Optimization of Fin Spacing by Analyzing the Heat Transfer through Rectangular Fin Array Configurations (Natural Convection)

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 985
Optimization of Fin spacing by analyzing the heat transfer through
rectangular fin array configurations (Natural convection)
Aditya Yardi1, Ashish Karguppikar2, Gourav Tanksale3, Kuldeepak Sharma4
1,2,3,4 Dept. of Mechanical Engineering, KLS’s Gogte Institute of Technology, Belagavi, Karnataka, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - The objective of the project is to optimize the
fin spacing by experimentally investigating the steady state
heat transfer by natural convection through the four
samples of the vertical rectangular fin configurations with
pre-determined dimensions of the base plate and different
number of fins. The fins were attached to the base plate to
enhance the heat transfer through it and the samples of fins
were installed inside an air duct of fixed dimensions. The
experiments were conducted one by one on every fin sample.
For a fixed temperature difference between the base plate
and the air duct temperature, the heat transfer values were
noted down. The results were then compared by creating
similar models using the ANSYS 12.0 Workbench and
simulation was carried out in ANSYS CFX software. It was
observed that the experimental and analytical results were
comparable. As the fin spacing decreases, the heat transfer
through the base plate increases and it was observed that
the optimization takes place for the fin spacing range of
20.5mm –16mm. Then the heat transfer starts decreasing
giving rise to a bell shaped curve of heat transfer versus fin
spacing.
Key Words: Natural convection, heat transfer, fin
temperature, fin efficiency, fin effectiveness, fin
spacing, heat transfer co-efficient, steady state
condition
List of symbols
A = total convective surface area (m2)
Z = fin height (m)
k = thermal conductivity [W/(m K)]
L = fin length (m)
s = fin spacing (m)
t = fin thickness (m)
T3 = ambient temperature (K)
Tfilm = film temperature (K)
T1 = base plate temperature (K)
∆T = difference between base temperature and ambient
temperature (K)
g = gravitational acceleration (m/s2)
GrL= Grashoff’s number
Nu = Nusselt number
Pr = Prandtl number
ν = kinematic viscosity (m2/s)
Ao = cross-section area of fin (m)
h = average convection heat transfer coefficient
[W/(m2 K)]
h1 = analytical convection heat transfer coefficient
[W/(m2 K)]
h2 = experimental convection heat transfer coefficient
[W/(m2 K)]
Q = power input to the heater (W)
1. INTRODUCTION
Fins are extended surfaces which help to increase the
heat transfer from the surface and thus help to reduce the
temperature of the surface. The three important modes of
heat transfer are: Conduction, convection, and radiation.
Hence the heat transfer from an object can be increased by:
Increasing the temperature gradient between the object
and the environment, increasing the convective heat
transfer coefficient, or increasing the surface area of the
object. Increasing the surface area is the most economical
solution.
The assumptions need to be made while calculating the
heat transfer through fins: Steady state heat transfer is
considered. The properties of the material are constant
(independent of temperature). There is no internal heat
generation. The heat conduction happens in one dimension
only. The material has uniform cross-sectional area.
Convection occurs uniformly across the surface area.
Some of the examples of fins are thin rods on the
condenser of refrigerator, coolers of SMPS, coolers of the
engines, etc.
1.1 Literature Survey
The horizontal orientation of rectangular fins is
observed to have relatively poor heat transfer ability and
hence the vertical orientation ensures better heat transfer
and heat dissipation. The heat transfer from the finned
surfaces to the ambient atmosphere occurs by convection
and radiation. But due to relatively low values of emissivity
of the fin materials such as aluminium, duralumin and steel
alloys, the radiation effect on the heat transfer can be
neglected. Hence the principles of convection are applied to
obtain the heat transfer through fins.
The mode of energy transfer between a solid surface
and the adjacent liquid or gas that is in motion is called

convection. Faster fluid motion results in greater heat
transfer by convection. [1]
There are two types of convection processes: Natural
convection and Forced convection. If the fluid motion is
caused by buoyancy forces that are induced by density
differences due to the variation of temperature in the fluid,
the convection is called natural (or free) convection. If the
fluid is forced to flow over the surface by external means
such as a pump, fan, etc. the convection is called forced
convection.
1.2 Fin Efficiency
Fin efficiency can be defined as the ratio of actual heat
transfer rate from the fin to the ideal heat transfer rate
from the fin if the entire fin were at base temperature. [3]
ɳ fin= Q fin/Q fin max
To find the heat transfer rate for different cases:
CASE 1: The fin is very long, and the temperature at the
end of fin is essentially that of the surrounding fluid
Q = √(hPkAo) x (To - T∞)
CASE 2: The fin is of finite length and loses heat by
convection from its end.
Q =
√(hPkAo) x (To - T∞) x ((sin(mL)+(h/mk).cosh
(mL))/(cosh(mL)+(h/mk).sin(mL)))
CASE 3: The end of fin is insulated so that 𝑑𝑇/𝑑𝑥=0 at x=L
Q = √(hPkAo) x (To - T∞).tanh(mL)
In practical applications, fins have varying cross-sectional
areas depending upon their applications.
To find fin efficiency for the above 3 cases:
CASE 1: ɳ f = 1/mL
CASE 2: ɳ f = tanh (mL)
CASE 3: ɳ f = tanh (mL)/mL
1.3 Fin Effectiveness
The fin effectiveness can be defined as – The ratio of heat
transfer with fin to the heat transfer without fin. [3]
μ = Q with fin/Q without fin
2. DESIGN OF THE FIN SAMPLES
The models of the four samples were created in the Solid
Edge V19 software. The dimensions of the fins and the base
plate were determined suitably to accommodate the
assembly into the opening provided in the air duct. Fig.1, 2,
3 and 4 indicate the designs of the four samples of the fin
configuration. The base plate dimensions 110mm x 107mm
remain fixed. Along the length of 107mm, a space of 7.5
mm is provided on both the sides to drill the holes of 4mm
and for all the samples, the equi-spaced fins are machined
within a width of 92mm with the fin-spacing changing for
every sample.
Fig -1: Four-fin sample
Fig -2: Five-fin sample
Fig -3: Six-fin sample

Fig -4: Eight-fin sample
3. CONSTRUCTION OF THE SAMPLES
The four fin samples were produced by milling process.
The material chosen was Mild Steel EN8 as it was easily
available and cost effective. The workpiece dimensions are
115mm x 112mm x 20mm. The fins were machined on a
milling machine using the cutters of suitable dimensions.
Figures 9, 10, 11 and 12 indicate the 4, 5, 6 and 8 fin
samples having a spacing of 28mm, 20.5mm, 16mm and
10.85mm respectively.
Fig -5: Four-fin sample with 28mm fin spacing
Fig -6: Five-fin sample with 20.5mm fin spacing
Fig -7: . Six-fin sample with 16mm fin spacing
Fig -8: Eight-fin sample with 10.85mm fin spacing

4. EXPERIMENTATION
The experimentation was first done on the 4 fin
configuration in which the machined sample was screw
fitted into the duct of the experimental setup and the input
was given as the temperature difference between
surrounding air temperature and the base temperature of
the sample. The heat input for maintaining respective
temperature difference was assumed as the heat output.
The same set of experiments was carried out for 5, 6 and 8
fin samples.
4.1 Apparatus
The apparatus consists of a duct of dimension 150mm x
130mm x 1000mm into which the fin samples were screw
fitted with the help of a back plate. The back plate was
provided with a circuit board which connects the
thermocouples. The back plate was also provided with
holes to screw fit the sample on it. The heater plate was
sandwiched between the fin sample and insulator pad
attached to the back plate. The circuit was provided with
three thermocouples out of which, first is on the base of
fins, second is fixed in the middle of the fin and the third
one is suspended in the duct to measure the air
temperature around the fins. The equipment was provided
with voltmeter, ammeter and a digital temperature
indicator. The heater was controlled by a dimmer stat. The
specifications of the apparatus are:
1. Duct size: 0.13m x 0.15m
2. Dimmer stat: 0-270 Volts; 2 Amperes
3. Temperature Indicator: 0-200˚C
4. Fin Material: Steel EN8
5. Size of the Fin: 0.11m x 0.107m x 0.002m
Fig -9: Experimental Setup
Fig -10: Magnified view of the five-fin sample installed
inside the air duct
Fig -11: Assembly of fins, heater, insulating pad and back
plate
Fig -12: Rear view of the assembly (indicating the circuit
for the thermocouples)

4.2 Experimental Procedure
Before starting with the experimentation, all the
electrical connections and the location of the
thermocouples were checked. After the initial checks, the
calibration of thermocouples was done at atmospheric
temperature. The power supply was switched on and the
voltage was set by a dimmer stat to get the temperature
difference of 15°C between base temperature and the
surrounding fin temperature. The readings of voltmeter,
ammeter and digital temperature were noted at the steady
state condition. The steady state observations were
confirmed by noting the set of observations after 15
minutes duration until two successive sets of observations
were exactly identical.
The same procedure was repeated for temperature
differences of 25°C, 50°C and 60°C for each of the fin
samples and the corresponding observations were noted.
The observations are tabulated as follows.
Temperatures (°C)
Voltag
e (V)
Curren
t (A)
Heat
Transfe
r (W)
∆T =
(Tbase -
Tambient
) (°C)Tbas
e
Tfin Tambien
t
49.
2
48.
5
33.1 39 0.224 8.736 16.1
49.
5
48.
5
33.1 36 0.214 7.704 16.4
48.
4
47.
7
33.8 34 0.196 6.660 14.6
48.
6
48.
0
34.2 34 0.196 6.660 14.4
Table -1: For ∆T ≈ 15°C for 4 fins with 28mm spacing
Temperatures (°C)
Voltag
e (V)
Curren
t (A)
Heat
Transfe
r (W)
∆T =
(Tbase -
Tambient
) (°C)Tbas
e
Tfin Tambien
t
42.
6
43.
8
30.9 35 0.207 7.245 12.9
44.
8
45.
8
31.1 39 0.228 8.892 14.7
44.
8
45.
9
30.5 39 0.229 8.931 15.4
Table -2: For ∆T ≈ 15°C for 5 fins with 20.5mm spacing
Temperatures (°C)
Voltag
e (V)
Curren
t (A)
Heat
Transfe
r (W)
∆T =
(Tbase -
Tambient
) (°C)Tbas
e
Tfin Tambien
t
45.
0
44.
1
30.4 37 0.215 7.955 14.6
46.
5
45.
6
31.6 38 0.222 8.436 14.9
47.
2
46.
0
32.0 39 0.227 8.853 15.2
Table -3: For ∆T ≈ 15°C for 6 fins with 16mm spacing
Temperatures (°C)
Voltag
e (V)
Curren
t (A)
Heat
Transfe
r (W)
∆T =
(Tbase -
Tambient
) (°C)
Tbas
e
Tfin Tambien
t
49.
6
49.
0
34.2 34 0.234 7.956 15.4
48.
7
48.
3
34.1 34 0.230 7.820 14.6
49.
4
48.
9
34.2 35 0.238 8.330 15.2
49.
8
49.
3
34.4 35 0.238 8.330 15.4
Table -4: For ∆T ≈ 15°C for 8 fins with 10.85mm spacing
The value of heat transfer co-efficient was calculated
using the experimental data for all the temperature
differences and fin samples using the co-relations from the
Heat and mass transfer data hand book.
4.3 Formulae and Calculations
Calculations for heat transfer coefficient (h) based on the
base temperature (Analytical):
For 4 fins and ΔT=25°C,
Tfilm= (T1+T3)/2 = (55.4+31)/2 = 43.2°C
Properties of air at 43.2°C
𝜈 = 17.28 x 10-6 m2/s
Pr = .6987
k = .02778 W/mK
Grashoff’s number, GrL= (gβ(T1−T3)Z3)/ν2
β= 1/ Tfilm where Tfilm is in Kelvin (K)
GrL =
(9.81 x (1/ (273+43.2))x(55.4−31)x(.11)3)/ (17.28x10−6)2
GrL = 3.37 x 106
GrL x Pr = 2.357x106

From heat transfer data book, page 136
Nu = .59(GrL x Pr).25
Nu = .59(2.357x106).25
Nu = 23.11
To find heat transfer coefficient (h1)
Nu = (h1x Z)/k
h1 = (Nu x k)/Z
h1 = (23.11 x .02778)/ .11 = 5.83 W/m2K
To calculate heat transfer coefficient (h2) experimentally
Q = h2 x A x ΔT
h2 = Q/(A x ΔT) = 11.83/(.0241 x 25) = 19.63W/m2K
Where A = total convective area
Q = supplied wattage
Average heat transfer coefficient (h)
h = (h1+h2)/2 = (5.83 + 19.63)/2 = 12.73W/m2K
The formulae for calculations are referred from heat and
mass transfer data hand book. [4]
Similarly the heat transfer coefficient for all fin samples is
calculated.
5. ANALYSIS
In this project, the analysis of heat transfer through the
rectangular fin array configurations consisting of 4, 5, 6
and 8 fins with the spacing of 28, 20.5, 16 and 10.85
respectively was done so as to find out the optimized
spacing for the given fixed base plate area.
The analysis consists of comparing the results of
experiments done for each of the above fin configuration
with the results of software for the respective
configurations and then finding the error involved. Initially
the analysis was carried out in the ANSYS APDL software to
model and obtain the results, but the results were not
satisfactory as the software was not identifying the fluid
surrounding the fins. To tackle this problem, the analysis
was carried in ANSYS FLUENT but later on it was identified
that it is used for the forced convection problems and not
for steady state problems. Later by doing some more
literature survey, it was established that the ANSYS CFX
software is the most suitable software for the analysis of
fins in the steady state condition and the results were
found satisfactory.
Similar to the working environment and the fin samples,
the models were created in the ANSYS 12.0 Workbench. An
enclosure of volume equal to the volume of the air duct was
created around the fin sample. Meshing is done by the CFX
Mesh method. Then the boundary conditions were given as
follows:
1. The fin and base plate assembly was assigned as solid
domain and the enclosure was assigned as fluid domain.
The back surface of the base plate was assigned the
temperature value as obtained from the experiment.
2. The remaining surfaces of the fin and base plate
assembly were assigned a convective heat transfer co-
efficient and air duct temperature as obtained from the
experiment.
3. The bottom face of the enclosure was assigned as ‘Inlet’
with atmospheric pressure and the value of surrounding
fin temperature obtained from the experiment.
4. The top face of the enclosure was assigned as air
‘Outlet’ with atmospheric pressure.
5. The remaining walls of the enclosure were assigned as
‘Adiabatic’ to prevent the heat transfer through the
enclosure.
Then the number of iterations and the RMS value was
specified. The ANSYS 12.0 CFX results were obtained as
follows:
Fig -13: Heat transfer of 4 fin sample for ΔT=25˚C
Fig -14: Fin temperature of 4 fin sample for ΔT=25˚C

Fig -15: Heat transfer through back face of base plate for
8 fin sample for ΔT=25˚C
Fig -16: Side view indicating the temperature distribution
across fin width for 8 fin sample for ΔT=25˚C
6. RESULTS AND DISCUSSIONS
The experimental and analytical values of the heat transfer
through the four fin samples along with the percentage
errors were tabulated as follows.
From the tables given below, it can be observed that the
experimental and analytical values of heat transfer are
approximately equal. Also the experimental and analytical
values of the fin temperature are approximately equal. The
maximum error obtained is 12.43% which can be
considered to be within the permissible range.
No
. of
fin
s
Heat Transfer
(W)
%
Erro
r
Fin Temperature
(˚C)
%
Err
or
Qexperime
ntal
Qsimulati
on
T2experime
ntal
T2simulat
ion
4 6.66 6.12 8.18 48.0 48.3 0.76
5 8.93 7.82 12.4
3
45.9 46.0 0.21
6 8.85 7.94 10.2
7
46.0 47.0 2.13
8 8.33 7.65 8.16 49.3 49.6 0.60
Table -5: Results for ΔT=15˚C
No
. of
fin
s
Heat Transfer
(W)
%
Err
or
Fin Temperature
(˚C)
%
Err
or
Qexperime
ntal
Qsimulati
on
T2experime
ntal
T2simulat
ion
4 11.83 11.77 0.50 54.0 55.1 1.99
5 17.06 15.89 6.88 52.5 54.4 3.49
6 15.64 14.71 5.99 56.2 57.8 2.77
8 15.13 14.12 6.70 57.8 58.6 1.36
No
. of
fin
s
Heat Transfer
(W)
%
Err
or
Fin Temperature
(˚C)
%
Err
or
Qexperime
ntal
Qsimulati
on
T2experime
ntal
T2simulat
ion
4 33.53 32.36 3.49 80.3 81.5 1.47
5 35.49 34.13 3.84 83.4 84.0 0.71
6 41.42 39.43 4.80 84.0 87.3 3.78
8 46.48 42.37 8.84 83.4 84.4 1.18
No
. of
fin
s
Heat Transfer
(W)
%
Err
or
Fin Temperature
(˚C)
%
Err
or
Qexperime
ntal
Qsimulati
on
T2experime
ntal
T2simulat
ion
4 45.59 43.55 4.47 94.1 95.9 1.88
5 66.63 64.73 2.86 88.8 93 4.51
6 51.50 49.43 4.02 93.4 94 0.64
8 49.38 47.08 4.66 91.9 93.7 1.92

7. CONCLUSION
The graph of the heat transfer versus fin spacing is plotted
for the specified values of temperature difference ΔT= 15˚C,
25˚C, 50˚C and 60˚C. From this graph it can be observed
that for the curves of ΔT= 15˚C, 25˚C and 60˚C, the heat
transfer is maximum for the fin spacing of 20.5mm i.e. for
the five-fin sample, indicating that it is the optimum fin
spacing for these temperature differences. However for the
curve of ΔT= 50˚C, it can be seen that the maximum heat
transfer occurs at a fin spacing of 10.85mm i.e. for the
eight-fin sample. To ensure the correctness of the readings,
the experiments were re-conducted for ΔT= 50˚C.
Hence it can be concluded that from a broader perspective
the spacing of 20.5mm can be considered as the optimum
fin spacing to obtain maximum heat transfer from the given
area of the base plate i.e. 110mm x 107 mm for the
specified material and conditions.
It can also be concluded that the existing thermocouples
have to be replaced by better quality ones and they have to
be calibrated for different temperatures before conducting
the experiment.
Fig -17: Comparison of Heat Transfer by experiment and
simulation
8. REFERENCES
[1] J. P. Holman, Heat transfer: Tata McGraw Hill, 9th
Edition, 2008.
[2] H. Yuncu, B. Yazicioglu, Optimum fin spacing of
rectangular fins on a vertical base in free convection heat
transfer: Springer, Journal of Heat and Mass Transfer,
2006.
[3] Yunus A Cengel, Heat Transfer, a practical
approach: Tata McGraw Hill, 3rd Edition, 2007.
[4] S. Subramanyan, C .P. Kothandaraman, Heat and
mass transfer data hand book, 8th Edition.: New Age
International Publishers, 2014.
[5] K. N. Vijaykumar, Dhanawade Kavita, Dhanawade
Hanamanth S, Natural convection heat transfer flow
visualization of perforated fin arrays by CFD simulation:
International Journal of Research in Engineering and
Technology, 2013.
ACKNOWLEDGEMENT
We express our deep gratitude towards Dr. A. S.
Deshpande, Principal, Gogte Institute of Technology,
Belagavi, for his support and motivation. We express our
sincere thanks to Prof. R. J. Naik, Head of Department,
Mechanical Engineering, Gogte Institute of Technology, for
his encouragement and co-operation. We express our
sincere thanks to our guide Dr. V. S. Majali, Gogte Institute
of Technology, for his guidance and constant motivation.
We are thankful to Prof. Rajshekhar Unni, Jain College of
Engineering, Belagavi, for his support. We express our
heartfelt thanks to Prof. Vivek. V. Kulkarni, Prof. M. D.
Deshpande, Prof. S. I. Bekinal and Prof. Sachin. C. Kulkarni
for their constant support. We are grateful to Mr. A. P.
Deshpande, Mr. Santosh Pandit and Mr. Basavaraj
Chougula for their support and co-operation. We would
like to express our gratitude to Matruchhaya Engineering,
Udyambag, Belagavi for supporting us with the
manufacturing aspects of the project. We thank all the
teaching and non-teaching staff for their co-operation.
We would like to express our gratitude towards our
parents and friends for their kind co-operation and for
encouraging us continuously.
Qexperimental
Qsimulation

BIOGRAPHIES
Name: Aditya Yardi
Achievements: Secured 1st
place in National Level
Technical Fest ‘Paanchajanya’
2012 Quiz Competition. Secured
1st place in National Level
Technical Fest ‘Avalanche’ 2015
Paper Presentation. Bagged 2nd
place in Technical Fest ‘Invento’
2015 Paper presentation.
Name: Ashish Karguppikar
Achievements: Co-ordinated
and participated in a one week
workshop on ‘Micro-controller
and Embedded Programming’
conducted by Advanced
Electronic Systems in KLS’s
Gogte Institute of technology.
Represented South zone in
‘Vidyabharathi’ National Level
Handball Tournament held at
Gwalior in 2009-2010. Attended
a basic industrial training at
AKP Foundries (Training
Period: 10 days).
Name: Gourav Tanksale
Achievements: Attended
training for software’s like Catia
V5 and AutoCAD 10.
Participated in technical fests in
college in competitions like
Quiz, Simplex to Complex, etc.
Name: Kuldeepak Sharma
Achievements:
Participated in ‘Technophilia
Workshop on Haptic robotic
arm’ in KLS’s Gogte Institute of
Technology. Bagged 2nd place in
Robo-wars competition in
Technical fest in KLS’s Gogte
Institute of Technology. Actively
participated in cultural activities
and social welfare activities.

Optimization of Fin Spacing by Analyzing the Heat Transfer through Rectangular Fin Array Configurations (Natural Convection)

More Related Content

What's hot (19)

Similar to Optimization of Fin Spacing by Analyzing the Heat Transfer through Rectangular Fin Array Configurations (Natural Convection) (20)

More from IRJET Journal (20)

Recently uploaded (20)

Optimization of Fin Spacing by Analyzing the Heat Transfer through Rectangular Fin Array Configurations (Natural Convection)