Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
Experimental Investigation on C and V
Shaped Inline and Staggered Fins Array
Using Forced Convective Heat Transfer
Sujan T N1, Mr. Krishnamurthy K N2 & Mr. Akash Deep B N3
1
M Tech. Student, Department of Thermal Power Engineering, PG Studies-VTU-Mysuru,
Karnataka, India
2
Assistant Prof, Department of Thermal Power Engineering, Centre for Post-Graduate Studies
VTU, Mysuru, Karnataka, India
3
Assistant Prof, Department of Mechanical Engineering, KSSEM, Bengaluru, Karnataka,
India
Abstract-In orders to facilitate better heat transfer,
various types of fins are studied extensively and
various modifications are made in the design till
date. Geometry of fin arrays plays an important
role in heat transfer characteristics. This research
was conducted in order to study C and V shaped
fins with inline and staggered arrangement and
makes comparisons on the basis of heat transfer
and pressure drop characteristics. The result shows
C shaped staggered arrangement is better in terms
of heat transfer and pressure drop performance as
compared to V shaped fins. The heat transfer
coefficient for C shaped staggered fins are in the
range of 51 – 80 W/m2K while for V shaped
staggered arrangement, it is found to be in the
range of 41 – 71 W/m2K for a Reynolds number in
the range of 10000 – 35000. The pressure drop for
C shaped staggered fins was found to be lower than
corresponding to V shaped fins and is obtained in
the range of 10 – 45 N/m2 while for V shaped fins,
in the range of 23 – 93 N/m2. Overall analysis
shows C shaped fins are more attractive than V
shaped fins in terms of energy saving as well as
heat transfer characteristics.
Key words: V-shaped Pin fins, C-shaped pin fins,
Inline Arrangement, Staggered Arrangement, Heat
Transfer Enhancement, Pressure Drop.
1. Introduction
The thermal energy present in any matter
when comes in thermal contact with another matter
having different thermal energy causes the
phenomenon of heat transfer. The driving force in
order to occur heat transfer is the temperature
difference. No matter how much thermal energy is
present in two bodies, if there is no temperature
difference, heat transfer does not occur. Heat
transfer is energy in transit and it is also known as
Imperial Journal of Interdisciplinary Research (IJIR)
boundary phenomenon. All the heat transfer
processes that occur in nature obey the law of
conservation of energy which is also known as first
law of thermodynamics.
With the demand of the new technology, many
products in the industries are focused to make
compact in size, economical and energy efficient.
Various electronic devices are strictly focused to
make them very small so as to provide sufficient
flexibility in portable and aesthetic aspects. Equal
efforts are also concentrated on compact engines
and many other mechanical products. These all
systems dissipate heat and have to be removed
efficiently for smooth operation of the system. Heat
transfer enhancement (HTE) techniques were
studied with the help of the V shaped ribs. They
conducted experiment in order to determine heat
transfer factors, pressure drop parameters and
thermal performance factors with Reynolds number
in the range 1000 – 30000 and took rib height to
hydraulic diameter ratio to be 0.06 and angle of
attack of 600 for backward and forward flows. It is
also found that the thermal performance factor is
decreased with increasing in Reynolds number. The
fanning friction factor and pressure drop were
calculated using isothermal condition. They found
that the V ribs which point downstream have
largest heat transfer enhancement and also friction
factors. [1,2]. Experiment was repeated for ribs for
enhancing convective heat transfer by increasing
turbulence on heat transfer surfaces. They created
the roughness by repeated ribs techniques and heat
flux was taken uniform. The angle of attack was
chosen to be 450 or 600 relative to flow direction
[3]. Conducted experiment on natural convection
heat transfer over vertical V- shaped partition
plates with bottom spacing of 20 mm and without
bottom spacing. They found that the vertical V
shaped fins are far better for heat transfer
enhancement as compared to smooth vertical
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
surface, as they create turbulence in the flow [4].
Entropy generation analysis for laminar flow
through a circular duct with three different shaped
longitudinal fins was performed. After that they
concluded that increasing the Reynolds number the
entropy generation decreases and pumping power
of heat transfer increases [5]. For high thermal
efficiency in a gas turbine, they did two- pass
rotating rectangular channels with five different
orientations of 450 V-shaped rib turbulators. By
this rotation effects shows an increase in the
Nusselt number ratio in the first pass trailing
surface and second pass leading surface [6,7].
Experimental set – up was designed and fabricated
for inline and staggered arrangement. A uniform
heat generation and equal weight of fins are
maintained for the comparison. Different types of
fin configurations viz., solid, hollow, solid pin fin
with a single perforation solid pin fin with four
perforations and solid fin with knurling, having
equal weight are considered for the study [8,9].
Experimentshows that the use of the cylindrical
perforated pin fins leads to heat transfer
enhancement than the solid cylindrical fins.
Enhancement efficiencies mainly depend on the
clearance ratio and inter-fin spacing ratio. Small
clearance ratio and small inter-fin spacing ratio and
comparatively with smaller Reynolds numbers are
suggested for higher thermal performance [10].
From the above literature V-shaped ribs are used to
enhance heat transfer rate has done. But C-shaped
fins are not used; also long fins are not used. As a
result of this an experiment study of inline Cshaped fins, inline V-shaped fins and staggered Cshaped fins, staggered V-shaped fins are designed
to determine heat transfer characteristics. To
achieve the higher transfer rate, by considering the
friction factor and pressure drop. Also in order to
obtain the computational results of the experiment,
CFD analysis is carried out.
Symbols
Abbreviations
Kinematic viscosity
µ
Dynamic viscosity
K
Kelvin
ρ
Density
k
Thermal conductivity
h
Heat transfer co-efficient
Vmean
Free stream velocity of air
Re
Reynolds number
Nu
Nusselt number
To
Average temperature
Tin
inlet temperature
Imperial Journal of Interdisciplinary Research (IJIR)
Tout
outlet temperature
f
Fanning friction factor
Aw
Wetted area
dh
Hydraulic diameter
B
Breadth of duct
H
Height of duct
L
Length of duct
n
Number of fins
ƞ
Enhancement of efficiency
Atotal
Total Area
AS
Surface area of fins
Tbase
Base plate temperature
2.0 Experimental Set-up
The heat transfer equipment includes
fallowing major components in the system as
shown in fig 3.
1. Tunnel
2. Heater unit
3. Base plate
4. Control Panel
2.1 Tunnel
The wind tunnel consists of a heating unit
at the bottom, inlet section and outlet section, had
an internal cross-section of 150 mm width and 150
mm of breadth and length 600 mm. The fin model
is fixed to the base plate which is placed in the
wind tunnel, it is made up of mild steel sheet of
small thickness of 8 mm and sides are insulated by
paint and Fiberglass reinforced plastic, the inlet
section is made in such a way that the blower outlet
is connected to the that by the application of pipe.
The air coming out from the blower is directly
entered into the inlet section and passed around the
fins and exited through the outlet. The outlet is also
designed in such a way that there is no obstruction
to the flow of air, it is providing smooth flow of air
movement.
2.2 Heating unit
In this equipment 250 W mica heater is
used which is having a cross-section of 250 mm
length and 125 mm width. The power supply to the
heating unit was connected through the controlling
knob. Two layers of the insulating material such as
asbestos and glass wool each having 5mm
thickness was used at the bottom surface to avoid
temperature distribution at the bottom side and to
maintain unidirectional heat transfer. At the top
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
surface of the heating plate, copper plate of same
dimension was fixed to get efficient heat transfer to
the model.
2.3 Base Plate
It consists of rectangular plate at base
having the dimension 250 mm x 125 mm, thickness
is 6 mm. Pin fins & base plate are made of same
material of Aluminium 6061. Base plate is placed
on the heater setup firmly with the help of two steel
bars and bolts. Base plate and fins are fixed by
permanent gas welding process.
are installed in the setup. Two thermocouples are
installed to measure inlet and outlet temperature of
air at inlet section and outlet section respectively.
One thermocouple is fixed at the bottom plate to
measure base plate temperature and remaining 18
thermocouples are fixed at the fin surfaces. Digital
portable anemometer is used to measure the
velocity of air which is coming from blower.
Figure 2: Photographic View of base Plates
Figure 1: 3D model of C & V shaped fins inline
arrangement and staggered arrangement
Inline arrangement contains nine fins
each having height of 80 mm, longitudinal distance
between each fins are 60 mm and transverse
distance between each fins is 30 mm. Staggered
arrangement contains eight fins each having height
of 80 mm, longitudinal distance between each fins
are 60 mm and transverse distance between each
fins is 15 mm, thickness of fin is 3 mm for both
arrangement as shown in fig 1 &2. For taking the
temperature distribution in the fins two M5 hole
was made to fix the thermocouples at a distance of
20 mm from top and bottom for each fin.
Figure 3: Experimental setup
3. Mathematical Relationship
Governing Equation:
The convective heat transfer rate Q
convection from electrically heated test surface is
calculated by using equ. (2,4)
Qconv.= Qelect. - Qcond.-Qrad. (1)
Where: Q indicates the heat transfer rate
in which subscripts conv., elect., cond. and rad.
denotes convection, electrical, conduction and
radiation, respectively. The electrical heat input is
calculated from the electrical potential and current
supplied to the surface.
2.4 Control Panel
Qelect.= I
It consists of mainly heat input control and
various indicating devices which indicate the
reading taken by the various components like
Digital voltmeter, Digital ammeter, Rheostat
electric heater controller, Temperature selector.
The main switch is used to supply and to cut off the
power source and fuse is also adopted to avoid
breakdown of the system in case of power
fluctuation. For measuring the temperature
distribution in the model 21 K-type thermocouples
Imperial Journal of Interdisciplinary Research (IJIR)
V
(2)
Where: I is current flowing through the
heater and V is voltage.
The total area is equal to the sum of the
projected area and surface area contribution from
the pin fins. These two areas can be related to each
other by [4]
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
ATotal= (number of fins
Wetted area of plate
surface area of fins) +
Wetted area of plate (Aw) = [Cross sectional area of
Cross sectional area of
plate – (number of fins
fins)]
ATotal = (n As ) + Aw
(3)
The heat transfer from the test section by
convection can be expressed as
Q conv. = h
W
(4)
Hence, the average convective heat
transfer coefficient can be calculated viaequ. (5)
W/m2-K
h=
(5)
Reynolds number [1], [3]
(6)
Hydraulic diameter
m
(7)
= Volume of duct- (n Volume of fins)
= B H L- (n Volume of fins) (8)
= Wetted surface
= 2 (B + H) L + [n
(2 Area of fins)]
(Surface Area) –
(9)
The dimensionless groups are calculated as fallows
[1], [3]
(10)
The experimental pressure drops over the test
section in the finned duct will be measured under
the heated flow conditions.
Fanning friction factor [1]
f = 17.098
Re-0.449
(11)
Pa
(12)
Darcy-Weisbach equation
ΔP =
Enhancement of Efficiency
The effectiveness of the heat transfer for a
constant pumping powerwas useful to determine
the enhancement of a heat transfer. The
enhancement efficiency is the ratio of heat transfer
coefficient with Fins to without Fins.[4]
Imperial Journal of Interdisciplinary Research (IJIR)
Ƞ
= 51.09
(1+ )0.1028
( ) 0.0812
(13)
4. Results and Discussion
In the present analysis forced convection
experiment was carried out for Reynolds number
ranging from 10000 to 35000 i.e. under turbulent
conditions. Using centrifugal blower forced air was
supplied over C- shaped and V-shaped fins through
the duct with different velocity such as 2m/s,
3.5m/s, and 5m/s. Constant heat rate was
maintained of 69.84 W to the base plate and all
heat losses was measured to obtained actual heat
dissipated from fin array by convection. The
temperature of base plate gradually increase with
respect to time and reaches steady state such that
temperature of the base plate becomes constant,
and fin surface temperature was noted as average
temperature and further calculations has carried
out. These temperatures are used to determine all
the heat transfer performance parameters for all
conditions and smooth curves are drawn with
respect to variations in Reynolds number.
4.1. Nusselt number
The forced convection is carried by
supplying constant heat input of 69.84 W and
varying the velocities like 2 m/s, 3.5 m/s and 5 m/s
respectively for the V-shaped fins and C-shaped
fins for inline and staggered arrangement. Fig.4
shows the comparative relation between Reynolds
number and Nusselt number for V-shaped fins and
C-shaped fins using inline and staggered
arrangement. The Nusselt number for C-shaped
fins and V-shaped fins, for inline arrangement were
lies in the range of 159 to 291 and 128 to 260
respectively. For staggered arrangement Nusselt
number were lies in the range of 195 to 308 and
161 to 281 respectively.
The dimensionless Nusselt number was
dependent on the thermal properties of air flowing
over it and Reynolds number. When the Reynolds
number increases the dimensionless Nusselt
number increases, this is due to the developed
turbulent flow of air through the fins. From the
above fig. 4 the Nusselt number increases for fin
with C-shaped for staggered compared to inline Vshaped fins, inline C-shaped fins, staggered Vshaped fins with increase in Reynolds number.
Because V-shaped fins, early flow separation and
wide wake formation takes place at the edge of the
fin body. But in C-shaped fins, the flow separation
will delay as compare to V-shaped fins and narrow
wake formation takes place.
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
Fig 4: Comparison between the V-shaped fins and
C-shaped fins in inline & staggered arrangement.
4.2. Heat transfer co-efficient
From the experimental data a comparative
relations of heat transfer coefficient and Nusselt
number for different fin shapes corresponding to
different Reynolds number are shown in Fig 5 The
heat transfer co-efficient will increase with increase
in Reynolds number. The heat transfer can be
increased by increase in the area exposed to the
flowing fluid.
For the heat input 69.84 W and Reynolds number
in the range of 11000 to 32000, The heat transfer
co-efficient (h) for C-shaped fins and V-shaped
fins, for inline arrangement was lies in the range of
43 W/m2-K to 77 W/m2-K and 34 W/m2-K to 68
W/m2-K respectively. For staggered arrangement
was a lie in the range of 51 W/m2-K to 80 W/m2-K
and 41 W/m2-K to 71 W/m2-K respectively.
From the experimental data a comparative relations
of heat transfer coefficient and Nusselt number for
different fin shape and arrangement corresponding
to different Reynolds number are shown in Fig 5. It
can observe that heat transfer co-efficient (h) with
respect to Reynolds number for C-shape fins with
both inline and staggered arrangement was
comparatively higher than the V-shape fins with
both inline and staggered arrangement. The
probable reason behind that was the C-shaped fins
provides greater heat transfer surface between the
plate and the fluid and hence it has higher heat
transfer coefficient. It also worth mentioning that
as using staggered arrangement fins, weight of heat
sink decreases, which place an important role for
the applications in which weight was considered
has an important matter.
Imperial Journal of Interdisciplinary Research (IJIR)
Fig 5: Variation of heat transfer co-efficient (h) Vs
Reynolds number (Re)
4.3 Pressure drop calculations
4.3.1 Effects of fanning frictionfactor
Fig 6: Variation of friction factor (f) Vs Reynolds
number (Re) for inline arrangement
Fig 7: Variation of friction factor (f) Vs Reynolds
number (Re) for staggered arrangement
Figure 6 & 7 shows the relationship between
Reynolds number and friction factor. The graph
shows as the Reynolds number is increased, the
friction factor was decreased. The reason is, as the
fluid flow increases, the inertia force dominates the
shear force caused by the surface of the plate and
leads to decrement in friction factor. As it can be
seen in the graph, the friction factor is obtained
(0.1072 to 0.1642) & (0.1052 to 0.16076). If the
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
nature of the data is to be interpreted; the friction
factor for the V-shaped fins was higher than that of
the corresponding C-shaped fins. The smooth
section of the C-shaped fins provides less
resistance to the flow and hence it leads to lower
pressure drop.
4.3.3 Enhancement of Efficiency
4.3.2 Effects of pressure drop
Fig. 10 Effect of Reynolds number on enhancement of
efficiency
Fig 8: Variation of Pressure drop (ΔP) Vs Reynolds
number for inline arrangement
Fig.10 shows the comparative results of Vshaped fins and C-shape fins for inline & staggered
arrangement. The effectiveness of V-shaped fins
and C-shape fins in inline & staggered arrangement
was 1.37 to 1.93, 1.37 to 1.94, 1.35 to 1.89, and
1.39 to 1.98 for the range of Reynolds number
11000 to 32000 respectively. The results show that
the effectiveness of C-shaped fins with staggered
arrangement higher when compared to other fin
shapes and arrangement. Since C-shaped fins with
staggered arrangement has more heat transfer area
and lowerobstruction compare to other fins.
Because C-shaped staggered fins has more area
exposed to the heat transfer and it will dissipate
more amount of heat to the surrounding compare to
other fin patterns.
5. Conclusion
Fig 9: Variation of Pressure drop (ΔP) Vs Reynolds
number for inline arrangement
Figure 8 & 9 illuminates the relationship
between Reynolds number and pressure drop for
heat input 69.84 W. The graph shows as the
Reynolds number is increased, the pressure drop is
increased. For inline arrangement, C-shaped fins
pressure drop is 11.18 to 45.93 Pa but V-shaped
fins lies 23.50 to 97.64 Pa. For staggered
arrangement, C-shaped fins pressure drop lays in
10.66 to 44.15 Pa but V-shaped fins lie 22.47 to
92.78 Pa. Almost 50% of pressure drop is
decreases for C-shaped fins with respect to Vshaped fins. From the nature of graph it can be
observed that pressure drop for C-shaped fins
provides less resistance to the flow compare to Vshaped fins in both inline and staggered
arrangement.
Imperial Journal of Interdisciplinary Research (IJIR)
The experimental research was conducted in order
to investigate on the heat transfer performance of
C-shaped and V-shaped fins. The inline and the
staggered arrangement of the fins were studied.
The thermal performance and effectiveness are
compared with varying Reynolds number and for
constant heat input of 69.84 W for forced
convection. The pressure drop across the fins was
determined. Some of the conclusions was derived
from experimental research are discussed below.
 In the wider picture, heat transfer and pressure
drop performance for C-shaped fins was better
than V-shaped fins. The C-shaped fins with
staggered arrangement performed better than
corresponding V-shaped fins.
 The Nusselt number for C-shaped staggered
arranged fins for Q = 69.84 W was obtained to be
in the range, 195 to 308 and is higher than the
corresponding V-shaped fins which is in the
range 161 to 281 for Reynolds number 11000 to
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Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-9, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
32000. The higher Nusselt number for C-shaped
fins showed better heat transfer performance.
 The convective heat transfer coefficient (h) for
C-shaped staggered arranged fins showed
attractive results in the range of 51 to 80W/m2-K
than corresponding V- shaped fins with h in the
range of 41 to 71 W/m2-K for given range of
Reynolds number.
 The results showed less friction factor for Cshaped fins than V-shaped fins. The smooth
surface of C-shaped fins gave better results. The
friction factor for C-shaped fins was obtained in
the range 0.1073 – 0.1642 which was lesser than
corresponding V-shaped fins with values in the
range 0.13452 – 0.2075.
 The pressure drop for C-shaped fins was lesser
compared to V-shaped. This suggests, the blower
with lower capacity can be used if C shaped fins
are used as compared to V-shaped ones. So Cshaped fins are energy efficient than
corresponding V-shaped fins.
 It also importance to mention that as change in
arrangement from inline to stagger the weight of
heat sink decreases, which place an important
role for the applications in which weight, was
considered as an essential matter.
[2]
[3]
[4]
[5]
[6]
6. Acknowledgement
I wish to express my sincere and heart full
thanks to our guide Mr. Krishnamurthy K N,
Assistant Professor, Department of Thermal Power
Engineering, Centre for Post-Graduate studies
VTU, Mysuru for his valuable guidance, patience,
inspiration and continuous supervision during the
entire course of this project work and successful
completion of the same on time.
[7]
[8]
[9]
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