improving heat transfer by employing fin array of various

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



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



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.



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





Fig. 11. velocity vector in plane located between two successive fins

Fig. 10. stream lines behavior around fins domain



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. 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.




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

improving heat transfer by employing fin array of various

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