Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

Diyala Journal of Engineering Sciences

Journal homepage: https://djes.info/index.php/djes

ISSN: 1999-8716 (Print); 2616-6909 (Online)

Effect of Hump Configurations of Porous Square Cavity on Free

Convection Heat Transfer
Ahmed A. Fadhil1, Itimad D.J. Azzawi1*, I.M. Mahbubul2 and M. Hasannuzaman3
1
Department of Mechanical Engineering, University of Diyala, 32001 Diyala, Iraq
2
Institute of Energy Engineering, Dhaka University of Engineering & Technology, Gazipur 1707, Bangladesh
3
Higher Institution Centre of Excellence (HICoE), UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R&D, University
Malaya, Jalan Pantai Baharu, 59990 Kuala Lumpur, Malaysia

ARTICLE INFO ABSTRACT

Free convection is widely used in engineering applications, including solar energy,
Article history: electronic devices, nuclear energy and heat exchangers. A computational simulation
Received January 1, 2023
Revised June 7, 2023 utilising Ansys Fluent-CFD was used to examine the natural convection heat transfer
Accepted June 17, 2023 inside a square cavity filled with pure water and saturated metal foam as a porous
Available online September 1, 2023 medium (porosity ɛ=0.9). The enclosure’s lower wavy wall exhibits a high temperature
(Th), whereas the side and upper walls display a low temperature (Tc). For different
Keywords: Rayleigh numbers, the study examines hump configuration and the bottom wall hump
Wavy porous square enclosure number (N). The predominant design of heat transmission was improved using the
Hump configuration circular hump design parameters of ɛ=0.9, N=4 and Tc=25 °C for different Ra. The
Number of humps novelty of the research included determining the optimal design for the square enclosure.
Free convection This approach involved estimating the effects of hump configuration and the number of
Heat transfer enhancement. humps for the bottom wall of the enclosure. These parameters have not been studied yet.
The optimum case showed the highest heat transfer coefficient (h) at the circular hump,
N=4 and Ra=30103, whereas the standard case obtained N=0 and Ra=5103. The CFD
simulation results indicate that the primary objective of the study was achieved through
the optimal design, resulting in a significant enhancement of hydrothermal performance
for heat transfer enhancement and energy enhancement 1.13 times compared with the
standard case.

1. Introduction studies, several researchers focused on free

convection inside cavities and fluid flow
Owing to the substantial and persistent without magnetohydrodynamics (MHD)
growth in energy consumption rates and the because of its wide applications. The re-
rising scarcity of conventional energy sources searchers focused on several techniques that
accompanied by high prices, a result of proved to be very effective in improving heat
industrial development following the mid- transfer. One of these techniques is
20th-century industrial revolution, the energy manipulation and changes in the geometry of the
crisis is considered one of the most critical cavities. Other techniques include nanofluid
problems confronting the world. Thus, usage, porous medium and magneto-
researchers are deliberately attempting to hydrodynamic (MHD).
improve the performance of heat exchange A numerical simulation was conducted to
systems and change their size to reduce their study the natural convection in a triangle
rates of thermal energy usage. In subsequent
*
Corresponding author.
E-mail address: itimaddawood_eng@uodiyala.edu.iq
DOI: 10.24237/djes.2023.160301
This work is licensed under a Creative Commons Attribution 4.0 International License.

1
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

enclosure filled with water and a porous having an inner solid block. When the straight
medium for various Rayleigh numbers (Ra), bottom wall of the cavity was replaced with a
heater locations (Ph), heater lengths (Lh) and wavy wall, significant enhancement in free
inclination angles (θ). An increase in heat convection heat transfer was achieved [16].
transfer indices with higher values of (Lh) and Khalil et al. used computational simulation
(θ=0) was observed at high levels of (CFD-Fluent) to study natural convection heat
Ra. Response surface methodology (RSM) was transfer inside a wavy porous trapezoidal
applied for optimisation investigation of aspect enclosure. According to a study, an increase in
ratios (L/H) (Ra) and porosity, and the highest heat transfer of 3.37 times was achieved by
heat transfer was recorded at the lowest value of utilising a combination of four waves (N=4) and
porosity and the highest L/H value [1]. an amplitude of 20 mm (a=20 mm); further
Numerous studies on the utilisation of enhancement was observed at a Hartman
nanofluids in containers of varying shapes, with number of 40 (Ha=40) [17]. A previous study
and without the impact of magnetic field was conducted to analyse free convection inside
intensity, have been conducted. These studies a square enclosure with oblique undulation-
revealed an improvement in heat transfer sided walls. Numerical simulation findings
through an elevation in its indicators with an reveal that increasing the amplitude of the two-
increase in Ra and nanoparticle concentration, sided undulation walls of the cavity slightly
while also considering alterations in container enhanced the transfer of heat [18]. Several
dimensions. These results were obtained from studies on the utilisation of square-geometry
multiple sources [2–5]. Al-Damook et al. structures to enhance heat transfer have been
evaluated the natural convection with MHD and conducted. The results demonstrate that the
metal foam in an L-shaped cavity. The study implementation of this approach effectively
found that MHD and oblique angles of a cavity enhances the heat transfer effect, as evidenced
have a widespread impact on heat transfer. As by previous research [19-20]. The influence of
porosity decreases, heat transfer indicators the aspect ratio of the right-side wall of a square
improve, along with reduced surface enclosure on natural convection was studied
temperature and entropy generation and an with various numbers of waves by numerical
increase in aspect ratio. These findings are simulation, The simulation findings showed that
relevant to the field of academic research on the cooling efficiency of the heat source
heat transfer [6]. Previous literature on heat increased gradually with growth increasing in
transfer has been extensively reviewed by aspect ratio [21]. The increase in aspect ratio
numerous authors, who have investigated and Ra leads to the increase in heat transmission
porosity and its potential to enhance heat inside a horizontal and shallow wavy chamber
transfer in porous fluids. The findings indicate that has a bottom wavy wall and upper and side
that porosity has a significant impact on heat straight walls; heat transfer declined with an
transfer, and researchers are recommended to increase in the non-dimensional length of wave
explore its utilisation in future research according to simulation findings [22]. The
endeavours [7-8]. Several researchers placement of the geometry affects the heat
previously investigated the impact of magnetic transfer enhancement given that the
fields on heat transfer in liquid-filled cavities acceleration, in this case, influences the
with varying geometries. They observed that movement of the liquid inside the enclosure, as
higher Hartman numbers (Ha) corresponded to well as increases the movement of the liquid and
greater electrical conductivity and vortex its mixing due to the difference in liquid
motion within the cavities, ultimately resulting temperature. Moolya et al. investigated free
in improved heat transfer rates. They also convection within a rectangular enclosure filled
studied the MHD direction, which significantly with the fluid and showed a significant
increase and enhance heat transfer [9–15]. enhancement in local Nusselt number as an
Azizul et al. studied numerically free convection indicator of heat transfer due to an inclination of
inside a square cavity filled with nanofluid and the geometry of the rectangular cavity [23]. The

2
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

work focuses on the enhancement of the free Figure 1. The cavity’s side and top walls have a
convection inside a porous wavy square low temperature of Tc=25 °C. The bottom wall
chamber filled with pure water and saturated has a variable hot temperature (Th) expressed in
porous media with porosity level of (ɛ=0.9). The terms of Ra, with investigations into the hump
analysis also considers the impact of hump configuration (circular, triangle, square, up
configuration for the bottom wall of the semi-circle, and down semi-circle) and number
container and the number of humps (N) on heat of humps (N=0, 1, 2, 3 and 4) with no-slip
transfer rates. Recent literature on wavy porous conditions (v=u=0).
square cavities has not fully analysed these
parameters. The computational simulation of 2.2 Mesh study
ANSYS FLUENT-CFD-R20 for laminar flow,
2D steady state and single phase utilised in this The mesh verification study selected a
investigation to explain the effect of hump suitable grid size to guarantee that the
configure and N on heat transfer indicators, algorithms used in this analysis are unaffected
namely, heat transfer coefficient (h) and heat by grid size or size elements. This approach
transfer rate (Q). would minimise the computer load, amount of
time and expense required to complete the
2. Numerical methodology investigation. Therefore, a porous square wavy
2.1 Model description and problem cavity surface with the following grid size value
characterisation (2, 1.75, 1.5, 1.25, 1, 0.8, 0.7 and 0.5) was
divided into eight structures (triangles mesh).
The current study focuses on addressing Heat transfer coefficient (h) and heat transfer
heat transfer inside porous square cavity issues rate (Q) at Ra=(5 and 30)103 observation
through the examination of some parameters to values were utilised to assess this verification.
improve their thermal performance, ultimately The results showed no changes in (h and Q) at
resulting in enhanced heat transfer indicators. the size element of 0.7 mm and below. Hence,
The model used in this study is a 2D square all computational approaches in this work
cavity (HH) containing pure water and a should depend on this information to produce
saturated metal foam porous medium shown in precise results.

Figure 1. Model used with boundary conditions.

3
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

𝑄𝐸𝑛ℎ𝑎𝑛𝑐𝑒𝑑
2.3 Mathematical formula and the hypotheses ( ). (6)
𝑄𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
where (𝑄𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 ) is standard energy
The Ansys-Fluent program was used to
enhancement for a straight square chamber
analyse the natural free convection heat
(N=0).
transmission rate and thermal efficiency within
a square enclosure containing pure water and 2.4 Procedure of computational solution
saturated metal foam as a porous material. The
simulations were performed with specific Upon inputting the designated parameters,
parameters, including 2D, laminar, steady state, specifically the activation of energy and
incompressible flow, single-phase and water imposition of laminar flow, the Ansys-Fluent
fluid properties. The hydraulic properties of was configured with the setup field. Moreover,
water, except for density, remain unaffected by input water flow characteristics (Density ρ=997
temperature increases, thereby validating the kg/𝑚3 , Specific heat cp=4180 J/kg.K, Thermal
use of the Forchheimer–Darcy law in this conductivity k=0.607 W/m.K, Dynamic
simulation. In addition, given the significant viscosity µ=0.000891 Ns/𝑚2 and Thermal
inertial effects observed, the governing Expansion Coefficient β=0.000247 1/K) [17]
equations [1] used are as follows: activated cell zone condition (porous zone with
Continuity equation the magnitude of porosity) and added boundary
∂u ∂v
+ ∂y =0 (1) condition and reference value. Coupled
∂x
x-momentum equation algorithm is the second-order upwind scheme
∂u ∂𝑣 ∂p ∂2 𝑢 ∂2 𝑢 for pressure, momentum and energy in each X–
ρ(u ∂x + v ∂y ) = -ɛ2 ∂x + εμ( ∂x2 + ∂𝑦 2 ) − Y direction. The equations are then iteratively
ρCɛ2 μɛ2 solved in several attempts to achieve
𝑢|U| − 𝑢 (2)
𝐾0.5 𝐾 convergence in the results after hybrid
y-momentum equation initialisation and run calculation. Subsequently,
∂u ∂𝑣 ∂p ∂2 𝑣 ∂2 𝑣
ρ(u ∂x + v ∂y ) = -ɛ2 ∂y + εμ(∂x2 + ∂𝑦 2) + the indices of the heat transfer rate are calculated
ρCɛ2 μɛ2 in a porous square enclosure. The residual
ɛ2 ρβg(T − Tc) − 𝑢|U| − 𝑢 (3) values of the monitors are established to be
𝐾0.5 𝐾
energy equation below 10-6 for the continuity, momentum and
∂T ∂T ∂2 T ∂2 T energy.
𝑢 ∂x + 𝑣 ∂y = α𝑒 ( ∂x2 + ∂y2 ) (4)
𝑘
where |𝑈| = √𝑢2 + 𝑣 2 , αe=𝜌𝐶𝑒 or 𝛼𝑒 = 3. Results and discussion
𝑝
𝜀𝑘𝑤 +(1−𝜖)𝑘𝐴𝑙 3.1 Validation study
is the effective thermal diffusivity,
𝜌𝐶𝑝
and ke is the effective thermal conductivity [17]. A study was conducted to assess the current
The ratio of the enhanced heat transfer ANSYS Fluent-CFD-R20 code and compare it
with the work of Calcagni et al. [24] on square
coefficient (ℎEnhanced ) to the standard heat
cavities at Ra=104. The resulting contour graphics
transfer coefficient (ℎ𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 ) is referred to as
for isotherm lines at heat source length=1/5 (left)
heat transfer enhancement and can be and at heat source length=4/5 (right) were found
represented by the following formula: to be highly similar, as illustrated in Figures 2 (A
ℎ
( ℎ𝐸𝑛ℎ𝑎𝑛𝑐𝑒𝑑 ), (5) and B). Furthermore, numerical calculations were
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
where (ℎ𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 ) is the standard heat transfer conducted for all cases of Ra=103, 104, 105 and 106
coefficient for a straight square chamber (N=0). for the above heat sources, based on the
The ratio of the enhanced thermal energy experimental findings of Calcagni et al. [24]. A
considerable level of convergence was observed
transfer rate (𝑄𝐸𝑛ℎ𝑎𝑛𝑐𝑒𝑑 ) to the standard thermal
when comparing the findings with the prior
energy transfer rate (𝑄𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 ) referred to as
research, with an error rate that did not exceed 3%
the energy enhancement and can be represented to 4%, as shown in Figure 2 (C).
by the following formula:

4
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

3.2 Effect of hump configuration isotherms and stream functions that show the
effect of hump configuration on heat transfer
A numerical simulation was performed to indicators (h and Q) inside the enclosure for
examine the effect of the lower wall hump various Ra and ɛ=0.9, Tc=25 °C.
configuration of the porous square enclosure.
Figure 5 presents the graphic contours of

14

curent CFD study at ɛ=1/5 and 4/5

12
ɛ=1/5
A 10 ɛ=4/5

Nu
C 6

B 2

0
1000 10000 100000 1000000
Ra

Figure 2. Validation isotherm lines at heat source length=1/5 (Left) and isotherms at heat source length=4/5 (Right)
of Calcagni et al. [24] (A), current CFD study (B) and Calcagni et al. [24] with data (C).

Figure 3 (left) illustrates that the values of h configuration on heat transfer enhancement and
remain nearly constant for the first three values energy enhancement as functions of Ra
of Ra= (5,10,15)103 for all hump compared with a straight wall (standard). The
configurations except square. Thereafter, h figure also illustrates the augmentation of heat
gradually increases with increasing Ra. The transfer and energy through different hump
circular hump at Ra=30103 resulted in the configurations, excluding the square hump. The
highest (h) value. The heat transfer rate inside values of heat transfer enhancement and energy
the enclosure increased linearly with increasing enhancement are almost constant at all Ra
Ra values, as depicted in Figure 3 (right), levels. A marginal decrease was observed at a
leading to improved heat transfer. The high value of Ra (Ra=30103), indicating that
comparison of humps showed that the square the circular hump achieved more significant
hump was the least effective in enhancing heat heat transfer convection and thermal energy
transfer. Furthermore, consistency in the enhancement. The findings from Eqs. (5) and
magnitudes of h and Q was observed for the (6) indicate that a square hump resulted in the
straight wall (standard) and triangle hump, poorest heat transfer and thermal energy when
indicating convergence. By contrast, the circular compared with a flat or straight bottom wall.
hump achieves high heat transfer rate values at Figure 5 (right) shows isotherm graphic
the maximum value of Ra (Ra=30103). contours for various hump configurations. The
Furthermore, Figure 4 provides numerical temperature gradient within the enclosure
estimations for the influence of hump increases as the hump configuration changes,

5
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

leading to an increase in Ra. As a result, heat is enhanced from (Ѱmax=0.001603) at the flat
transfers from a hot, wavy bottom wall to the bottom wall to (Ѱmax=0.001616) at the circular
cold sides and upper walls. The circular hump hump bottom wall at Ra=5103. Similarly, the
and Ra=30103 are found to be the most maximum flow strength also improves
favourable conditions for achieving optimal from (Ѱmax=0.01354) at the flat bottom wall to
heat transfer, whereas the square hump results in (Ѱmax=0.01617) at the circular hump and
the worst outcomes. These observations can be Ra=30103. The presence of a circular hump
attributed to greater thermal interference within an enclosure results in the movement of
occurring at higher Ra values, owing to vortices from the hot lower space to the cold
increased flow intensity. This effect is reversed upper space. In the case of a square hump, a
at lower Ra values. Figure 5 (left) illustrates the stream function is hindered by pressure drops
formation of two large-scale vortices within an and collisions between vortices within the
enclosure, rotating in the opposite direction hump. Consequently, circulation in the upper
while maintaining comparable dimensions and space of the enclosure is impeded.
strengths, as characterised by the same Ra and
hump number (N). However, the flow strength

0.85 32
102
102

straight
0.8 29.5
27 circular hump
0.75 triangle hump
24.5
0.7 22 square hump
h(W/m2.K)

straight 19.5
Q(W)

0.65
circrlar hump 17
0.6 triangle hump 14.5
0.55 12
0.5 9.5
7
0.45
4.5
0.4 2
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Ra Ra 103
103
Figure 3. Heat transfer coefficient h (Left) and heat transfer rate Q (Right) for different Ra and hump configure at N=4,
Tc=25 °C, ɛ=0.9.

1.2 1.2

1.1 1.1
Energy enhancement

Heat transfer enhancement

1 1
straight circular hump straight
0.9 0.9 circular hump
triangle hump square hump triangle hump
0.8 0.8 square hump

0.7 0.7

0.6 0.6
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Ra 103 Ra 103

Figure 4. Energy enhancement (Left) and heat transfer enhancement (Right) for various Ra and hump configure at
N=4, Tc=25 °C and ɛ=0.9.

6
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

Ra=5103 Ra=30103 Ra=5103 Ra=30103

Ѱmax= 0.001603 Ѱmax= 0.01354

Ѱmax= 0.001616 Ѱmax= 0.016175

Ѱmax= 0.001606 Ѱmax= 0.01356

Ѱmax= 0.001597 Ѱmax= 0.01349

Figure 5. Stream functions (Left) and isotherms (Right) at Ra=(5 and 30)103 for different configuration of hump
flat bottom wall (F), circular hump (C), triangle hump (T) and square hump (S) at Tc=25 °C, N=4, ɛ=0.9.

After identifying and selecting the optimal Ra=(5, 10, 15) 103 prior to progressively
case from the illustrated cases in Figure 5, escalating with increasing Ra. The highest value
namely, the circular hump, numerical of h was observed at the circular hump and
simulations were conducted to evaluate whether Ra=30103. The heat transfer rate, as measured
any enhancements in heat transfer and thermal by parameter Q, exhibits a nearly linear increase
energy can be observed by comparing the with increasing Ra. Figure 6 (Right) illustrates
upward and downward semi-circular that the highest heat transfer rate is observed at
configurations. The simulation findings indicate the circular hump with a Ra of 30103. Figure 7
that the circular hump configuration remains the displays streamline and isotherm contours for
optimal scenario as it generates the most circular, upstream semi-circular and
elevated values for heat transfer indices, h and downstream semi-circular humps. Figure 7
Q. Figure 6 (left) illustrates that the circular (right) depicts a thermal gradient from the hot
hump arrangement attained the greatest value of lower wall to the cold side and top walls of the
h, which remained constant for the three initial cavity, as well as a decrease in heat transmission

7
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

in the upstream semi-circular and downstream graphic contours for Ra=5103 as the minimum
semi-circular hump configurations when Ra and Ra=30103 as the maximum, with the
compared with the circular hump. Figure 7 (left) following boundary conditions: Tc=25 °C, ɛ=0.9
shows how the flow strength decreased from and circular hump. In the present study, we
(Ѱmax=0.001616) at the circular hump to examined several hump numbers (N=0, 1, 2, 3
(Ѱmax=0.001581) at the downstream semi- and 4). The simulation results indicate that an
circular hump at Ra=5103 and from increase in N and Ra leads to a stronger flow and
(Ѱmax=0.016175) to (Ѱmax=0.0134) at higher temperature intensity. The stream
3
Ra=3010 due to low flow and the low functions exhibit the highest strength (Ѱmax=
influence of vortices movement. Figure 7 0.016175) at a high Ra (Ra=30103) when N=4,
displays a pressure drop that arises in resulting in the expansion of vortex movement
conjunction with the downstream semi-circular towards the upper space of the enclosure,
hump configuration. The effect of the circular counter to the flow along the straight bottom
hump on heat transfer is detailed in the above wall (N=0). Figure 10 (right) depicts heat
section. transfer from a hot lower wall to a cold, upper
and side walls. The increase in the value of the
3.3 Effect of bottom wall's hump number (N) parameter N leads to the dominance of heat
transfer by convection, counter to the case,
The impact of N on heat transfer and thermal
where N=0, presenting dominant conduction. At
energy was investigated using numerical
simulation on a hot bottom wall. Figure 10 N=4 and Ra=30103, a higher amount of heat is
shows streamlines (left) and isotherms (right) of
.

9 35
102

102

Circular hump
8
30 Up Semi-circular hump
7 Dwon Semi-circular hump
25
6
h(W/m2.K)

5 20
Q(W)

4 Circular hump
15
3 Up Semi-circular hump
10
2 Downe Semi-circular hump
5
1

0 0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Ra 103 Ra 103

Figure 6. Heat transfer coefficient h (Left) and heat transfer rate Q (Right) for different Ra and hump configuration
at N=4, Tc=25 °C and ɛ=0.9.

8
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

Ra=5103 Ra=3010 Ra=5103 Ra=30103

3
Ѱmax= Ѱmax= 0.016175
0.001616

(C)

Ѱmax= 0.001589 Ѱmax= 0.01350

(U)

Ѱmax= 0.001581 Ѱmax= 0.01340

(D)

Figure 7. Stream functions (Left) and Isotherms (Right) at Ra=(5 and 30) × 10 3 for various hump configure circular
hump (C), Up semi-circular hump (U) and Down semi-circular hump (D) at N=4, Tc= 5 °C and ɛ=0.9.

transferred in a porous square enclosure due to resulting in improved heat transfer. The value of
the presence of significant thermal advection. h was found to be the lowest when additional
This phenomenon occurs at the maximum value straight walls (N=0) were used, whereas the
of Ra, which corresponds to the maximum highest value of h was observed when continuity
intensity of flow contrast between regions with increased with N, as shown in Figure 8 (left).
different Ra values. Figure 8 shows the effect of Figure 8 (right) demonstrates that as the Ra and
the number of humps on the heat transfer N increases, the values of Q inside the enclosure
coefficient and heat transfer rate. The study steadily increases in behaviour that resembles
shows enhancements in heat transfer and linearity. The highest rate of heat transfer was
thermal energy within a square cavity that achieved at Ra=30103. The lowest value of Q
contains pores, where the Ra varies. The h occurred at Ra=5103 and N=0. The highest
values remain constant for the three initial value of Q was observed when N=4, indicating
values of Ra, namely, (5, 10, 15) 103. that N=4 achieved optimal enhanced heat
However, at Ra=30103, the h value peaks. This transfer. The emergence of upward vortices
increase in convection within the cavity is could facilitate the intermingling of fluid layers.
directly related to an increase in N and Ra, Figure 9 illustrates the impact of the number of

9
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

humps (N) on heat transfer and thermal energy remain constant for all Ra. The highest heat
enhancement. At a constant Ra, heat transfer transfer enhancement and energy enhancement
enhancement and energy enhancement occurred at N=4 and Ra=5103, representing
experience N increases. Moreover, this 1.13 times the standard case at boundary
enhancement is found to gradually lessen with conditions: Tc=25 °C, ɛ=0.9 and circular hump.
increasing Ra. The similarity between the This finding indicates that N=4 is the optimal
behaviour of N=0 and N=1 is observed with the parameter.
enhancement from 1 at N=0 to 1.07 at N=1,
whereas the heat transfer and thermal energy
8.6
102

N=0 N=1 N=2 N=0 N=1

102
29.5
8.4 N=3 N=4 N=2 N=3
N=4
8.2 24.5
h(W/m2.K)

8
Q(W)
19.5
7.8
7.6 14.5
7.4
9.5
7.2
7 4.5
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Ra 103 Ra 103

Figure 8. Heat transfer coefficient h (Left) and heat transfer rate Q (Right) for different Ra and N at Tc=25 °C, ɛ=0.9,
and circular hump.

1.14 1.14

1.12 1.12
Heat transfer enhancement
Energy enhancement

1.1 1.1
1.08 1.08
1.06 1.06
1.04 N=0 N=1 N=0 N=1
1.04
N=2 N=3 N=2 N=3
1.02 N=4 N=4
1.02
1
1
0.98
0 5 10 15 20 25 30 35 0.98
0 5 10 15 20 25 30 35
Ra 103
Ra 103

Figure 9. Energy enhancement (Left) and heat transfer enhancement (Right) for different Ra and N at Tc=25 °C,
ɛ=0.9 and circular hump.

10
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

Ra=5103 Ra=30103 Ra=5103 Ra=30103

Ѱmax= 0.001603 Ѱmax= 0.01354

N=0

Ѱmax= 0.001609 Ѱmax= 0.01613

N=1

Ѱmax= 0.001614 Ѱmax= 0.01614

N=2

Ѱmax= 0.001615 Ѱmax= 0.01615

N=3

Ѱmax= 0.001616 Ѱmax= 0.016175

N=4

Figure 10. Stream functions (Left) and Isotherms (Right) at Ra=(5 and 30)× 103 for different N at ɛ=0.9, Tc=25 °C,
and circular hump.

4. Conclusions
The main conclusions are outlined, as follows:
The current study has investigated the 1. The utilisation of a hump configuration
impacts of a hump configuration and N on free instead of a straight bottom wall results in
convection heat transfer in a porous square improvements in the heat transfer coefficient
chamber containing pure water and saturated by (h), heat transfer rate (Q), heat transfer
a porous medium (ɛ=0.9). The influence of enhancement and thermal energy
different hump configurations (circular, enhancement. For various Ra, the average
triangle, square, up semi-circular and down improvement in h and Q at the circular hump
semi-circular) and numbers of the lower wall is 1.13 times greater than that of the standard
humps (N=0, 1, 2, 3 and 4) are examined with a case (N=0).
range of Ra (5, 10, 15, 20, 25 and 30) 103.
Ansys Fluent-CFD was applied in this analysis 2. Circular hump achieves the highest values of
to observe the enhancement of heat transfer h and Q when considering the effect of up
indicators (h and Q). semi-circular and down semi-circular hump.

11
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

A comparison amongst circular, up semi- Sci, vol. 174, May 2020, doi:
circular and down semi-circular humps is 10.1016/j.ijmecsci.2020.105470.
[6] A. Al-damook and I. D. J. Azzawi, “MHD Natural
conducted to show their influences on free Convection of Water in An L-Shaped Container
convection inside the square cavity. Filled with An Aluminium Metal Foam,” J Heat
Transfer, Feb. 2022, doi: 10.1115/1.4055942.
3. Figure 8 demonstrates that the heat transfer [7] A. Kasaeian et al., “Nanofluid flow and heat
indicators exhibit improvement with an transfer in porous media: A review of the latest
increase in the number of lower wall humps developments,” International Journal of Heat and
(N). The highest average enhancement of Mass Transfer, vol. 107. Elsevier Ltd, pp. 778–
791, Apr. 01, 2017. doi:
heat transfer indices for h and Q, compared
10.1016/j.ijheatmasstransfer.2016.11.074.
with the standard case (N=0), is 1.13 times at [8] C. C. Cho, “Effects of porous medium and wavy
N=4 across various Ra. surface on heat transfer and entropy generation of
Cu-water nanofluid natural convection in square
Subsequently, this experiment proved that cavity containing partially-heated surface,”
the wavy bottom wall enclosure with a circular International Communications in Heat and Mass
hump provides an enhancement in heat transfer Transfer, vol. 119, Dec. 2020, doi:
and thermal energy more than the straight 10.1016/j.icheatmasstransfer.2020.104925.
[9] Y. Ma, R. Mohebbi, M. M. Rashidi, O. Manca, and
bottom wall enclosure, and it supported the Z. Yang, “Numerical investigation of MHD effects
hypotheses mentioned in a large number of on nanofluid heat transfer in a baffled U-shaped
previous literatures. enclosure using lattice Boltzmann method,” J
Therm Anal Calorim, vol. 135, no. 6, pp. 3197–
References 3213, Mar. 2019, doi: 10.1007/s10973-018-7518-
y.
[1] I. D. J. Azzawi and A. Al-damook, “Multi- [10] C. C. Liao and W. K. Li, “Assessment of the
objective optimum design of porous triangular magnetic field influence on heat transfer transition
chamber using RSM,” International of natural convection within a square cavity,” Case
Communications in Heat and Mass Transfer, vol. Studies in Thermal Engineering, vol. 28, Dec.
130, Jan. 2022, doi: 2021, doi: 10.1016/j.csite.2021.101638.
10.1016/j.icheatmasstransfer.2021.105774. [11] B. Chandra Shekar, C. Haritha, and N. Kishan,
[2] R. Mohebbi, M. Izadi, H. Sajjadi, A. A. Delouei, “Magnetohydrodynamic convection in a porous
and M. A. Sheremet, “Examining of nanofluid square cavity filled by a nanofluid with viscous
natural convection heat transfer in a Γ-shaped dissipation effects,” Proceedings of the Institution
enclosure including a rectangular hot obstacle of Mechanical Engineers, Part E: Journal of
using the lattice Boltzmann method,” Physica A: Process Mechanical Engineering, vol. 233, no. 3,
Statistical Mechanics and its Applications, vol. pp. 474–488, Jun. 2019, doi:
526, Jul. 2019, doi: 10.1016/j.physa.2019.04.067. 10.1177/0954408918765314.
[3] M. Shekaramiz, S. Fathi, H. A. Ataabadi, H. [12] S. Sivasankaran and C. J. Ho, “Effect of
Kazemi-Varnamkhasti, and D. Toghraie, “MHD temperature dependent properties on MHD
nanofluid free convection inside the wavy convection of water near its density maximum in a
triangular cavity considering periodic temperature square cavity,” International Journal of Thermal
boundary condition and velocity slip Sciences, vol. 47, no. 9, pp. 1184–1194, Sep. 2008,
mechanisms,” International Journal of Thermal doi: 10.1016/j.ijthermalsci.2007.10.001.
Sciences, vol. 170, Dec. 2021, doi: [13] B. Ghasemi, S. M. Aminossadati, and A. Raisi,
10.1016/j.ijthermalsci.2021.107179. “Magnetic field effect on natural convection in a
[4] B. AL-Muhjaa and K. Al-Farhany, “Numerical nanofluid-filled square enclosure,” International
Investigation of the Effect of Baffle Inclination Journal of Thermal Sciences, vol. 50, no. 9, pp.
Angle on Nanofluid Natural Convection Heat 1748–1756, Sep. 2011, doi:
Transfer in A Square Enclosure,” Al-Qadisiyah 10.1016/j.ijthermalsci.2011.04.010.
Journal for Engineering Sciences, vol. 12, no. 2, [14] P. X. Yu, J. X. Qiu, Q. Qin, and Z. F. Tian,
pp. 61–71, Jun. 2019, doi: “Numerical investigation of natural convection in
10.30772/qjes.v12i2.589. a rectangular cavity under different directions of
[5] S. Aghakhani, A. H. Pordanjani, M. Afrand, M. uniform magnetic field,” Int J Heat Mass Transf,
Sharifpur, and J. P. Meyer, “Natural convective vol. 67, pp. 1131–1144, 2013, doi:
heat transfer and entropy generation of 10.1016/j.ijheatmasstransfer.2013.08.087.
alumina/water nanofluid in a tilted enclosure with [15] M. Sathiyamoorthy and A. Chamkha, “Effect of
an elliptic constant temperature: Applying magnetic field on natural convection flow in a
magnetic field and radiation effects,” Int J Mech liquid gallium filled square cavity for linearly

12
 Ahmed A. Fadhil, Itimad D.J. Azzawi I.M. Mahbubul and M. Hasannuzaman/ Diyala Journal of Engineering Sciences Vol (16) No 3, 2023: 1-13

heated side wall(s),” International Journal of

Thermal Sciences, vol. 49, no. 9, pp. 1856–1865,
Sep. 2010, doi:
10.1016/j.ijthermalsci.2010.04.014.
[16] F. M. Azizul, A. I. Alsabery, and I. Hashim,
“Heatlines visualisation of mixed convection flow
in a wavy heated cavity filled with nanofluids and
having an inner solid block,” Int J Mech Sci, vol.
175, Jun. 2020, doi:
10.1016/j.ijmecsci.2020.105529.
[17] W. H. Khalil, I. D. J. Azzawi, and A. Al-damook,
“The optimisation of MHD free convection inside
porous trapezoidal cavity with the wavy bottom
wall using response surface method,”
International Communications in Heat and Mass
Transfer, vol. 134, May 2022, doi:
10.1016/j.icheatmasstransfer.2022.106035.
[18] W. Al-Kouz, K. B. Saleem, and A. Chamkha,
“Numerical investigation of rarefied gaseous flows
in an oblique wavy sided walls square cavity,”
International Communications in Heat and Mass
Transfer, vol. 116, Jul. 2020, doi:
10.1016/j.icheatmasstransfer.2020.104719.
[19] D. K. Mandal, N. Biswas, N. K. Manna, R. S. R.
Gorla, and A. J. Chamkha, “Magneto-
hydrothermal performance of hybrid nanofluid
flow through a non-Darcian porous complex wavy
enclosure,” European Physical Journal: Special
Topics, vol. 231, no. 13–14, pp. 2695–2712, Sep.
2022, doi: 10.1140/epjs/s11734-022-00595-6.
[20] P. S. Rao and P. Barman, “Natural convection in a
wavy porous cavity subjected to a partial heat
source,” International Communications in Heat
and Mass Transfer, vol. 120, Jan. 2021, doi:
10.1016/j.icheatmasstransfer.2020.105007.
[21] P. Barman and P. S. Rao, “Effect of aspect ratio on
natural convection in a wavy porous cavity
submitted to a partial heat source,” International
Communications in Heat and Mass Transfer, vol.
126, Jul. 2021, doi:
10.1016/j.icheatmasstransfer.2021.105453.
[22] Y. Varol and H. F. Oztop, “Free convection in a
shallow wavy enclosure,” International
Communications in Heat and Mass Transfer, vol.
33, no. 6, pp. 764–771, Jul. 2006, doi:
10.1016/j.icheatmasstransfer.2006.02.004.
[23] S. Moolya and S. Anbalgan, “Optimization of the
effect of Prandtl number, inclination angle,
magnetic field, and Richardson number on double-
diffusive mixed convection flow in a rectangular
domain,” International Communications in Heat
and Mass Transfer, vol. 126, Jul. 2021, doi:
10.1016/j.icheatmasstransfer.2021.105358.
[24] B. Calcagni, F. Marsili, and M. Paroncini, “Natural
convective heat transfer in square enclosures
heated from below,” in Applied Thermal
Engineering, Nov. 2005, pp. 2522–2531. doi:
10.1016/j.applthermaleng.2004.11.032.

13