Ijmet 10 01 051
Ijmet 10 01 051
Ijmet 10 01 051
Volume 10, Issue 01, January 2019, pp. 493–506, Article ID: IJMET_10_01_051
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=01
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
ABSTRACT
In this paper, the natural convection heat transfer in a cubic enclosure provided with
inclined baffles attached to the two adiabatic sides, heated from the bottom is studied
experimentally and numerically to assess the effect of the baffles on the heat transfer
process inside the enclosure. Two different configurations have been considered. The first
configuration corresponds to the heated from the bottom with uniform heat flux using two
baffles attached to the left and right walls, while the second configuration corresponding
that the enclosure’s floor has parallel bands that are heated to a constant, high
temperature and the bands are separated by gaps that are kept at a lower temperature
that is also constant and single baffle attached to the left wall. In both cases, the top wall
is kept at a lower temperature than the bottom wall and the inclined baffles are well
covered with an insulating material. The inclination angles of the baffles range as (0o ≤
and ≥ 150o). The governing parameter, Rayleigh number, is fixed within 2.6x1011. In
numerical solution, a commercial software package has been used for a 2-D computation,
and the effect of turbulence is modelled by using (k-ε) model. Depending on its
orientation, the partial baffle has been found to change significantly the flow field which
in turn causes a reduction to the heat exchange inside the enclosure due to the damping
caused to the flow field. For all cases, the insulated baffle with any inclination angle
caused a reduction to the heat exchange inside the enclosure due to the damping caused
to the flow field. Also, a good agreement has been obtained between experimental
measurements and numerical results.
Keywords: natural convection, turbulence, enclosure, inclined partial baffles.
Cite this Article: Nabil Jamil Yasin and Dhia Al-Deen H. Alwan, Experimental and
Numerical Investigation for the Natural Convection Heat Transfer in an Enclosure Having
Baffles, International Journal of Mechanical Engineering and Technology, 10(01), 2019,
pp.493–506
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&Type=01
1. INTRODUCTION
Natural convection heat transfer in differentially heated baffled cavities are used in a various
industrial application such as heating and ventilation of a living space, fire in building solar
thermal collector system. The baffles are added to improve and control the heat transfer and fluid
flow characteristics. Studies of various aspects of this problem have been carried out by many
researchers both theoretically and experimentally. Some studies focused on the natural
convection inside enclosure motivated by heating and cooling the horizontal walls, while the
vertical walls are insulated. While others discussed natural convection in an enclosure heated and
cooled through the vertical walls while the horizontal walls are kept adiabatic, the matter which
has received a great consideration in studies, that is due to much industrial application use these
concepts. Nansteel and Greif [1] studied the convection heat transfer process and fluid flow
occurring in the 2D rectangular enclosure fitted with partial vertical divisions. The horizontal
walls of the enclosure were adiabatic, while the vertical walls were maintained at different
temperatures. The effect of the baffles on the heat transfer across the enclosure was determined
and a correlation for the Nusselt number as a function of Rayleigh and baffle lengths were
generated for both conducting and non-conducting baffle materials. Bajorek and Llyod [2]
investigated the natural convection heat transfer within a baffled enclosure of aspect ratio (1).
The vertical walls were maintained isothermally at different temperatures, while the horizontal
walls and the baffles were insulated. They found that the baffles significantly influenced the heat
transfer rate. Nansteel and Greif [3] investigated the effect of the baffle or orientation on the heat
transfer and fluid flow in a rectangular enclosure fitted with a vertical adiabatic baffle. The baffle
was oriented parallel to the vertical isothermal walls, one of which was heated and the other
cooled while all other surfaces of the enclosure were insulated. The effect of the transverse
location was examined and reported. Frederick [4] studied natural convection in an air-filled,
differentially heated, inclined square cavity, with a diathermic baffle on its cold wall numerically.
The baffle cause convection suppression and heat transfer reduction up to 47% relative to the
undivided cavity at the same Rayleigh number, baffle length, and inclination. Neymark et. al. [5]
studied the effect of internal baffles on the flow and heat transfer characteristics of air and water
filled partially divided enclosures at high flux Rayleigh number. Experiments were conducted
using a representative cubic geometry differentially heated from the side with an internal partial
vertical baffle. The study showed that the Nusselt number became a strong function of aperture
width, and the temperature difference across the aperture approached the overall enclosure
temperature difference. Ambarita. et al. [6]were studied a differentially heated square cavity,
formed from two horizontal adiabatic walls and two vertical isothermal walls, with two perfectly
insulated baffles attached to its horizontal walls numerically. It was observed that the two baffles
trap some fluid in the cavity and affected the flow fields. Also, it was found that Nusselt Number
is an increasing function of Rayleigh number, a decreasing one of baffle length, and strongly
depends on baffle position. Ghassemi et. al. [7] investigated the effect of two insulated horizontal
baffles placed at the walls of a differentially heated square cavity numerically. The vertical walls
are maintained at different temperatures while the horizontal walls are adiabatic. The result shows
that the two baffles trap some fluid in the cavity and affect the flow. Asif, et al [8] were carried
out a numerical study to investigate the mixed convective two-dimensional flows in a vertical
enclosure with heated baffles on side walls. All walls are assumed to be adiabatic, but baffles are
considered as isothermally heated. Heated baffles are placed both at the left and right wall of the
enclosure. It was observed that maximum heating efficiency is found at a higher value of
Reynolds and Richardson number. Abid [9] studied the natural convection of an air-filled
partitioned rectangular enclosure numerically. Top and bottom of the enclosure were adiabatic;
the two vertical walls are isothermal. Two perfectly insulated baffles were attached to its
horizontal walls at a symmetric position. The results of the values of average Nusselt number and
maximum absolute stream function have been confirmed by comparing it with similar previous
works using the same boundary conditions and a good agreement was obtained. Mushatet[10]
investigated the laminar natural convection inside a rectangular cavity containing two cylindrical
obstacles numerically. The cavity was differentially heated. The governing partial differential
equations are solved using stream function and vorticity method. The effect of the distance
between the obstacles has been tested. The results show that the fluid flow and temperature fields
significantly depend on the distance between the obstacles for the studied Rayleigh numbers.
Mushatet [11] investigated the turbulent natural convection heat transfer and fluid flow inside a
square enclosure having two conducting solid baffles numerically. Fully elliptic Navier-Stokes
and energy equations are discretized using finite volume method along with staggered grid
techniques. The results show that the rate of heat transfer is increased with the increase of
Rayleigh number especially for the region near the baffles. Varol, et. al. [12] studied
experimentally and numerically the natural convection heat transfer in an adiabatic inclined one-
fin attached one side of the square enclosure. The bottom wall of the enclosure has a higher
temperature than that of the top wall while vertical walls are adiabatic. It was observed that the
inclination angle affects the flow strength and temperature distribution. Enayati, et.al [13] carried
out a 3-D large eddy simulations (LES) of natural convection in a laterally heated cylindrical
reactor. The objective was to understand the effect of the opening area of the baffle on the flow
pattern and temperature distribution inside the reactor. The baffles considered in this study are
annular hollow discs with different opening areas. Velocity and temperature distributions across
the different planes and lines are analyzed in order to obtain information on the flow and heat
transfer processes resulting from various baffle openings. Pushpa, et.al [14] examines the
influence of a circular thin baffle on the convection in a vertical annular enclosure. The inner and
outer cylindrical walls and the baffle are retained with different temperatures and concentrations,
while the upper and lower boundaries are kept at adiabatic and impermeable. It has been observed
that the baffle size and location has a very important role in controlling the convective flow and
the corresponding heat and mass transport characteristics.
In this work, experiments and computation are conducted to investigate the effects of
adiabatic partition and its inclination on the natural convection heat transfer in a cubic enclosure.
Two configurations were considered. In the first configuration, two baffles were fixed to the
adiabatic side’s walls of the enclosure and the bottom wall was heated with constant heat flux,
while in the second configuration, single baffle was attached to the left wall of the enclosure
while the bottom wall was heated with separated, parallel high-temperature bands to mimic rows
of heated equipment. For both cases the top wall was maintain a constant lower temperature and
the baffles can vary its orientation with respect to the horizontal side of the enclosure. The present
work aim to show how the angle of the inclination can affect the flow and thermal field
characteristics of the inclined baffled enclosure in the turbulent natural convection under the
above boundary conditions.
2. SIMULATION SETUP
The CFD software Fluent-ANSYS15, with 8,200 finite-volume-method cells were used for the
simulation of the steady-flow RANS scheme with the standard k-ε turbulence model and standard
wall functions; and governing equations are those associated with turbulent natural convection.
The boundary condition is: Non-slip condition on all surfaces (U=0, V=0), the enclosure filled
with a fluid of Prandtl number (Pr = 0.725). The fluids properties correspond to those of air are
assumed to be constant; but Boussinesq approximation applies for the temperature-induced
change in density giving rise to buoyancy. The schematic of the Physical situation of two
configurations under study are shown in figures (1) and (2) which is a middle section of a cubic
enclosure with a perfectly insulated vertical walls to be kept in adiabatic conditions. The baffle
with length (B) and thickness of (t) located in the middle of the vertical walls and inclined with
inclination angles ranged (0o ≤ Angle ≤ 150o) as shown in the figures. The top wall of the
enclosure is kept at constant temperature. For case (1), the bottom hot wall keeps at uniform heat
flux. Two baffles with different inclination angles denoted by (θ), and (β) are used for the analysis
of this case. The bottom wall of the enclosure was keeps at uniform heat flux as shown in Fig.(1).
A high Rayleigh number (Ra=2.6x1011) was considered during investigation. For case (2), the
bottom hot wall exposed to step function heating with alternating temperatures of 358K and 381K
respectively, in 12 steps as shown in Fig.(2). The top wall is isothermal at 275K. Rayleigh number
value is 109 indicating that the buoyancy-induced flow inside the enclosure is turbulent. All other
boundary conditions are shown in the mentioned figures.
Figure (1): Schematic drawing for the enclosure corresponding to case (1)
Figure (2): Schematic drawing for the enclosure corresponding to case (2)
3. EXPERIMENTAL SETUP
Figure (3) shows the experimental apparatus which used for this work. The main part of the test
rig is a cubic enclosure (30x30x30cm) which constructed from three sides by the use of low
conductivity block wood, and from the front side by the use of double pan glass window to allow
visualize. The top side is constructed from pure aluminium sheet (0.1mm) fabricated as fully
closed container with gate to use as crashing ice-vessel, and covered from all outsides by (25mm
thickness) styrol-board to insure constant temperature of the top wall at about 2oC ±0.5oC. A
drain pipe is connected to the bottom of the crashing ice-vessel to drain molten ice water
continually and prevents the forming of high temperature film of water beneath the crashing ice.
After steady state condition reached in the enclosure, the amount of molten ice water is collected
in a scaled beaker for 10 minutes, to calculate the amount of heat received from the enclosure by
the ice to melt in this period of time. The thermodynamic heat balance equation
non-heat conductive partial partition was fabricated from thin metal coated from the two sides
with rubber with overall thickness (t=0.005m).
dT
.H
dy y =0 q ′′H
Nu x = − = (2)
Th − Tc k (Thx − Tc )
And the average Nusselt number can be calculated according to:
H
Nu = ∫ Nu x dx (3)
0
Rayleigh number can be calculated according to:
gβ H 4 q ′′
Ra = ( 4)
kυα
The experimental test repeated three times for each case of partition inclination angle. Each
experimental test required at least 90 minutes to reach study state condition. The steady state
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Experimental and Numerical Investigation for the Natural Convection Heat Transfer in an Enclosure
Having Baffles
condition materializes when the 9 thermocouples interplant in the heating Aluminum plate
measured the same temperature measured in the 4 thermocouples interplant in the ring guard
heater and the 4 thermocouples interplant in the base guard heater. The thermal physical
properties of the air are measured according to the bulk mean temperature of the average
temperature of the heating wall and the cooling wall temperature. According to the uncertainty
analysis given by Holman [17], Nusselt number uncertainty analysis shows that the maximum
error is (±0.552). Repeatability check details of the temperature distribution measured for three
times repeated tests for each run tests, show that the percentage difference in the readings is not
exceed 5% for all readings.
Case (1)
Figure (4) shows the collection of (β=0) and (θ) changes from 0o to 150o. The left column shows
the local Nusselt number with (x=0→0.3m) experimentally and numerically which shows that
local Nusselt number increase with (x) to some value and then decrease depends on the baffle
inclination angles, and upon the direction of the cell circulating. Generally, Nusselt number
decrease as (θ) increase up to 90o and then it will increase slightly up to (θ =150o). The flow field
contour at the middle column and the temperature distribution column right column explain this
situation. When (θ =0), the whole of the enclosure act to transfer the heat from the bottom wall
to the top wall but, when (θ) increase a part of the enclosure act as heat trap, and this trap increase
as (θ = 90o), and two circulating cells start to form, one of a hot air near the hot wall and other
cold near the cold wall with little mixing between them at the centre of the enclosure. As (θ)
increase farther up, main circulating cell will form with another small one which results
increasing the local Nusselt number. Figure (5) shows the collection of (β=60) and (θ) changes
from 0o to 150o in the same manner as before. The maximum local Nusselt number shift more to
the left due to the effect of right baffle, and a two cells forms earlier as (θ =0o). When (θ =30o)
the lower cell shown to be contracted and divided into two cells in the vertical direction, and then
the two cells divided into six cells with small sub-cells as (θ =60o) in a symmetry shape. When
(θ =90o) the upper half forms one main cell but the lower half of the enclosure forms three main
cells with many sub-cells in the two half’s. The cells start to form inverse S-shape for (θ =120o)
with some sub-cells and the number of cells reduces as (θ =150o). The multi cells forms reduce
the heat exchange between the hot & cold walls, and that is explain the reason of reduce the level
of local Nusselt number in this case. The maximum local Nusselt number noticed when (θ =0o)
and then when (θ =150o).Figure (6) shows the collection of (θ =150o) and (β) changes from 0o to
150o. The large cells in this collection is the reason of relative high local Nusselt number, but the
difficulty of the fluid flow in the cases of (β=60o, 90o, 120o) cases the reduction of it. Figure (7)
shows the local Nusselt number with x-position on the left of each sub-figure and average Nusselt
number with inclination angles on the right of each sub-figure from (1) to (4) as a compact of
each collection which are discussed. The right figures show clearly that the average Nusselt
number decrease as the inclination angles of the baffles increase for all collections and then
increase. For all cases, the long insulated baffle of any inclination angle causes a reduction to the
heat exchange inside the enclosure due to the damping cause to the flow field.
Case (2)
Figure (8) show the contours of velocity magnitude (m/s) for the enclosure with and without
partial partition with different inclination angle. For the purpose of illustration, the bottom of the
box will be divided into (12) strips so that the number (1) represents the first left strip as shown
in the top of the figure. Part (A) represent the enclosure without partition. Inspection of the figure
shows that the space above strip number (1) has a small revise circulation portion in the corner
of the enclosure causes a reduction in the heat exchange, whereas the space above strip number
(12) shows stagnation causes lower heat exchange in compare with all other strips. Moreover, it
seems that maximum velocity occurs in the strips number 5 and 6 that is explain the high
exchange of heat at that strips. Due to the circulation of flow anticlockwise the upstream of the
flow in the first strips (1-6) causes a higher heat exchange compare with the strips (7-12). Part
(B) represents the enclosure with a partition inclined by 45o. The partition causes an obstruction
between the hot wall and the cold wall of the enclosure to the strips (1-5) which causes reduce
the heat exchange in these strips. Maximum velocity can be noticed over the strips (6). Strips (7-
10) also show high level of heat transfer due to the effect of the anticlockwise circulation of the
air flow. The left corner under the partition shows a revers flow cause reduce in the heat exchange.
Part (C) represents the enclosure with a partition inclined by 90o.This case the shows that there
is no direct contact in the circulation of air in the lower part with the cold surface of the enclosure,
which results in reduce the heat exchange compare with the previous cases that is because the
enclosure is divided in to two flow field, the upper part circulate anticlockwise whereas the lower
part circulate clockwise. The higher flow velocity noticed in strips (7-9). That is explained the
reason for the high level of heat exchange shifted to the right side of the enclosure compare with
previous cases. Part (D) represents the enclosure with a partition inclined by 135o. In this case
the main flow field circulates clockwise and the maximum flow velocity noticed above strips
number (5-7) and a film of Simi stagnation air formed in the upper portion of the enclosure cases
a kind of insulation between the main flow field and the cooling surface, causes a reduction in
heat exchange inside the enclosure.
Figure (9) shows numerically the contours of Static Temperature (K) for the enclosure with
and without partial partition with different inclination angles. Part (A) represent the enclosure
without partition, which shows that cold flow field (represented by green color) is come very
close to the bottom surface of the enclosure causes effective cooling to the hot wall. Part (B)
represent the enclosure with partition inclined by 45o shows an ineffective cooling field of yellow
color in the left side of the enclosure, whereas in part (C) of the 90o inclination angle and part (D)
of the 135o inclination angle show that the ineffective field of yellow color includes whole the
bottom side of the enclosure which reduce the heat exchange.
Figure (10) shows numerically the heat flux on the heating wall under different inclination
angles of the partial partition. At (0o) a high level of heat exchange between the heating surface
and the air flow in the enclosure was observed. The highest amount of heat flux with a maximum
heat flux about 1200 W/m2occurs in the left strips which represents the leading edge of the flow
with respect to the hot wall and reduce gradually at the trial edge. At 45o a reduction in the heat
flux to maximum of 900 W/m2 reduces to about 700 as a second maximum value was noticed. At
(90o) a maximum heat flux of 800 W/m2 was near the right side. Figure (11) shows a comparison
between the experimental results depends on the experimental tests and the numerical result. The
experimental local Nusselt number calculated according to equation (2) which shows that the
change of local Nusselt number with x-position experimentally and numerically have good
match.
Figure (4) Local Nusselt (upper row), contours of the velocity magnitude (m/s) on the (middle row), and
contours of the temperature (K) (lower row), (θ=0, β=0), (θ=90, β=0), and (θ=150, β=0)
Figure (5) Local Nusselt (upper row), contours of the velocity magnitude (m/s) on the (middle row), and
contours of the temperature (K) (lower row), (θ=0, β =0), (θ=90, β=0), and (θ=150, β=0)
Figure (7) Variation of local Nusselt Number with the x-distance for different baffles orientation θ and
β.
Figure (8) Contours of velocity magnitude (m/s) for the enclosure without partial partition and with
partial partition with different inclination angle.
Figure (9) Contours of static temperature (K) for the enclosure without partial partition and with partial
partition with different inclination angle.
Figure (10) Heat Flux on the heating wall under different inclination angles of the partial partition based
on Numerical results.
Figure (11) Comparison between the experimental and numerical results for the (Nu) values
( Num, Exp.).
5. CONCLUSION
In this investigation, the effect of attached an insulated baffles, oriented with couples of
inclination angles, in a facing sides of an cubic enclosure cold from the top by constant
temperature heated from the bottom with uniform heat flux or to a step function of high
temperatures. And, whereas other sides kept insulated, which has done experimentally and
numerically.The following is the important high marks in this investigation:
1. The experimental solution gets a good agreement with the numerical solution to the
problem.
2. The long insulated baffle of any inclination angle causes a reduction to the heat
exchange inside the enclosure due to the damping cause to the flow field.
3. Increasing the inclination angle of the partition allow increasing the cells inside the
enclosure.
4. The average Nusselt number decrease as the inclination angles of the baffles increase
for all collections and then increase.
5. The inclined partial partition can be assumed as damping mean to the flow field
velocity in a control manner help to keep the temperature of different power out
equipment’s in the same temperature.
It is recommended that further study to find an empirical equation to determine the average
and local Nusselt number as a function of Rayleigh number, (θ), and (β) angles.
NOMENCLATURES
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