Effect of External Flow Mode on Nanofluid Mixed Convective
Cooling Inside a Multi-Vented Cavity
ISMAIL ARROUB1,*, AHMED BAHLAOUI1, SOUFIANE BELHOUIDEG1, ABDELGHANI
RAJI2, MOHAMMED HASNAOUI3
1Research Laboratory in Physics and Sciences for Engineers (LRPSI),
Polydisciplinary Faculty, Sultan Moulay Slimane University,
B. P. 592, 23000, Béni-Mellal,
MOROCCO
2Energy and Materials Engineering Laboratory (LGEM),
Faculty of Sciences and Technics, Sultan Moulay Slimane University,
B. P. 523, 23000, Béni-Mellal,
MOROCCO
3Laboratory of Fluid Mechanics and Energetics (LMFE),
Faculty of Sciences Semlalia, Cadi Ayyad University,
B.P. 2390, Marrakesh,
MOROCCO
*Corresponding Author
Abstract: - The purpose of this paper is to study numerically laminar mixed convection in a multiple vented
cavity. This enclosure is continuously heated by constant temperature from the bottom wall, while the other
boundaries are presumably thermally insulated. The imposed water-Al2O3 nanofluid flow is injected or sucked.
The Influences of various control parameters, e.g.: Reynolds number Re, from 200 to 5000, the solid volume
fraction of nanoparticles, , from 0to 7 %, and external flow mode (injection or suction) on the thermal
patterns, the flow and the heat transfer within the enclosure are studied. Numerical results revealed that the
presence of nanoparticles contributes to enhancement in the heat exchange and increase in the mean
temperature within a cavity. Also, it was found that the heat performance and Applying the suction mode
enhances the efficiency of cooling compared to the injection mode.
Key-Words: - Numerical study, mixed convection, injection, suction, nanofluid, multiple vented cavity.
Received: May 11, 2023. Revised: October 13, 2023. Accepted: December 4, 2023. Published: December 31, 2023.
1 Introduction
Because of numerous applications, mixed
convection heat transfer has become a significant
phenomenon in engineering systems. Enhancing the
rate of heat exchange is crucial from an industrial
and energy-saving standpoint system. For
indication, a novel category of heat transfer fluid
known as nanofluid is created by suspending
nanoparticles in a base liquid like ethylene glycol or
water. It is anticipated that these nanofluids will
perform better in terms of heat transfer than
traditional heat exchange fluids. The explanationis
that the dissolved particles noticeably boost the
nanofluids thermal conductivity which increases
thermal transport and enhances heat transfer, [1].
Along these lines, many studies in heated enclosures
have been conducted.
Several articles have been published to promote
heat exchange via natural convection in the context
of differentially heated cavities subjected to constant
heating. The author [2], numerically studied the
natural convection with H2O-nanofluids in the
inclined cavity. The findings led to the conclusion
that nanoparticles in suspension significantly
improve the heat exchange rate. Moreover, the
minimum / (maximum) heat transfer occurs at
= 90° / ( = 30° or 45°) according to Ra. In the
same framework, the study [3], examined the effects
of changing the nanofluid characteristics in
rectangular cavities. They noted that according to
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
231
Volume 18, 2023
the Rayleigh number, Ra, type (Al2O3 or CuO), and
volume fraction of the nanoparticles, the mean Nu,
changed. In addition, it was discovered that Nu was
more responsive to the viscosity models than the
thermal conductivity models at high Ra. Recently,
the author [4], investigated the characteristics of
buoyancy-driven nanofluid heat transfer inside
differently heated rectangular cavities. According to
the study’s findings, there is a particle loading that
maximizes heat transfer. The same author [5], has
constructed two empirical formulas assessment of
dynamic viscosity and effective thermal
conductivity of nanofluids. Another study related to
a square enclosure with differential heating that is
filled with Al2O3-water nanofluids is analyzed, [6].
The results appear that nanofluids display higher
heat exchange rates than water. The natural
convection stream of CuO-water nanofluid in
inclined differently heated cavities was analyzed,
[7]. It was discovered that the heat exchange
efficiency was strongly based on particle diameter
rather than its concentration within the base liquid.
Also, the combination of aspect ratio and inclination
angle affects the heat exchange and hysteresis
region.
In most cases of natural convection in the
cavity, heating is varied and heaters are placed in
the cavity or on the side walls. When linear heating
is applied, such a problem was addressed, [8].
Authors have shown that linearly increasing wall
temperature has a higher heat exchange rate in
comparison with linearly decreasing wall
temperature. In this situation, the authors [9],
displayed a numerical study utilizing Cu-water
nanofluid. The existence of nanoparticles includes a
clear impact with wavering behaviors for the stream
and temperature areas. When the heater is used, we
quote the study [10]. It has been observed that as the
heater's length increases, Nu reduces. An additional
digital investigation was conducted, [11].
Simulations indicate that heat exchange can be
improved more effectively by expanding the number
of HACs than expanding the HAC's size.
Many studies on this subject are concerned
basically with applications involving forced
convection. In this context, an experimental and
numerical study was conducted, [12], [13] to
examine the cooling achievement of forced
convection with heat sink microchannel design
nanofluid. The results showed that nanofluid cooled
the heat sink better than water and had a superior
heat exchange coefficient. In the studies, [14], [15]
the same problem is examined experimentally and
declared that even while the heat sink's thermal
resistance dropped, scattering that dispersing
nanoparticles in water significantly improved the
heat exchange coefficient overall.
Many studies on mixed convection in lid-driven
cavities containing nanofluids in different
geometries have been conducted recently. In this
case, authors [16], [17], observed that when Re
increases, the effect of solid concentration
diminishes. Also, they found that the particle
distribution depends on Rayleigh and Richardson
numbers. The problem of nanofluid mixed
convection is treated, [18], in the case of the square
cavity with a lid powered by a heat source and
locally heated from below. They demonstrated how
the rate of heat transfer drops as the volume
percentage of nanoparticles increases for large Ra.
Furthermore, it was discovered that the rate of heat
transmission rises as the heat source moves toward
the walls on the cold side. The authors [19],
numerically analyzed mixed convection flow in a
cavity operated by the lid and filled with nanofluid
and heated by sinusoidal heating in a situation
where the latter is variable. They demonstrated that,
for a given Grashof number, the rate of heat
transmission rises when the volume percentage of
nanoparticles increases and the Richardson number
decreases. In some studies related to the geometry of
square cavities with mobile lids and heating is
localized inside, [20]. The results of this study
showed that, when the diameter of the nanoparticles
increases, a reduction of Nu for all Ri is observed.
Relatively little study has been done in the past
few decades on mixed convection for nanofluids in
vented cavities with constant heat flux or
temperature. This kind of issue is crucial for many
different kinds of technology applications.
Therefore, the authors [21], carried out a numerical
analysis of the situation with applying uniform heat
flow. The rate of heat transfers at the heat source
area increased and average bulk temperature
decreased as solid concentration increased,
according to the presented results. The authors [22],
reexamined the same topic for various port locations
in the event of completely continuous heating. It
was discovered that the Bottom-Top configuration
benefits more from the addition nanoparticles than
the other configurations that were taken into
consideration. Nanofluid mixed convective cooling
in a vented cavity locally heated on one side by a
heat source, was investigated numerically, [23].
Their results showed that a full entropy production
in the cavity when a heater is embedded in the
bottom wall compared with others. The authors
[24], carried out a numerical analysis of mixed
convection across a ventilated square cavity with
Al2O3-water nanofluid under uniformly applied
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
232
Volume 18, 2023
temperature. The results presented revealed that the
inclusion of nanoparticles increases the Nu and
value of the pressure dropping coefficient. In the
case of a hot obstacle in the enclosure, [25], the
study's findings showed that the heat transfer rate
was increased for various Ri and outlet port
placements by incorporating nanoparticles into the
base fluid. The same study was examined, [26],
where two hot square obstacles are situated in the
cavity’s bottom wall and they concluded the same
remarks. The authors [27], [28], studied mixed
convection heat exchange of an Al2O3-water
nanofluid in ventilated cavities as a result of
incoming and outgoing flow by application of the
two modes of injection and suction for various
heating purposes. In these studies, adding
nanoparticles positively impacts the heat exchange,
but it also increase the average temperature in the
cavity.
The study of mixed convection in an enclosure
that is isothermally heated and vented by multiple
ports utilizing two separate modes and nanofluid has
not yet been studied, according to the research
currently available quoted in the literature review
above. Therefore, this research is focused on
studying such problems, because of many modern
processes, like design for solar collectors, the
thermal design constructions, cooling process for
electronic circuits and heat exchangers, [29], [30],
[31], [32]. Hence, the effects of key variables on
flow and energy fields are investigated and
analyzed. These parameters include the Reynolds
number, the concentration of nanoparticles, and
imposed flow (injection or suction).
2 Description of the Problem
Figure 1 displays a schematic illustration of a
studied configuration. It is made up of an A = 2
rectangular horizontally vented cavity. It is assumed
that all borders are thermally insulated, whereas the
lower wall is heated at constant temperature.
Throughout the two openings on the bottoms of the
right and left vertical walls, an external nanofluid
stream is forced through the cavity by injection
(Figure 1a) and suction (Figure 1b), subjecting the
physical system to the force. To ensure the
ventilation process, a third opening is situated in the
center of the upper wall. We assume that there is no
slip occurring between the two phases and pure
water and nanoparticles are in a condition of thermal
stability.
(a)
(b)
Fig. 1: The problem's geometry: a) Injection mode
and b) Suction mode
As is shown in Table 1, [33], the
thermophysical characteristics of the alumina
nanoparticles under investigation and pure water are
evaluated during average nanofluid temperature
(T = 32°C). With the exception of density with the
force of buoyancy, Boussinesq's approximation is
still correct, the parameters of the nanofluid are
taken to be constant. It is assumed that the flow in
this investigation is laminar and two-dimensional.
The nanofluid utilized is Newtonian and
incompressible. Moreover, thermal radiation and
viscous dissipation are not taken into consideration.
Table 1. Thermophysical characteristics of both
nanoparticles and water, T = 32°C, [33]
3 Mathematical Modeling
The general equations governing the convection
processes for Newtonian nano-fluid are obtained
using the fundamental principles of conservation of
energy, momentum, and mass. Solving the problem
described by these conservation equations consists
(H2O)
(Al2O3)
102 (kg/m3)
9.95
39.70
cp (J/kg.K)
4178
765
(W/m.K)
0.62
36
10-5 (K-1)
32.06
0.846
µ 10-6 (N.s/m2)
769
---
fo (kg/m3) at
T = 293 K
998.29
---
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
233
Volume 18, 2023
2
22
22
t Re Pr (1 )
11
Re
1
(1 )
(1 )
f
s
s
fs
f
nf
f
s
f
Ω Ω Ω Ra
uv
xy
T
x
ΩΩ
xy
of determining the various unknown quantities u,
v, P and T involved in these equations.
Considering the hypotheses previously cited, the
basic dimensionless formulas governing the
movement of the nanofluid and the heat transfers in
mixed convection are:
- The continuity equation:
uv
0
xy
(1)
- The conservation of momentum equation
● Following ox direction:
nf
nf
22
R nf 22
nf
1g
du 1 P u u
(T T )
dt ρx xy
(2)
● Following oy direction:
nf
nf
22
R nf 22
nf
1g
dv 1 P v v
(T T )
dt ρy xy
(3)
With P, designates the effective pressure of the
nanofluid.
- The energy conservation equation
22
nf 22
dT T T
dt xy
(4)
Therefore, under the above-mentioned equations
and using the stream function and vorticity
definitions, the differential equation system that
controls the transport of a nanofluid in the cavity in
two dimensions may be expressed as:
2
2
2
2
nf
nf
nf
y
Ω
x
Ω
x
T
g
)(
y
Ω
v
x
Ω
u
t
Ω
(5)
2
2
2
2
nf y
T
x
T
y
T
v
x
T
u
t
T
(6)
2
2
2
2
yx
(7)
For a two-dimensional flow, the following
relations correlate the velocity components to the
vorticity and the stream function:
y
Ψ
u
;
x
Ψ
v
,
y
u
x
v
(8)
The following correlations are the expressions
for Effective density, thermal diffusivity, heat
capacitance, and thermal expansion coefficient of
nanofluid, in that order, [11], [34]:
fsnf )1(
(9)
nfp
nf
nf )c(
(10)
fpspnfp)c( )1()c( )c(
(11)
ffssnf )1( )(
(12)
The following correlations, can be used to
predict effective dynamic viscosity,
nf, and
effective thermal conductivity,
nf: utilizing a vast
array of data from experiments collected by various
studies, [5]:
10 0 03
0 4 0 66 0 66
1 4 4
.
. . .
s
nf f s
fr f
T
. Re Pr T
(13)
03 1 03
1
1 34 87
nf f ..
sf
. d / d
(14)
The strength of equations (13) and (14) were
recently tested through an examination of
comparison using multiple experimental databases
compared to those employed in generating them.
The results showed a fairly good degree of
acceptance, in addition to the fact that both of them
precisely approximate the results from experiments
that form their basis, [35], [36].
Hence, the dimensionless variables listed below
should be used:
H/LA
,
H/hB
,
H/xx
,
H/yy
,
o
u/uu
,
o
u/vv
,
H/utt o
,
)TT/()TT(T CHC
,
Hu/ΨΨ o
,
fo /νHuRe
o
u/H
,
ff /ανPr
,ν/αH)T-T(β g Ra ffCHf
3
.
The equations that govern the problem without
dimensions formulation are provided by including
the variables without dimensions and given as:
(15)
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
234
Volume 18, 2023
2
2
2
2
fp
sp
f
nf
y
T
x
T
)c(
)c(
)1(
Pr Re
1
y
T
v
x
T
u
t
T
(16)
Ω
y
Ψ
x
Ψ
2
2
2
2
(17)
Here are the definitions of vorticity and the
dimensionless stream function:
y
u
x
v
x
Ψ
v ;
y
Ψ
u
and
(18)
3.1 Border Conditions
When used the two ventilation modes, the same
boundary conditions in the without dimensions form
are established as follows:
u = v = 0 no-slip flow condition for the sides
T = 1 and
= 0 in the lower horizontal hot side
0
n
T
in adiabatic sides
n The outside perpendicular to the proposed
adiabatic side
Suitable boundary conditions without dimensions
about suction or injection scenarios can be
expressed as:
Injection case:
u = 1 , T = v =
= 0 ,
= y in cavity’s left
entrance
u = -1, T = v =
= 0,
= -y in cavity’s right
entrance
= -B within the top output and the right input
= B within the top output and the left input
Suction case:
T = 0 in a top input
u = -1, v = 0,
= -y,
= 0 in a left output
u = 1, v = 0,
= y,
= 0 in a right output
= -B within a top input and a left output
= B within a top input and a right output
About the vorticity, which is unknown on the solid
boundary, the author, [37], found an approximation
relation, was used for its stability and accuracy, such
as:
W1W
2
1WW ΨΨ
Δη
3
Ω
2
1
Ω
(19)
Is utilized because of its precision and stability,
where w denotes a wall, for a space step that is
taken in the wall's normal orientation.
3.2 Heat Transfer Calculation
In engineering applications, the total heat
transmission throughout the cavity is a crucial
metric. The mean Nusselt number, Nu, along a
bottom active wall is used to express it, and it is
assessed as follows [38]:
dx
y
T
A
1
= Nu
0y
A
0
f
nf
(20)
4 Numerical Solution Procedure
A finite difference approach was utilized to
discretize equations that govern the system, which
are Eqs. (15), (16) and (17), in combination with
their related boundaries. A second-order central
difference method approximated the diffusive terms'
first and second derivatives. In addition, a second-
order upwind differencing method was applied to
advection terms to prevent probable instabilities that
are often seen in mixed convection challenges.
Temporal integration for Eqs. (15) and (16) were
then carried out using an alternating direction
implicit (ADI) approach. Using the point sequential
over-relaxation method (PSOR) at every time step,
the Poisson equation, Eq. (17), was solved. For a
grid (201101) used in this work, the optimal over-
relaxation coefficient was 1.95. The agreement on
convergence criteria
ji,
1n
ji,
ji,
n
ji,
1n
ji,
5
10
was met for
every step, this
n
ji,
is the stream
function result for the nth execution level at node
(i,j). According to the governing parameter values, a
range of time stepping sizes
35 1010 t
were
chosen.
5 Validation of Code and Studies on
Grid Independence
In numerical modeling, computational code
validation is crucial. Verifying the accuracy of this
numerical code was done by contrasting our
findings with numerical results reported in the study
[21], of mixed convection flows in a vented square
cavity filled with CuO-water nanofluid that were
heated locally by a constant flux. Figure 2 displays
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
235
Volume 18, 2023
comparative findings for Re = 100 based on Nu
assessed on the heated portion on the lower wall.
When changing from 0 to 5% and Ri = 0.1, 1, and
10, the highest variances seen stay under 1.02%.
Additionally, Our code was confirmed by
comparing it to the experiment results of the authors
[39], for natural convection in a square cavity
containing an alumina-water nanofluid and heated
differently for H L = 25 mm 25 mm, different
values of Ra and . Comparing findings
with the highest differences of about 4.5% are
shown in Table 2 and pertain to Nu assessed against
the hot wall. Therefore, these findings guarantee the
correctness of the current code used to investigate
the considered problem.
Fig. 2: Comparing Nu, for Re = 100 and various
values of and Ri in vented square cavity exposed
to copper-water nanofluid
Table 2. Verification of the numeric code for
various values of Ra using Nu assessed on hot wall
in square cavity that contains Al2O3 and water
nanofluid
To verify that the solution was grid-
independent, a full mesh testing process was carried
out. For both the x and y axes, a uniform size of grid
201101 is employed in all calculations for this
investigation. By contrasting the findings from this
grid with those from a finer grid of 321161, grid
sensitivity research has been carried out (Table 3).
Indeed, in terms of max and Nu, the highest relative
error generated is less than 1.06 percent and 1.76
percent, respectively.
Table 3. Examination results of grid independence
with 1 and 2 corresponds to (201×101) and
(321×161) respectively for various Re and values
for the suction and the injection forced flow
6 Findings and Discussions
We conduct numerical simulations to investigate the
temperature and convective flow patterns in a multi-
vented enclosure, heated with uniform hot
temperature at the bottom horizontal wall. This
simulation are performed for a Reynolds number
(Re) varied between 200 and 5000 and a volume
fraction of nanoparticles () that varies from 0% to
7%, while maintaining a fixed Rayleigh number of
Ra=106. The analysis evaluates the conjugate effects
of Re, and the applied flow mode via the cavity on
temperature distribution, cooling efficiency, and
fluid flow. It will be noted that, low values of Re
(Re 500) in the injection mode lead to unsteady
solutions, which do not clearly show up as dynamic
and thermal structures in the region of the instability
zone.
Figures 3a-3d show streamlines and isotherms
plots for the two cases = 0 (continuous line )
and = 0.07 (discontinuous line - - - ),
demonstrating the effect of Re on thermal fields and
dynamical in injection mode. Four closed-cell
structures are seen in the streamlines at the moderate
value of Re (Re = 600) (Figure 3a). Therefore, the
two cells in the highest part of the cavity on the
right (clockwise cell) and left (trigonometric cell)
correspond to those located above open lines of
forced flow caused by shear effects. Both with
heated walls, turning in opposite directions because
10
12
14
16
18
20
0 0.01 0.02 0.03 0.04 0.05
Shahi et al. [21]
Present work
Nu
Ri = 0.1
Ri = 1
Ri = 10
Ra
Current
study
Ho et al. [39]
(Experimental)
percentage
of
variation
7.5 105
7.91
7.6
4.08
1.5 106
9.801
9.4
4.26
2.5 106
11.79
11.3
4.33
3.3 106
12.54
12
4.5
= 0.04
= 0.07
max
Nu
max
Nu
Injection
flow
Re=600
1
0.279
18.892
0.279
19.327
2
0.281
19.191
0.281
19.665
Injection
flow
Re=2000
1
0.282
33.155
0.282
33.820
2
0.285
33.496
0.285
34.182
Suction
flow
Re=200
1
0.297
23.987
0.297
24.423
2
0.298
23.564
0.298
23.996
Suction
flow
Re=3000
1
0.284
96.540
0.284
98.717
2
0.284
97.214
0.284
99.575
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
236
Volume 18, 2023
of shear effects and free convection. By raising
from 0 to 0.07, qualitatively, a very small effect in
the stream pattern can be seen. There is an adequate
convective heat transfer entre the liquid and the
active horizontal wall, as indicated by the matching
isotherms that tighten at that level. In addition, there
are two cold zones which are delimited by an inlet
opening and that of the exit.
These two zones are brought eventually to a
uniform temperature that is equal to that of the
external environment. The presence of this
characteristic attests to an absence of heat
transmission via the active wall and the surrounding
walls. Furthermore, because the comparable
isotherms for the pure water and = 0.07 are well
spaced, the impact of is greatly noticeable where
the two little bottom cells are located. As the
influence of forced convection increases, an increase
in Re up to 1000 (Figure 3b) causes a rise in the size
as well as the intensity of the two lower cells (which
are compared to the higher cells), which allows
straightening of the open lines and consequently
leaving enough space in favor of the two cells. Re is
subsequently increased to 3000 and eventually 5000
(dominant forced convection regime) in order to
support the bottom cell, as Figures 3c-3d illustrate.
This improvement is to detriment of open lines
which become relatively straight. However, for high
numbers of Re, the thermal and dynamic structures
grow insensitive to the quantity of nanoparticles.
Near the heated wall, all isotherms condense, as
indicated by the corresponding isotherms, by
forming a distinguished and very thin thermal
boundary layer. This behavior testifies an intense
heat released via the open lines to the exterior either
directly or through the two lower cells.
The streamlines and isotherms are also
displayed in the enclosure in the suction case in
Figures 4a–4e for both = 0 (continuous line )
and = 0.07 (discontinuous line - - -) and different
Re values. As illustrated in Figure 4a, the
streamlines observed at low Re values (Re = 200)
demonstrate that the forced flow is sucked vertically
through the opening situated in the middle of the top
wall, then leaving horizontally the cavity from the
two vertical outlets. Therefore, the lower hot wall is
in direct contact with the horizontal and parallel
open lines, which allows a strong thermal exchange
of this wall and the fluid. The existence of two
large, enclosed cells defines the structure with the
same size and opposite senses, surmounting the
promoted flow's open lines and whose formation is
mostly caused by shear force compared to the larger
cells that are visible on injection, such cells are
straight, big, and intense (Figure 3a). In addition, the
dynamic structure is symmetrical about the middle
of the configuration, as demonstrated. The
associated isotherms are condensed as a beam in the
vicinity from the horizontal wall that is heated,
which forms a thermal boundary layer of low
thickness indicating a powerful convective heat
transmission from the fluid's wall. As a result, the
heat generated in the hot wall is immediately
evacuated via thermal boundary layer to exit. Maybe
said in this situation that the inertia forces dominate
over the forces of buoyancy. Besides, we note that
the thermally inactive zone (cold zone) occupies
almost the entire cavity. This behavior indicates that
the technique of suction is thermally stronger
compared to the injection mode. The two enclosed
cells sizes somewhat grow because of the increase
of the forced flow when Re is increased up to 600
and 1000 (Figures 4b-4c).
The isotherms demonstrate a reduction of the
cold zone relative to the boundary layer, indicating
an increase in the impact of forced convection. An
additional raise of Re up to 3000 and then 5000 does
not encourage the modification of the flow structure
(Figures 4d-4e) but contributes to the reduction of
the thermal border layer in favor of the cold region
and subsequently to the improvement of the thermal
transfer. In the end, it needs to be emphasized that
the existence of nanoparticles (from = 0 to =
0.07) does not modify the dynamic and thermal
structures, whatever the intensity of the forced flow.
We used Figure 5 to demonstrate the variation
between the Nu and the Re, and different values of
along the wall that is heated, to show the success
that modes performed during the heat removal
process. Overall, Nu increase with Re in both
modes. At Re 500, the rate of this growth gains
significance (beyond this threshold, an increase in
the curve's slope is seen). The intensity of the flow
supports this pattern that occurs as a result of the
inertia forces generated by the rise in Re.
On the other hand, Nu in the injection situation
is nearly constant as long as Re < 500. The
explanation for this outcome is that, over this range
of Re, natural convection predominates and
therefore, for any given Re, the impact on the
transmission of heat is insignificant. This result is
because the appearance of two closed cells which
delays the transfer of heat in the situation of low-
velocity flow through the fluid and heated wall.
About the suction mode, this single point does
not exist because of the imposed flow keeps the
heated wall entirely in direct contact, resulting in a
constant rise in Nu with Re. When ϕ is increased to
0.07, for a fixed value of Re, the convection
increases noticeably in both mode conditions. This
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
237
Volume 18, 2023
is because as ϕ increases, the nanofluid's effective
thermal conductivity also increases. More
specifically, Nu is raised for the more fortunate
scenario by raising ϕ from 0 to 0.07, used for
Re = 5000, from 106.26 / (49.43) to 116.17 / (53.55)
for the suction / (injection) case.
It should be mentioned that the difference
between suction and injection, improves heat
transfer more, resulting in more cavity cooling for
all Re values, whether the cavity is packed with
either nanofluid or water.
Fig. 3: Streamlines and isotherms, for = 0 (—) and = 0.07 (- - -), various values of Re, with injection case:
a) Re = 600, b) Re = 1000, c) Re = 3000 and d) Re = 5000
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
238
Volume 18, 2023
Fig. 4: Streamlines and isotherms, for = 0 (—) and = 0.07 (- - -), various values of Re, with suction case:
a) Re = 200, b) Re = 600, c) Re = 1000, d) Re = 3000 and e) Re = 5000
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
239
Volume 18, 2023
Furthermore, in mixed or forced convection
(moderate Re values), the suction case thermal
performance is more noticeable. This revealed result
proves the originality of our work since the most of
earlier research examined the injection mode while
examining the ventilated systems' thermal
capabilities. Quantitatively, for ϕ = 0.04 and Re =
1000 Nu rises from 23.59 to 58.23 when switching
from injection to suction mode which corresponds
to a multiplication of the heat transfer rate of almost
2.5.
Fig. 5: Variations of Nu, with respect to Re for
various values of in both injection and suction
mode.
It should be emphasized that oscillatory action
is frequently seen during the time of a shift from one
flow to another structure to another, when the
heating is applied by the bottom or when Ra is
sufficiently high and Re is less than the critical
value. Thus, in the mode of injection, unsteady
periodic solutions have been obtained; they are
marked by full circles in Figure 5. For such cases,
Nu is averaged over multiple flow cycles. When Re
rises over a critical value, these unstable solutions
vanish. For more precision, the existence of these
periodic solutions is restricted with
(200 ≤ Re ≤ 500) depending on .
Figures 6a–6b provide an example of a typical
periodic solution and show the unsteady periodic
regime in terms of min and Nu, in the injection
mode, for Re = 300 and = 0.04. The nature of the
For Nu, the fluctuations are sinusoidal, although this
sinusoidal behavior is lost for min during a short
interval. Both variables (min and Nu) oscillate at
identical periods in space and time. By the norm of
the author [40], the analogous trajectory in the
(min, Nu) phase plane is a straightforward closed
curve of the P1-type.
The cycle's limits are projected in the phase
plane in Figure 6c. Figure 6b shows streamlines and
isotherms at specific moments that correspond to the
characters ‘a’ to ‘e’ throughout one flow cycle.
Fig. 6: Periodic oscillations, obtained for Re = 300
and = 0.04 in the injection case: a) variations with
time of min, b) variations with time of Nu and
c) projection at a phase plane min-Nu.
Figures 7a–7e show that as the cycle evolves,
there are minor changes to the temperature and flow
structure within the enclosure. But it is to indicate
that an alternation of appearance and disappearance
of the two cells below the forced lines is marked.
The existence of these convective cells is favored by
natural convection's significance. This observed
phenomenon is justified by the competition between
natural and forced convection, which causes the
appearance of an oscillatory regime. In addition, the
corresponding isotherms show clearly that, there is
some complication in the temperature distribution
within the cavity in the lower center section.
(Deformation of isotherms) because of this area’s
complicated flow structure, located where two small
cells are situated.
0
20
40
60
80
100
120
Suction
Injection
Nu
Periodic solution
.
.
..
..
..
Re
200 500 1000 2000 5000
-0.2796
-0.2793
-0.2790
-0.2787
360 370 380 390 400
a)
min
t
15.5
16.0
16.5
17.0
360 370 380 390 400
b)
Nu
t
.
. .
. .
a
b
c
d
e
15.5
16.0
16.5
17.0
-0.2796 -0.2794 -0.2792 -0.2790 -0.2788 -0.2786
min
Nu
c)
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
240
Volume 18, 2023
Fig. 7: Streamlines and isotherms, during one flow cycle, in injection case, for Re = 300 and = 0.04
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
241
Volume 18, 2023
The improvement of the heat exchange by the
suction mode’s accomplishment is demonstrated in
Figure 8 regarding the injection case, presents the
variation with Re of the parameter
mod suction injection injection
E = Nu - Nu ) / N[( ] 0u 10
. For
any value of , Emod crosses as a monotonous way
with Re up to a maximum value that corresponds to
a critical Re (Rec = 1500). Quantitatively, in the
case of = 0.07, Emod reaches its maximum value
which is approximately 150% (ie, the amount of
heat released is amplified by 2.5 times). Beyond
Rec, any increase in Re involves a drastic reduction
of Emod. The consequence of this analysis shows the
contribution of the suction case is favored by Re as
Re < 1500. On the other hand, for a given Re, we
deduce that, the contribution of the suction case is
supported by for Re < 500.
Fig. 8: Variations of the heat exchange improvement
by ventilation mode, Emod, with Re, and various
values of
The heat-producing potential of the
nanoparticles transfer improvement, for the two
ventilation modes, is displayed in Figure 9
concerning variations with Re of the parameter
nf nf f f
E = Nu - Nu ) [( ] ×/ Nu 100
for = 0.04 and
0.07. In the injection mode, Enf increases
monotonically through Re until a maximum amount
is reached, obtained for Rec = 600, which equals
6.5% / (9%) for = 0.04 / (0.07). Beyond Rec, Enf
remains almost constant. For the suction mode, Enf
increases significantly with Re as long as the latter
is greater than 1000. Below this value, Enf is
insensitive to any disturbance of Re. It is useful to
mention that adding nanoparticles will make the
suction mode more advantageous for improving heat
exchange in comparison with the injection one for
low and high Re. Also, it is noted that the difference
in term of Enf, resulting from the augmentation of
from 0.04 to 0.07 keeps the same value for both
modes and which is equal to 2.5%. However, for the
injection case with Re ˂ 500, this value is
approximately 0.3%.
Fig. 9: Variations of the heat transfer improvement
by nanoparticles addition, Enf, with Re, for various
values of in both modes
It is essential to give particular consideration to
the assessment of the cavity's average temperature
in such situations. Therefore, Figure 10 shows
variations of this parameter relation to Re for the
two ventilation cases and various values of .
Specifically, in the injection case, raising Re to a
critical number Rec = 500 raises the average
temperature
T
, which strongly depends on . A
constant Nu value in this Re region justifies this
cavity reheating. (Figure 5 for the injection mode).
Beyond Rec, this tendency is reversed because the
growing effect of Re is demonstrated by a drop of
T
; this conduct is the result of the prevailing forced
convection, which favors the evacuation of heat
towards the exit and consequently assists in keeping
the cavity cold. For the suction mode, the evolution
of the average temperature
T
is distinguished by a
notable reduction as Re increases. This is because of
the higher heat exchange by convection with the rise
in the flow velocity. Also, the positive impact of the
insertion of nanoparticles on average temperature is
observed. In addition, it is underlined to mention
that the results of
T
obtained in the suction mode
are lower than those obtained in the injection mode,
the suction case effectively cools the cavity. For
clarity, it should be mentioned that switching from
the injection to the suction type results of
T
in the
40
60
80
100
120
140
160
Emod%
Re
200 500 1000 2000 5000
Periodic solution
.
.
.
.
..
.
.
.
..
2
4
6
8
10
Enf %
200 500 1000 2000 5000
.
.
.
..
.
Re
Suction
Injection
Periodic solution
.
.
.
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
242
Volume 18, 2023
reduction of almost 86% for Re = 1000 and
= 0.04.
Fig. 10: Variations, of the mean temperature,
T
,
with Re, for different values of in both modes.
7 Conclusions
Nanofluid mixed convection in a multi-vented
cavity heated from the bottom has been studied by
taking injection and suction cases of forced external
flows. Considering the results, the following
conclusions have been drawn:
Increasing the volume fraction of nanoparticles
increases the rate of heat transmission for all
values of Re in both modes; such behavior is
weak for low values of Re in injection mode.
The mean temperature is significantly raised
with dispersed nanoparticles within the
enclosure for the two modes of forced flow.
A higher thermal efficiency is achieved in the
suction mode by increasing heat transport
across the cavity, with or without nanoparticles.
Applying the suction mode usually results in
improved cavity cooling because it reduces the
average temperature values.
References:
[1] R. Y. Jou and S. C. Tzeng, Numerical
research of nature convective heat transfer
enhancement filled with nanofluids in
rectangular enclosures, International
Communications in Heat and Mass Transfer,
Vol. 33, 2006, pp. 727-736.
[2] K. Kahveci, Buoyancy driven heat transfer of
nanofluids in a tilted enclosure, Journal of
Heat Transfer, Vol. 132, No 6, 2010, p.
062501.
[3] E. Abu-Nada, Z. Masoud, H. F. Oztop and A.
Compo, Effect of nanofluid variable
properties on natural convection in
enclosures, International Journal of Thermal
Sciences, Vol. 49, No 3, 2010, pp. 479-491.
[4] M. Corcione, Heat transfer features of
buoyancy-driven nanofluids inside
rectangular enclosures differentially heated
at the sidewalls, International Journal of
Thermal Sciences, Vol. 49, No 9, 2010, pp.
1536-1546.
[5] M. Corcione, Empirical correlating equations
for predicting the effective thermal
conductivity and dynamic viscosity of
nanofluids, Energy Conversion and
Management, Vol. 52, No 1, 2011, pp. 789-
793.
[6] F. H. Lai and Y. T. Yang, Lattice Boltzmann
simulation of natural convection heat transfer
of Al2O3/water nanofluids in a square
enclosure, International Journal of Thermal
Sciences, Vol. 50, No 10, 2011, pp. 1930-
1941.
[7] M. Bouhalleb and H. Abbassi, Numerical
investigation of heat transfer by CuO-water
nanofluid in rectangular enclosures, Heat
Transfer Engineering, Vol. 37, No 1, 2016,
pp. 13-23.
[8] A. A. Abbasian Arani, M. Mahmoodi and S.
M. Sebdani, On the cooling process of
nanofluid in a square enclosure with linear
temperature distribution on left wall, Journal
of Applied Fluid Mechanics, Vol. 7, No. 4,
2014, pp. 591-601.
[9] G. Wang, X. Meng, M. Zeng, H. Ozoe and
Q. W. Wang, Natural convection heat
transfer of copper-water nanofluid in a
square cavity with time-periodic boundary
temperature, Heat Transfer Engineering,
Vol. 35, 2014, pp. 630-640.
[10] A. H. Mahmoudi, M. Shahi, A. H. Raouf and
A. Ghasemian, Numerical study of natural
convection cooling of horizontal heat source
mounted in a square cavity filled with
nanofluid, International Communications in
Heat and Mass Transfer, Vol. 37, 2010, pp.
1135-1141.
[11] F. Garoosi, G. Bagheri and F. Talebi,
Numerical simulation of natural convection
of nanofluids in a square cavity with several
pairs of heaters and coolers (HACs) inside,
International Journal of Heat and Mass
Transfer, Vol. 67, 2013, pp. 362-376.
[12] C. J. Ho, L. C. Wei and Z. W. Li, An
experimental investigation of forced
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
T
Re
Periodic solution
.
Suction
Injection
.
.
..
.
..
.
.
500 1000 2000 5000
200
.
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
243
Volume 18, 2023
convective cooling performance of a
microchannel heat sink with Al2O3/water
nanofluid, Applied Thermal Engineering,
Vol. 30, No 2, 2010, pp. 96-103.
[13] S. M. H. Hashemi, S. A. Fazeli, H.
Zirakzadeh and M. Ashjaee, Study of heat
transfer enhancement in a nanofluid-cooled
miniature heat sink, International
Communications in Heat and Mass Transfer,
Vol. 39, No 6, 2012, pp. 877-884.
[14] S. A. Fazeli, S. M. H. Hashemi, H.
Zirakzadeh and M. Ashjaee, Experimental
and numerical investigation of heat transfer
in a miniature heat sink utilizing silica
nanofluid, Superlattices and Microstructures,
Vol. 51, No 2, 2012, pp. 247-264.
[15] H. Zirakzadeh, A. Mashayekh, H. N. Bidgoli
and M. Ashjaee, Experimental investigation
of heat transfer in a novel heat sink by means
of alumina nanofluids, Heat Transfer
Research, Vol. 43, No 8, 2012, pp. 709-720.
[16] F. Talebi, A. H. Mahmoudi and M. Shahi,
Numerical study of mixed convection flows
in a square lid-driven cavity utilizing
nanofluid, International Communications in
Heat and Mass Transfer, Vol. 37, No 1,
2010, pp. 79-90.
[17] F. Garoosi, S. Garoosi and K. Hooman,
Numerical simulation of natural convection
and mixed convection of the nanofluid in a
square cavity using Buongiorno model,
Powder Technology, Vol. 268, 2014, pp.
279-292.
[18] S. M. Sebdani, M. Mahmoodi and S. M.
Hashemi, Effect of nanofluid variable
properties on mixed convection in a square
cavity, International Journal of Thermal
Sciences, Vol. 52, 2012, pp. 112-126.
[19] A. A. Abbasian Arani, S. M. Sebdani, M.
Mahmoodi, A. Ardeshiri and M. Aliakbari,
Numerical study of mixed convection flow in
a lid-driven cavity with sinusoidal heating on
sidewalls using nanofluid, Superlattices and
Microstructures, Vol. 51, No 6, 2012, pp.
893-911.
[20] M. Kalteh, K. Javaherdeh and T. Azarbarzin,
Numerical solution of nanofluid mixed
convection heat transfer in a lid-driven
square cavity with a triangular heat source,
Powder Technology, Vol. 253, 2014, pp.
780-788.
[21] M. Shahi, A. H. Mahmoudi and F. Talebi,
Numerical study of mixed convective
cooling in a square cavity ventilated and
partially heated from the below utilizing
nanofluid, International Communications in
Heat and Mass Transfer, Vol. 37, No 2,
2010, pp. 201-213.
[22] A. H. Mahmoudi, M. Shahi and F. Talebi,
"Effect of inlet and outlet location on the
mixed convective cooling inside the
ventilated cavity subjected to an external
nanofluid", International Communications in
Heat and Mass Transfer, Vol. 37, No 8,
2010, pp. 1158-1173.
[23] A. H. Mahmoudi and K. Hooman, Effect of a
discrete heat source location on entropy
generation in mixed convective cooling of a
nanofluid inside the ventilated cavity,
International Journal of Exergy, Vol. 13,
2013, pp. 299-319.
[24] E. Sourtiji, M. Gorji-Bandpy, D. D. Ganji
and S. F. Hosseinizadeh, Numerical analysis
of mixed convection heat transfer of Al2O3-
water nanofluid in a ventilated cavity
considering different positions of the outlet
port, Powder Technology, Vol. 262, 2014,
pp. 71-81.
[25] A. A. Mehrizi, M. Farhadi, H. H. Afroozi, K.
Sedighi and A. A. R. Darz, Mixed
convection heat transfer in a ventilated cavity
with hot obstacle: effect of nanofluid and
outlet port location, International
Communications in Heat and Mass Transfer,
Vol. 39, 2012, pp. 1000-1008.
[26] M. H. Esfe, S. Niazi, S. S. M. Esforjani and
M. Akbari, Mixed convection flow and heat
transfer in a ventilated inclined cavity
containing hot obstacles subjected to a
nanofluid, Heat Transfer Research, Vol. 45,
No 4, 2014, pp. 309-338.
[27] I. Arroub, A. Bahlaoui, A. Raji, M. Hasnaoui
and M. Naïmi, Cooling Enhancement by
Nanofluid Mixed Convection inside a
Horizontal Vented Cavity Submitted to
Sinusoidal Heating, Engineering
Computations, Vol. 35, No. 4, 2018, pp.
1747-1773.
[28] I. Arroub, A. Bahlaoui, S. Belhouideg, A.
Raji and M. Hasnaoui, Numerical
Investigation of Mixed Convection in a
Tilted Multi-Vented Cavity Filled with
Nanofluid Considering Different Positions of
the Outlet Port, AIP Conference
Proceedings, Vol. 2761, No. 1, 2023, p.
040027.
[29] A.S. Rikani, Numerical analysis of free heat
transfer properties of flat panel solar
collectors with different geometries, Journal
of Research in Science, Engineering and
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
244
Volume 18, 2023
Technology, Vol. 9, No. 01, 2021, pp. 95-
116.
[30] M Sultan, S., Tso, C. P., & M N, E. E.
(2020). A case study on effect of inclination
angle on performance of photovoltaic solar
thermal collector in forced fluid mode,
Renewable Energy Research and
Applications, Vol. 1, No. 2, 2020,pp 187-
196.
[31] N. A. Qasem, A. Abderrahmane, S. Ahmed,
O. Younis, K. Guedri, Z. Said, A. Mourad,
Effect of a rotating cylinder on convective
flow, heat and entropy production of a 3D
wavy enclosure filled by a phase change
material, Applied Thermal Engineering, Vol.
214, 2022, p. 118818.
[32] M. M. Bhatti, A. Riaz, L. Zhang, S. M. Sait,
R. Ellahi, Biologically inspired thermal
transport on the rheology of Williamson
hydromagnetic nanofluid flow with
convection: An entropy analysis, Journal of
Thermal Analysis and Calorimetry, Vol. 144,
2021, pp. 2187-2202.
[33] F. P. Incropera and D. P. DeWitt,
Introduction to Heat Transfer, Wiley New
York, 2002.
[34] I. Arroub, A. Bahlaoui, A. Raji, M. Hasnaoui
and M. Naïmi, Varying Heating Effect on
Mixed Convection of Nanofluids in a Vented
Horizontal Cavity with Injection or Suction,
Heat Transfer Engineering, Vol. 40, No. 11,
2019, pp. 941-958.
[35] M. Corcione, M. Cianfrini and A. Quintino,
Two-phase mixture modeling of natural
convection of nanofluids with temperature-
dependent properties, International Journal
of Thermal Sciences, Vol. 71, 2013, pp. 182-
195.
[36] M. Corcione, M. Cianfrini and A. Quintino,
Enhanced natural convection heat transfer of
nanofluids in enclosures with two adjacent
walls heated and the two opposite walls
cooled, International Journal of Heat and
Mass Transfer, Vol. 88, 2015, pp. 902-913.
[37] L. C. Woods, A note on the numerical
solution of fourth order differential
equations, Aeronautical Quarterly, Vol. 5,
No 4, 1954, pp. 176-184.
[38] I. Arroub, A. Bahlaoui, S. Belhouideg, A.
Raji and M. Hasnaoui, Combined effects of
inclination angle and imposed flow on mixed
convective cooling inside a vented cavity
crossed by nanofluids, Physical Chemistry
Research, Vol. 11, No.3, 2023, pp. 631-642.
[39] C. J. Ho, W. K. Liu, Y. S. Chang and C. C.
Lin, Natural convection heat transfer of
alumina-water nanofluid in vertical square
enclosures: An experimental study,
International Journal of Thermal Sciences,
Vol. 49, 2010, pp. 1345-1353.
[40] T. B. Lennie, D. P. McKenzie, D. R. Moore
and N. O. Weiss, The breakdown of steady
convection, Journal of Fluid Mechanics, Vol.
188, 1988, pp. 47-85.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.19
Ismail Arroub, Ahmed Bahlaoui,
Soufiane Belhouideg, Abdelghani Raji,
Mohammed Hasnaoui
E-ISSN: 2224-3461
245
Volume 18, 2023
