with the SIMPLER algorithm. The impacts of
different parameters on the local Nusselt number are
examined. Loenko et al. [35] dedicated the
mathematical modeling of the term gravitational
convection of a non-Newtonian fluid in a shut
enclosure cavity with a local source of inner
volumetric warmth generation. The Ostwald-de
Waele power-law model describes the behavior of
the fluid. The influences of thermal Rayleigh
number, power-law index, and thermal conductivity
ratio on warmth transfer and flowing form are
reviewed. Dogonchi et al. [36] numerically studied
the part of natural convection and thermic radiation
on the thermo-hydrodynamics of warmth transfer of
nanofluids in a ring between a corrugated circular
cylinder and a diamond-shaped fence subjected to an
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invariant magnetic field. The effects of maintaining
physical parameters, thermal Rayleigh number,
radiation parameter, Hartmann number, factor ratio,
the form aspect of nanoparticles, and solid volume
particle of nanoparticles on the thermo-
hydrodynamics of the flowing are reviewed. It
evolves evident that the local warmth transfer rate
lowers with increasing aspect ratio in the non-
attendance of Hartmann number. Oudina et al. [37]
numerically analyzed the effects of the place of a
thermic source on the floating convection of
nanofluids in an annular area. Five different positions
of thermal sources alongside the internal cylinder of
the annular space were studied. The main purpose is
to determine the optimal placement of the source to
maximize or minimize the thermic transportation at
various values of thermal Rayleigh number and
various volume particles of the nanoparticle. The
place of the heat source has a deep effect on the
flowing and temperature patterns as agreeably as the
heat transfer of the discreet source to the nanofluid.
Laidoudi et al. [38] investigated numerically two-
dimensional buoyancy-driven flowing in a shut
annular area. The studied field includes a pair of
circular cylinders of identical size arranged in a team
enclosed in a circular loaded with incompressible
Newtonian fluid. The influences of the thermic
buoyancy force, the thermophysical aspects of the
fluid, the length of the internal cylinders on the
flowing patterns interior the circular field, and the
rate of warmth transfer exchanged between the
internal cylinders and the flowing of the fluid have
been studied. The results showed that the studied
guiding parameters affect significantly. An addition
in the diameter of the internal cylinders creates the
influence of buoyancy force on fluid flowing and
warmth transfer insignificant for any values of
thermophysical parameters. Nguyen et al. [39]
simulated the thermic conduct in a curved porous
field is examined in the formation of an ethylene
glycol-founded nanofluid. The term radiative source
was presented and nanoparticles of various forms
namely: Platelets, bricks, cylindrical and spherical
are distributed within the basis fluid. The effects of
permeability, voltage, radiation parameters, and
nanoparticle form on streamlines, isotherms, Nusselt
number have been indicated. Ranges of specified
parameters are included, which are: the voltages the
Darcy number the shape of the nanoparticles, and the
radiative factor. The results showed that the
convection increases with the height of Da. The
convective flowing evolves more powerful due to the
addition of higher voltage. Umavathi et al. [40]
studied double-diffusive convection in a saturated
horizontal permeable coating of a saturated
incompressible torque stress nanofluid with thermal
conductivity and viscosity depending on the volume
fraction of the nanoparticles. Nonlinear theory based
on the Fourier series approach representation is used
to capture the conduct of warmth and mass transfer.
The torque constraint parameter is found to improve
the stability of the approach in the stationary and
oscillatory convection modes. Viscosity proportion
and conductivity proportion both improve warmth
and mass transfer. The transitory Nusselt number
turns out to be oscillatory when the time is little.
However, when time evolves extremely
considerably, any three values of the transitory
Nusselt number come to their steady-state values.
Lakshmi et al. [41] analytically studied natural
convection in cylindrical permeable rings flooded by
a nano liquid whose internal and external
perpendicular radial fences are respectively subjected
to invariant fluxes of warmth and mass utilizing the
changed Buongiorno-Darcy model (MBDM ) and
Oseen's linearization method. The thermophysical
properties of a permeable medium flooded with nano
liquid are sported employing phenomenological rules
and mix hypothesis. The influence of different
parameters and the particular impacts of five various
forms of copper nanoparticles on speed, temperature,
and warmth transportation is located. From the
investigation, it is evident that the accumulation of a
dilute concentration of nanoparticles raises the
sufficient thermic conductivity of the technique and
thus rises the speed and warmth transportation, and
reduces the temperature. The highest warmth
transport is performed in a superficial cylindrical ring
analogized to square and long circular rings.
Increasing the radius of the internal solid cylinder
aims to reduce warmth transport. Mehryan et al. [42]
numerically studied the natural convection of Ag-
MgO/water nanofluids in a permeable fence utilizing
a local thermic non-equilibrium model. Darcy's
model is used. The key parameters of this analysis are
the thermal Rayleigh number, the porosity, the
volume particle of the nanoparticles, the interface
convective warmth transfer coefficient, and the
thermic conductivity proportion of two permeable
phases. It is demonstrated that the dispersion of Ag-
MgO hybrid nanoparticles in water extremely
reduces the heat transportation through two phases of
the porous enclosure. Abdulkadhim et al. [43]
summarized previous studies relating to heat flow in
enclosures of different square, rectangular and
triangular enclosure geometries. Enclosures filled
with different fluids such as traditional fluids and
nanofluids, Newtonian and non-Newtonian fluids,
and multilayer techniques. Different numerical
models have been reworded. The effect of diverse
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parameters such as Rayleigh, Darcy, Bejan, and
Hartmann numbers, the charging of nanofluids,
various thermic cases of the devoted border
conditions, the angle of tilt, the number of
undulations, the presence of 'an internal body, and
considerable other parameters affecting and hardly
impacting entropy generation and warmth transfer
has been defined. Alomar et al. [44, 45] suggested a
numerical investigation on natural convection in a
non-Darcy permeable layer surrounded by two
horizontal areas including sinusoidal temperature
shapes with phase and wavenumber variance.
Simulations have been executed for wide fields of
coefficient of inactivity, thermal conductivity ratio,
phase shift, modified Rayleigh number, wavelength,
and dimensionless heat transfer coefficient. A
considerable improvement of the fluid, solid and
global Nusselt numbers were marked with a decrease
in Fs/Pr* and β and an increase in k, K r, and H. The
influence of H on the non-equilibrium zone is more
obvious than Kr. Ali et al. [46] numerically studied
the mixed convection caused by two aligned
horizontal agitated cylinders implanted in a square
fence with symmetrical spaces on the inferior and
superior surfaces of the fence. The parameters were
protected a broad field of gap size between two
cylinders, opening vent, Reynolds number, and
Richardson number, while Prandtl number remained
fixed. The numerical effects show that the mean of
the hectic cylinders raised with the increase of Ri, Re,
and the beginning of the vent. The optimal
improvement was found when the gap size was under
the full aperture size case.
Nowadays, air-cooling has also become insufficient
and more and more people are moving towards
nanofluid cooling. In this context, we conducted a
numerical study on the cooling of a heating system
simulating a microprocessor like those that equip
PCs. We used nanofluid cooling in a box in order to
show the cooling efficiency on the one hand and to
determine the parameters that can affect it on the
other hand. To protect microprocessors at high
frequencies against excessive heating, the use of
another cooling system is essential. We then
proposed to carry out a numerical study on a
prototype of a nanofluid box in order to evacuate the
heat emanating from a thermal source simulating a
microprocessor.
2 Problem modeling and resolution
First, we present the geometry and the system of
equations that governs the flow and the transfer of
heat by convection with the use of nanoparticles.
Then, we will present how the resolution of our two-
dimensional problem is implemented by the fluent
software.
2.1 Geometry and problem formulation
The current model consists of a box enclosure loaded
with an Ethylene Glycol–Copper nanofluid (figure.
1). A warmth fount of rib w and relatively elevated
temperature (Th) is found at the level of the heat-
insulated lower border. whilst the borders of the box
of the fence are retained at a somewhat more inferior
temperature (Tc). The thermal Rayleigh's number,
Rat, ranges from 103 to 106. The flow is considered
to be two-dimensional, the flow is convection natural
laminar of nanofluid Ethylene Glycol–Copper (EG–
Cu ). The nanofluid is assumed incompressible and
Newtonian by negligible viscous diffusion and
pressure working. The thermophysical properties of
the nanofluid are supposed constant except for the
density, which changes according to the Boussinesq
approach. The Boussinesq approximation is used to
model the buoyancy effect. The acceleration due to
gravity acts in the negative y-direction.
Fig. 1 Schematic graph of the physical prototype
The dimensionless equations governing the laminar
flow of our problem below the non-dimensional
variables are written as follows [47-51]:
(1)
Continuity equation
(2)
Momentum equations
(3)
(4)
Energy equations
(5)
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Where: U and V are the dimensionless speeds in the
X and Y directions, respectively. The physical
characteristics of Ethylene Glycol and nanoparticles
are presented in Table 1.
Table 1 Physical characteristics of Ethylene Glycol
and Cu [52, 53]
E-G
1109
2400
0.26
6.5x10-4
0.02
Cu
8933
385
401
1.67x10-5
-
The effective nanofluid density () is given by
[54]:
(6)
The effective dynamic viscosity of nanofluid () is
presented by [54]:
(7)
The heat capacity of nanofluid is given by [54]:
(8)
The thermic expansion coefficient of the nanofluid is
defined through:
(9)
The effective thermal conductivity of the EG–Cu
nanofluid for spheroidal nanoparticles is [55]:
(10)
These various boundary conditions in
dimensional format can be summarized as:
The initial conditions are:
(11)
(12)
Moreover, the boundary limitations concerning
the problem are:
Along the sides of the enclosure (box):
(13)
(14)
Along the sides of the lower wall (CPU):
(15)
(16)
Alongside the horizontal side of the fence:
(17)
2.2 Numerical method
The equations are treated consecutively by utilizing
the isolated method. The use of fluent software
allows us to build a numerical model capable of
dealing with the problem of flowing and warmth
transfer by convection with the use of nanoparticles
for the two-dimensional case. First, it is necessary to
generate the mesh using Gambit software (see figure
2).This approach has the advantage of meeting the
mass, the conservation of the momentum, and the
energy in all the considered volumes as well as in all
the fields of calculation with the assessed boundary
conditions is founded on the finite volume approach.
To confirm a satisfactory solution in regions with a
high-temperature gradient, livery structured mesh
close was supposed. The second-order scheme was
thought since it allows some stability and minimizes
the numerical diffusion though it can make the
calculation diverge. The simple algorithm of
Patankar and Spalding [56] was employed for speed-
pressure coupling. In addition, the computational
residue was utilized to confirm the convergence and
the stability of the resolution.
Another helpful quantity like the Nusselt number for
every flank from the hot walls is perhaps chosen
afterward resolving the dominant equations from U,
V, and θ. The local Nusselt numbers from the right
side, left side, and topside from the hot walls
represented as [30]:
(18)
(19)
(20)
Therefore, the mean Nusselt number from every
flank from the hot wall is defined per incorporating
the local Nusselt number alongside the area of the
individual side from the hot walls [30]:
(21)
(22)
(23)
The total mean Nusselt numbers for the hot wall
perhaps received by incorporating the local Nusselt
numbers alongside the right, left, and top sides from
the hot walls.
(24)
The evolution of the mean Nusselt number for five
various grille dimensions is analyzed to examine the
freedom from the resolution with the grille
dimension. Three various outer wall heights of 0.5, 0.
4375, and 0.375 are evaluated, and the performance
for φ = 0.05, W=0.25, and Rat = 105 are shown in fig.
2. A mesh dimension of 100 × 100 meets the needs
of the investigation of network freedom and
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5,0x1031,0x1041,5x1042,0x104
4,0
4,5
5,0
5,5
6,0
6,5
7,0
7,5
8,0
100x100
Average Nusselt number, Nuavg
Mesh points
H=0.5
H=0.4375
H=0.375
103104105106
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Average Nusselt number, Nuavg
Rat
Current investigation, h=H/6
Aminossadati et al. [30], h=H/6
calculation time boundaries. The convergence
measure to lower the greatest residual mass from the
grille command volume below 10−12.
To give credibility to our current numerical study
with the presence of nanoparticles, the numerical
model was validated with the work of Aminossadati
et al. [30] who numerically studied two-dimensional
laminar natural convection into an isosceles
triangular fence with the use from nanofluids are
presented in fig. 3.
Fig. 2 Mesh independence analysis
Fig. 3. Comparison of the current investigation
versus Aminossadati et al. [30].
3. Results and commentary
In the current investigation, the solid volume
fragment (0 ≤ φ ≤ 0.05), the thermal Rayleigh number
is supposed to be in the following ranges (103≤ Rat ≤
106), the height of the box (0.3125≤H≤ 0.5), and the
length of each side of the hot wall is fixed at (W=0.
25). The influences of each of cited parameters are
analyzed individually in various sections.
The effect of the adding from copper nanoparticles in
the basis fluid about the streamlines and the
isotherms from diverse thermal Rayleigh
numbers Rat=104, 105, and 106 illustrated in figure 4,
which highlights in first the effect of the increase in
the thermal Rayleigh number about the flow from the
nanofluid (φ=0.05) and sheer ethylene glycol (φ=0).
From streamlines, there are considerable
dissimilarities in the central area, specifically when
the thermal Rayleigh number is large (Rat ≥ 105). The
addition of nanoparticles increases the intensity of
the streamlines, particularly within the central area.
Contrary, when the thermal Rayleigh number is
smaller, the weakening of the intensity from the flow
is noticed compared to the flow of the base fluid.
Nevertheless, nearby isothermal walls, the
dissimilarity into the greatness from the current
function is much little. From isotherms, moderately
large dissimilarities are followed into the central area
and near the lid and lowest walls whenever the
thermal Rayleigh number is large The temperature
gradient around the isothermal walls from the
nanofluid is lightly more considerable than that from
pure ethylene glycol, although the difference
increases with increasing thermal Rayleigh number,
demonstrating that greater warmth transfer, happens
when the operating fluid is a nanofluid. For every, the
thermic Rayleigh number values, the contours of the
streamlines and isotherms are symmetrical
concerning the perpendicular median of the box.
Increasing Rayleigh number intensifies convection,
buoyancy forces become stronger: the upper nodes
get stronger and then start to merge with the lower
ones due to the prevailing convective heat transfer
mode as shown in figure 4. At Rat=106, figure 4
shows that the isothermal lines change and ultimately
adopt the form of a mushroom either for the nanofluid
or the pure EG. The temperature diffusion is lowering
from the warm wall to the cold wall. The directorate
of deformity of the isotherms conforms to the
directorate of rotation of the streamlines. In the
laminar regime, it can be said that, underneath the
movement of the action of the particles which take
off for the warm wall at the level of the axis of
symmetry, the isothermal lines “vault” and move far
from the wall at this point. The worths from the
current functions for the nanofluid and the pure fluid
increase which means that the convection intensifies.
Comparison between nanofluid and pure fluid shows
that at heightened thermal Rayleigh number,
circulating cells from nanofluid are more powerful
than those from pure fluid, unlike at inferior thermal
Rayleigh number.
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Fig. 4. Isocurrents (left) and isotherms (right) from H=0.5, W=0.25, nanofluid
with φ = 0.05 (____) and pure fluid (− − −), (a) Rat=104, (b) Rat=105, (c) Rat=106
-4 -3 -2 -1 0 1 2 3 4
0,0
0,2
0,4
0,6
0,8
1,0
Ra
t
=104
Ra
t
=05Ra
t
=106
(Y=0.1)
X
Ø=0
Ø=0.05
a)
b)
c)
Figures 5a and 5b show the evolutions of the
dimensionless temperature (θ) and the perpendicular
component of the velocity (V) of the flow, on the
horizontal direction expanding on the upper flank
from the hot wall (Y = 0.1), respectively. These
figures make it possible to confirm the results
obtained previously and to understand the flow
behavior inside the box for the pure EG and the
nanofluid EG-Cu at various thermal Rayleigh
numerals. The evolutions of the dimensionless
temperature alongside the axis Y=0.1 increase for the
leftside of the box towards the side of the hot wall.
Along this axis, as the thermal Rayleigh number
raises the temperature lowers. At Rat=106, the EG–
Cu nanofluid exhibits more increased velocity and
more inferior temperature likened to pure fluid owing
to more powerful buoyant fluxes in increased thermal
Rayleigh numerals. The increase in the magnitude of
V with increasing thermal Rayleigh number is a
motion of more powerful floating fluxes in the
increased thermal Rayleigh number box. This
explains why heat transfer is in the convection mode
at high thermal Rayleigh number, while conduction
is accountable for warmth transfer in inferior thermal
Rayleigh number.
Fig. 5a Temperature form in Y = 0.1 from both pure
fluid and nanofluid (H =0.5, W=0.25)
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-4 -3 -2 -1 0 1 2 3 4
-100
-50
0
50
100
150
200
Ø=0
Ø=0.05
Ra
t
=105
Ra
t
=106
Ra
t
=104
V(Y=0.1)
X
0,00 0,01 0,02 0,03 0,04 0,05
4
5
6
7
8
9
10
11
12
Average Nusselt number, Nuavg
Ø
Rat=103
Rat=104
Rat=105
Rat=106
Fig. 7. Streamline (left) and isotherms (right) for Rat = 105, φ = 0.05, W = 0.25,
(a) H = 0.4375, (b) H = 0.375, (c) H = 0.3125.
= -0.978
=+0.978
= -0.791
=+0.791
= -0.611
=+0.611
Fig. 5b Perpendicular velocity form in Y = 0.1 from
both pure Fluid and Nanofluid (H =0.5, W=0.25)
The profile of the mean Nusselt number as a function
from the solid volume fraction is shown in figure 6.
We notice that the increase in inertial forces promotes
the warmth transfer process. Also, raising the solid
volume fraction of the nanoparticles improves the
heat transfer rate. This expansion is owing to the
improvement in the sufficient thermic conductivity of
the nanofluid as the volume of nanoparticles rises.
In figure 7, the influence of the box height (H) upon
the warmth transfer performance from the processor
cover box is examined. We consider that W = 0.25
and φ = 0.05. This figure illustrates the isocurrents
and isotherms for Rat = 105 and three various heights
(H = 0.3125, 0.375, and 0.4375).
a)
b)
c)
Fig. 6 Evolution from the mean Nusselt number a
fonction φ with various Rat (H =0.5, W=0.25)
The effects demonstrate that for all heights, two cells
are symmetric that is to say; the minimal and
maximal valors to the isocurrents of the two cells are
the same, and circulating counter-rotating inside the
box. When the values of the sides of the bottom wall
are fixed, as the height decreases, the box becomes
less, and the circulating cells evolve better defined.
Therefore, a decrease into height leads to a
diminution into the force from the rolling cells, not to
say that the rate of warmth transfer will be decreased
from high heights. When the top side from the
warmth source approaches the cold top wall and the
rate of conductive heat transfer should increase.
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0,30 0,35 0,40 0,45 0,50
6
8
10
12
14
16
18
Rat=103
Rat=104
Rat=105
Rat=106
H
Average Nusselt number, Nuavg, hot wall
0,00 0,01 0,02 0,03 0,04 0,05
0,98
1,00
1,02
1,04
1,06
1,08
1,10
1,12
1,14
1,16
Ø
Nuavg,nf/Nuavg, f
Rat=103
Rat=104
Rat=105
Rat=106
Figure 8 presents the development of the mean
Nusselt number as a function from the height (H) of
the upper wall for various thermal Rayleigh numbers.
At considerable values of the height H, a large
distance exists between the three sides of the hot wall
and the cold walls of the box. Therefore, as the
thermal Rayleigh number raises, the buoyancy
strengths and the convective flowing domain evolve
more powerful. Unlike small values of the height, the
space evolves less, determining the force of the
convective flowing area.
It is noted in this figure that for all valor of the
thermic Rayleigh number save from Rat = 106, the
mean Nusselt number of the hot wall lowers as the
warmth source displaces far from the cool wall. This
is due to the decrease of warmth transfer by
conduction. At Rat = 106, as height raise, the mean
Nusselt number first lowers and yet rises owing to the
reinforcement of floatable flows [30].
Fig. 8. Evolution of mean Nusselt number from hot
wall with H at different Rat (φ = 0.05, W =0.25).
Figure 9 illustrates the interpretation of the ratio of
the average Nusselt number of the nanofluid to the
average Nusselt number of the pure fluid (
) with the volume fraction φ at different
thermal Rayleigh numerals.
The evolutions show that an increase in the volume
fraction conducts to raise in the for
all the thermal Rayleigh numbers supposed. The rate
of this augmentation is considerably observable in
the results received.
Fig. 9 Variation of with φ at
different thermal Rayleigh number
4 Conclusion
A two-dimensional numerical investigation on the
improvement from the cooling of a CPU by the use
of nanofluids. The fluent software was used to create
the geometry and define the digital model of our
problem. The effects of thermal Rayleigh number
(103≤Rat≤106), nanoparticle solid volume fraction
(0≤ φ ≤5%), and top box height were investigated
numerically on flux, temperature fields, and the rate
of warmth transfer.
The main results are presented below:
* The utilization of nanoparticles in the basis fluid
increases the thermic conductivity of the fluid and
thus increases the warmth transfer.
* Thermal conduction within the fluid and between
the fluid and the nanoparticles appears to be the
dominant factor in this enhancement. It can be
noticed that these significant improvements. In
particular, we observed that the efficacious thermic
conductivity of this nanofluid increases with the
concentration from nanoparticles.
* For Rat=106 and H=0.5, the results show that the
increase into the solid volume fraction from the
nanoparticles (φ = 5%) conducts to an expansion in
the effective conductivity of the working fluid and
consequently the increase in transfer rate. the heat of
about ≈ 10% likened to the basis fluid instance. At
lower thermal Rayleigh numbers, the warmth transfer
rate rises always with the height of the enclosure
(box).
* The growth in the thermal Rayleigh number
amplifies the speed and temperature areas, thus
inducing a transition from a conduction mode to a
convection mode.
* The temperature and the flux fields are symmetrical
for all lengthiness. The most increased warmth
transfer rates are received from the inferior height.
Yet, from lengthier heights, the warmth transfer rate
initial lowers and then rises as the height raise
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Nomenclature Greek symbols
Specific heat, α Thermal diffusivity,
g Gravitational acceleration, β Thermal expansion coefficient, K-1
h Height of enclosure upper wall, m φ Solid volume fraction
H Dimensionless cold wall height (h/L µ Dynamic viscosity,
k Thermal conductivity, ν Kinematic viscosity,
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p Fluid pressure, Pa
P Dimensionless pressure
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