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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:01 98
182601-4747-IJMME-IJENS © February 2018 IJENS I J E N S
Improving Heat Transfer by Employing Fin Array of
Various Innovative Shapes in Natural Convection
M.J. ALshukri, N.A. Madlool, Nasr A. Jabbar Department of Mechanical Engineering, Faculty of Engineering,
University of Kufa, 21 Kufa, Najaf, Iraq
Abstract-- This study is a numerical study. It investigates the
steady state flow of fluid by natural convection in three
dimensions as well as the transfer of heat for a set of innovative
shapes of fin array. This study utilized four different shapes of
fin array as well as the absence of fins. The different forms are as
follows: straight, vertical (sine wave along y-axis), horizontal
(sine wave along z-axis) and sweep (sine wave along both y and z
axis). We examined the following parameters of the fin:
geometrical dimension and thermal properties. In the steady
state thermal analysis, an analysis of the differences in
temperature regarding the distance at which heat flow takes
place through the fin is carried out using CFX Ansys 15. The
result shows that the sine wave along z-axis increases the transfer
of heat more than the fin array of other shapes. Nusselt number
increased as a result of the increasing heat flux which is exerted
on the base as a boundary condition.
Index Term-- Heat transfer; fin array; natural convection;
CFX. 1. INTRODUCTION
Surfaces with fins are widely applied in engineering. They are
applied in the cooling of equipment and other related
applications. Fins are used to improve heat transfer because
they provide an extended surface area and improve mixing.
Dogan et al. [1] suggest using the most appropriate fin
geometry (which leads to the highest heat transfer rate) when
using fin array to improve the transfer of heat by natural
convection, provided it suits the available space and financial
consideration. A surface with fins increases the area available
for transferring heat in comparison with the base plate.
Nonetheless, the addition of fins reduces the flow rate.
Therefore, when poorly designed, there is possibility that fins
may not lead to an enhancement of the total heat transfer.
Accordingly, a knowledge of fin array geometry is important
to achieve a design that can greatly improve heat transfer.
According to Dogan et al. [1] the heat transferred by the heat
dissipating apparatus to the external ambient temperature is
gotten by employing the mechanisms of forced and natural
convections heat transfer. For the purpose of this study, we
shall focus on heat transfer associated with natural convection.
The use of rectangular fins has become popular because they
are inexpensive and easy to produce, while fins of other
shapes are not as popular. Increasing the rate at which heat is
transferred from systems by the process of natural convection
is usually achieved by the use of rectangular fins. In a bid to
increase the effectiveness of heat exchangers, a lot of attention
has been focused on applying diverse shapes of fins to achieve
greater transfer of heat. In recent times, the drastic
improvement in technological processes has reduced the
difficulties associated with the manufacturing of fins of other
shapes. Based on the above discussions, it is pertinent to carry
out a research on different fin shapes so as to achieve a design
showing great improvement in the transfer of heat.
A comprehensive literature review was carried out in this
paper. We started the review by examining the work by
Hagote and Dahake [2] on the transfer of heat by natural
convection from V fin array attached to heated plates inclined
at different angles. The observation was that the highest
average convective heat transfer coefficient was gotten at 60˚
V-fin array. Also, we found that an increase in the inclined
angle of the V-fins leads to an increase in the convective heat
transfer coefficient. In a study conducted by Sane et al. [3], it
was observed that the experimental results were identical to
the results gotten from CFD software with respect to
rectangular notched fin arrays in horizontal position radiating
heat by the process of natural convection; the sequence of
flow and the tendency of the coefficient of heat transfer did
not exceed 5% range. The study also shows that not only was
there was an increase in overall heat flux, there was also an
increase in the coefficient of heat transfer in response to an
increase in the depth of the notch. The excavated area that
forms the notch is filled with air that enters from the ends of
the fin, and this ensures that fresh cool air are brought in
contact with the surfaces of the hot fins. Also, the fluid flow
was visualized by simple smoke technique with the aid of
dhoop stick. Their observation was as follows: cold air was
drawn in through the fin’s bottom and exited through its
middle part, thereby constituting a single chimney. In a study
by Vinod and Taji [4], simple smoke technique involving
dhoop stick was used to perform visualization research on
rectangular fin arrays by changing the fin spacing. With
respect to 2, 4 and 6mm spacing, scattered flow pattern was
observed. However, single chimney pattern was recorded for
12mm fin spacing; this leads to a greater coefficient of heat
transfer. In a bid to modify the improvement of heat transfer
by normal and inverted notched fin arrays, an investigation
was performed by Surawanshi and Sane [5] to determine the
heat radiation by a fin array having an inverted notch at the
middle part of the fin’s bottom. Chaddock [6] carried out a
study involving heat transfer by natural convection and
radiation using 12 large fin arrays extending from a vertical
base. The study utilized only one value of the ratio of the
width of the base plate to the length of the fin, and the
thickness of the fin remained unchanged. The study used
different spacing and height of the fins as well as
demonstrated the value of radiation in computing total heat
transfer; it makes up about 20% of total heat transfer. A report
which defines the optimum fin spacing was presented at the
end of the study. Also, a study on heat transfer by natural
convection from fin arrays of rectangular shape attached to a
vertical surface was performed by Yazicioglu and Yüncü [7].
The study was to determine how heat transfer is influenced by
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fin height and spacing as well as difference in temperature
between the base of the fin and the surroundings. In the course
of the study, a relation was developed for optimum fin
spacing. Also, the influence of the height of the fin, its length
and its spacing on the interference of boundary layers, flow
pattern, and heat transfer was discussed. Aihara [8] studied the
transfer of heat by the processes of naturally occurring
convection and radiation involving 11 large fin arrays
extending from a vertical base. He examined the transfer of
heat from the base plate. The influence on the mean
coefficient of heat transfer by fin geometry and temperature
was investigated, and this led to an empirical correlation.
According to the data obtained from their experiment, they
suggested an average Nusselt number correlation. Over 300
sets of data obtained from experiments on various arrays of
highly polished vertical rectangular duralumin fins were
analyzed by Leung and Probert [9]. They reached the
conclusion that the influences of various geometric parameters
of fins determine the fin array orientation that will result in the
fastest rate of heat transfer. Further, they stated that two types
of fin arrays have non dimensional correlations of heat
transfer. With respect to heat transfer coefficient, one of the
pioneer experimental studies was carried out by Starner and
McManus [10]; the study involved four fin arrays with
different dimensions and orientations. Their study
demonstrated that if fins are wrongly applied to a surface,
there is the possibility of a reduction in total heat transfer
compared to only the base. Studies on the transfer of heat by
the process of natural convection from vertically and
horizontally attached fins of rectangular shape were carried
out by Yüncü and Anbar [11] as well as Güvenç and Yüncü
[12]. The different roles played by the fin spacing, height and
base with respect to the surrounding temperature difference
was studied. The influences of fin height, spacing, length and
the disparity in temperature between the fins and the ambient
area on heat transfer by free convection from thin fin arrays in
the horizontal position was studied by Baskaya et al. [13]. A
more recent study which investigated transfer of heat by the
process of natural convection and the features of the flow of
fluid from a layer of horizontal fluid which had fins attached
to its bottom surface was performed by Arquis and Rady [14].
They found the amount of convection cells between two
adjacent fins to be related to the height of the fin and Raleigh
number [15].
In line with the above analysis, the transfer of heat is
increased by the extra area made available by the added
surfaces. Also, it becomes obvious that heat transfer by natural
convection from fin arrays attached to the surface of the base
is highly dependent on geometric factors, which includes fin
length, height and spacing. A great number of studies has been
conducted on the transfer of heat from fins attached to a
horizontal surface. However, most of them have focused on
rectangular fin arrays. Because the flow sequence and
temperature gradient changes when geometrical factors of
rectangular fin arrays are changed, it becomes clear that
geometric factor of this type of fin array influence heat
transfer by natural convection. The above statement points to
the possibility of achieving higher heat transfer rates
compared to the transfer rate of rectangular fin arrays by the
use of other diverse fin shapes that possess better flow features
and distributions of temperature for the fluid in the channel of
the fin. Fins of various shapes other than rectangular fins are
not used often because they are hard to produce. In recent
times, however, advances in technology has reduced the
difficulty and cost of producing fins of other shapes. It is
pertinent to perform a numerical study on heat transfer by
natural convection from thin fins of diverse shapes; this is
because determination of the optimum shape can only be
achieved by studying temperature distributions and flow
sequence.
The present paper reports, by employing ANSYS 15.0
workbench, the fluid flow and heat transfer features of
different forms of fins (straight; sine wave y-axis; sine wave z-
axis; and sine wave in both axes, y and z) as shown in Fig. 1.
The transfer of heat by natural convection from fin arrays of
various shapes attached to a base plate in the horizontal
position was studied. For the sake of comparison, the total fin
area and the area of its base were considered identical. The
heights of the different fin shapes were taken as (65, 59.64, 55
and 52.75 mm) for longitudinal, sine-wave along z-axis, sine-
wave along y-axis and bi-axes sine-wave fin type respectively.
In order to obtain the optimal shape of a fin that results in high
amounts of coefficient of heat transfer, numerical results of
flow sequence and distributions of temperature within the
fluid in the two fin enclosure was used.
sine wave in both y and z axes fin
type
sine wave in y-axis fin type sine wave in z-axis fin type straight fin type
Fig. 1. Different shapes of fin arrays (Case studies)
Y
X Z
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2. PHYSICAL MODEL AND ANALYSIS
According to a study performed by Dogan et al. [1], regarding
a rectangular fin array in the vertical position which rises from
a rectangular base in the horizontal position, the ambient fluid
goes into the channel from the two open ends and form a
vertical component of velocity when heat is applied to the air
(single chimney pattern of flow). Nonetheless, if long fins are
used, the streams of air exit the channel with open top long
before they get to the fin’s middle area. When they reach the
mentioned areas, some of the air are drawn downwards, get
heated, and then rises (multiple chimney pattern of flow).
Figs. 2 and 3 show the sequences of flow that were observed
for rectangular shaped fin arrays. The observed flow
sequences demonstrates that fin geometry affects heat transfer
by natural convection from horizontally based fin arrays.
3. CFD MODELING AND SIMULATION
ANSYS 15.0 workbench was used for CFD modeling,
simulation and post processing, since it can solve convective
energy transfer by fluid flow and has conjugate heat transfer
(CHT) capability for solving conduction in solids [16].
Geometry simulation was performed using ANSYS
DesignModeler. In order to investigate mass and heat flow
from the fin, it is necessary to build a domain around the fin.
This is due to the fact that the area of interest lies outside the
fin, and it is the link between the air and the surface of the fin.
Therefore, it is necessary to have interactions between the
surface of the fin and the fluid domain made up of air. At first
the domain of the fin as well as the base was built and the
required domain of fluid size 130x100x65mm was built using
the ‘Enclosure’ option around the fin. The Advancing Front
Volume Mesher is the standard volume Mesher in a CFX-
Mesh. It makes automatic generation of tetrahedral mesh
possible using mesh generation methods that are efficient.
Meshes were built using high contact sizing relevance (dense
meshing near the fin surface), inflation growth rate of 1.2 and
total number of tetrahedral elements between 900 thousands to
one million [16].
4. BOUNDARY CONDITIONS
Under the setup of CFX of the ANSYS Workbench, the
‘Steady State’ analysis type was selected. The proper
boundary conditions were applied to the domains. Aluminum
and air were allocated respectively to the built solid and fluid
domain. The link between the surface of the solid and the fluid
was built with the option ‘Domain Interface’, and ‘Fluid
Solid’ interface was chosen under the basic settings. To
activate buoyancy in Y direction, the chosen Turbulence
model is Laminar. By using the boundary condition of
‘opening’ to all sides of the enclosure faces with exception of
the bottom face (set to adiabatic), the fluid domain size can be
lowered to a large degree, and it could be considered as the
condition of the atmosphere. Under fluid domain a layer
adjacent to the bottom face of fin base was set to adiabatic.
Under the domain fin and base, bottom surface of a base of the
fin, set the boundary condition to ‘Heat Flux’. The heat flux
was applied equal to the 𝑄𝑁/𝐴𝑏with range of 10-100W. The
boundary condition was set to adiabatic for other vertical sides
of the base plate. The residual is the main measure of
convergence. The run will be terminated by the CFX-Solver if
the calculated residuals of the equation (RMS type of residual)
are less than the value of the residual target. The target was set
to 1x10-6. Convergence of solutions was observed between
250 and 350 iterations. Residuals of the energy equations are
unchanged in a few situations (about 4x10-6). Therefore, for
the purpose of optimizing the computational time, the
maximal number of iterations was chosen as 400. Solutions
converged after 6 to 9 hours. When the solver was stopped,
the results were analyzed, and this constitute the post
processing step. Temperature distribution, heat flux along the
surface of the fin in addition to parameters like Nusselt
Number and coefficient of heat transfer can also be predicted
by computational analysis [16].
5. GOVERNING EQUATIONS
According to Dogan et al. [1], the temperature as well as the
velocity fields in the area between two fins are controlled by
conservation of mass, momentum and energy equations of the
fluid. These equations in addition to the three dimensional
heat conduction equations of the array of fins are given below.
The characteristics of the fluid and materials of the fin array
were considered as constants, with the exception of density
which is considered as a function of temperature only, 𝑞 =𝑞(𝑇). The reference density q1 was determined from the inlet
temperature. The variation in the Pr number according to
temperature was discovered to be insignificant, and a constant
value of Pr = 0.7 was utilized. Thus the equations of 3-D,
x
y
Fig. 2.Single chimney type flow pattern.
x
x
y
Fig. 3. Multiple chimney type flow pattern.
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steady, laminar and incompressible flow considered in these
studies are as follow:
Conservation of mass: 𝜕𝑢
𝜕𝑥+
𝜕𝑣
𝜕𝑦+
𝜕𝑤
𝜕𝑧= 0 ….(1)
Momentum conservation equation:
X-direction:
𝑢𝜕𝑢
𝜕𝑥+ 𝑣
𝜕𝑢
𝜕𝑦+ 𝑤
𝜕𝑢
𝜕𝑧= −
1
𝜌
𝜕𝑝
𝜕𝑥+ µ (
𝜕2𝑢
𝜕𝑥2+
𝜕2𝑢
𝜕𝑦2+
𝜕2𝑢
𝜕𝑧2) ....(2)
Y-direction:
𝑢𝜕𝑣
𝜕𝑥+ 𝑣
𝜕𝑣
𝜕𝑦+ 𝑤
𝜕𝑣
𝜕𝑧= −
1
𝜌
𝜕𝑝
𝜕𝑦+ µ (
𝜕2𝑣
𝜕𝑥2+
𝜕2𝑣
𝜕𝑦2+
𝜕2𝑣
𝜕𝑧2) + 𝑔𝛽(𝑇 − 𝑇∞)
....(3)
Z-direction:
𝑢𝜕𝑤
𝜕𝑥+ 𝑣
𝜕𝑤
𝜕𝑦+ 𝑤
𝜕𝑤
𝜕𝑧= −
1
𝜌
𝜕𝑝
𝜕𝑧+ µ(
𝜕2𝑤
𝜕𝑥2+
𝜕2𝑤
𝜕𝑦2+
𝜕2𝑤
𝜕𝑧2) .…(4)
Energy conservation equation:
𝑢𝜕𝑇
𝜕𝑥+ 𝑣
𝜕𝑇
𝜕𝑦+ 𝑤
𝜕𝑇
𝜕𝑧= 𝛼(
𝜕2𝑇
𝜕𝑥2+
𝜕2𝑇
𝜕𝑦2+
𝜕2𝑇
𝜕𝑧2) ….(5)
For fin array, Energy conservation equation: 𝜕2𝑇
𝜕𝑥2+
𝜕2𝑇
𝜕𝑦2+
𝜕2𝑇
𝜕𝑧2+
𝑄
𝑘𝑠= 0 ….(6)
Where 𝑘𝑠 is the thermal conductivity fluid
Net heat transfer can be calculated as:
𝑄𝑁 = ℎ𝑎𝐴𝑐∆𝑇 ….(7)
Where ℎ𝑎 is the average heat transfer coefficient, 𝐴𝑐 is the
convective heat transfer area and ∆𝑇 difference of average
surface temperature and ambient temperature
Also, loss of heat by conduction from the sides of the base
plate is determined by taking note of the temperature of side
of the base plate. Average coefficient of heat transfer by
convection,
ℎ𝑎 =𝑄𝑁
𝐴𝑐(𝑇𝑠−𝑇𝑎) ….(8)
Nusselt number;
𝑁𝑢 =ℎ𝑎𝐻
𝑘 ….(9)
Where H is the Fin height.
6. RESULTS AND DISCUSSION
6.1 Flow visualization
Figs. 4 and 5 show the velocity vectors of the straight fin array
at 100 watt heat input. As a result of none presence of
concavity and convexity, it is easy for the air flow to enter
through the fin ends as observed in the fin interspacing. The
air passes the fin surface and leaves at the top, thus the sliding
chimney flow sequence that results [16].
Figs. 6 and 7 show the velocity vectors of the z-axis fin array
at 100 watt heat input. As a result of the presence of concavity
and convexity in z-axis, the circulation of air will be happened
in the concave areas and air velocity increased. The circulation
causes an increase in the air velocity towards y-axis and it is
easy for the air flow to enter through the fin ends as observed
in the fin interspacing. The air passes the fin surface and leaves at the top, thus the sliding chimney flow sequence that
results.
Figs. 8 and 9 show the velocity vectors of y-axis fin array at
100 watt heat input. As a result of the presence of concavity
and convexity in y-axis, it is easy for the air flow to enter
through the fin ends as observed in the fin interspacing. Air
velocity will be reduced because of the concavity and
convexity in y-axis. The air passes the fin surface and leaves
at the top.
Fig. 5. velocity vector in plane located between two successive fins Fig. 4. stream lines behavior around fins domain
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Fig. 7. velocity vector in plane located between two successive fins Fig. 6. stream lines behavior around fins domain
Fig. 9. velocity vector in plane located between two successive fins Fig. 8. stream lines behavior around fins domain
Fig. 11. velocity vector in plane located between two successive fins
Fig. 10. stream lines behavior around fins domain
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Figs. 10 and 11 show the velocity vectors of y and z axes fin
array at 100 watt heat input. As a result of presence of
concavity and convexity in both axes, it is easy for the air flow
to enter through the fin ends as observed in the fin
interspacing. Air velocity will be reduced less than air velocity
of longitudinal shape because of the concavity and convexity
in both sides. The air passes the fin surface and leaving at the
top.
6.2 Temperature distribution and heat transfer
enhancement
CFD simulation of fin arrays performance characteristics is
shown. From the vectors of temperature zones around the
straight fin array shown in Figs. 12 and 13, it is obvious that
heat is added to the air entering from the bottom as it proceeds
towards the center of the fin, and it rises up because it expands
and becomes less dense; the central area of the fin is rendered
ineffectual since the hot airstream moves over that part and
does not cause great transfer of heat through that area. From vectors of temperature zones of sine wave in y- axis fin
arrays shown in Figs. 12 and 13, it is obvious that heat is
added to the air entering from the bottom as it proceeds
towards the center of the fin, and it rises up because it expands
and becomes less dense; the middle part of the fin is rendered
ineffectual based on the concave shape along the y- axis of the
fin which leads to eddy current of air.
Fig. 14. Temperature contour on fins surfaces Fig. 15. Temperature contour in perpendicular section normal to fins extension
Fig. 12. Temperature contour on fins surfaces Fig. 13. Temperature contour in perpendicular section normal to fins extension
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Fig. 16. Temperature contour on fins surfaces
Fig. 17. Temperature contour in perpendicular section normal to fins extension
From the vectors of temperature zones of sine wave in z- axis
fin arrays shown in Figs. 16 and 17, it is obvious that the air
entering from the bottom becomes heated as it proceeds to the
center of the fin and moves up as a result of density; the fin’s
middle area is rendered ineffectual as a result of the concavity
shape along z- axis of fin which leads to eddy current of air.
Thus, the heat transfer will be more sufficient and it will be
more enhanced in this type of fin array in comparison with
straight fin array. Furthermore, biaxial sine wave fin along
both axes y and z can be identical to the conditions of sine
wave along z axis in terms of eddy current. Thus, it will be the
best indication for heat transfer improvement as shown as in
Figs 18 and 19.
Fig.20 displays the improvement of heat transfer in the
different shapes of fin array in terms of NU with heat flux. As
shown in the above figure, the biaxial sine wave along z axis
of fin array gave the more enhancement of heat transfer in
comparison to the other cases. As a result to increasing in air
velocity cause good enhancement in heat transfer between fin
and air flow. As seen in this figure, the sine wave along y-axis
fin array gave fewer enhancements in heat transfer than other
cases.
Fig. 18. Temperature contour on fins surfaces Fig. 19. Temperature contour in perpendicular section normal to fins extension
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7. CONCLUSION
The free convective flow as well as transfer of heat was
compared for four different shapes of fin arrays in this
numerical study. The important conclusions from the results
obtained in this study are stated below:
(1) By employing equal fin base area and volume of fin
array, free convective flow and transfer of heat are
determined for four different fin arrays.
(2) Enhancement of heat transfer is directly proportional
to heat flux in terms of Nusselt number.
(3) Best enhancement of heat transfer was observed in
the type of sine wave along z-axis, and this
enhancement comes because of the following:
a) Air movement from the bottom through the
center of the fins.
b) Back towards the top towards the z-axis.
c) The concavity and convexity (towards the z-
axis)
(4) Sine wave along y-axis fin array gave less
enhancement of heat transfer.
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Fig. 20. Nusselt Number versus heat flux for different shapes of fin arrays