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Analysis of heat transfer through circular duct
using internal fins
Rahul P. Gangurde*1, Sarang V. Charmode*2, Dhanraj R. Upadhaye*3, Nikhil V. Minmule*4, Imran M.
Dabbewala*5
Mechanical Engineerinng,B.N.C.O.E.Pusad,Dist.Yavatmal Maharashtra.
[email protected]*1, [email protected]*2,
[email protected]*3, [email protected]*4,
[email protected]*5
ABSTRACT
The heat transfer rate to a fluid flowing in pipe can be
enhanced by the use of internal fins. This thesis
concerned with study of circular duct or tube of LFPC
with internal rectangular fins used to enhance their
heat transfer performance subjected to conduction and
natural convection heat transfer. All the main
parameters which can significantly influence the heat
transfer performance of finned tube have been
analyzed. Conduction and natural convection in a
horizontal tube without fins was taken as the reference
tube and compared it with rectangular fin profile. All
the computer simulation has been done on the ANSYS
WORKBECH 16.0 and CATIA V5R20. Heat transfer
equations such as conduction, convection and radiation
equations were used to solve for the fluid flow inside the
tube. we are considering application as LFPC of
‘Thermosyphon Solar Water Heater’. Aluminum is
used for the fin material and water is taken as the fluid
flowing inside the tube and the flow is taken as
turbulent. The heat transfer rate from the fins, outer
surface, inner surface has been calculated and
compared with without fin heat transfer rate. Also the
surface nusselt number and surface overall heat
transfer co-efficient has been found out. Then it was
found that the heat transfer through duct with fins is
more than that of without fin duct, as there is more
surface contact with water.
1. INTRODUCTION ABOUT FINS
The removal of excessive heat from system
components is essential to avoid the damaging effects of
burning or overheating. Therefore, the enhancement of heat
transfer is an important subject of thermal engineering. The
heat transfer from surfaces may in general be enhanced by
increasing the heat transfer coefficient between a surface
and its surroundings, by increasing the heat transfer area of
the surface, or by both. In most cases, the area of heat
transfer is increased by utilizing extended surfaces in the
form of fins attached to walls and surfaces. Extended
surfaces (fins) are frequently used in heat exchanging
devices for the purpose of increasing the heat transfer
between a primary surface and the surrounding fluid. Fins
as heat transfer enhancement devices have been quite
common.
A fin is a surface that extends from an object to
increase the rate of heat transfer to or from the environment
by increasing convection. The amount of conduction,
convection, or radiation of an object determines the amount
of heat it transfers. Increasing the temperature difference
between the object and the environment, increasing the
convection heat transfer coefficient, or increasing the
surface area of the object increases the heat transfer.
Sometimes it is not economical or it is not feasible to
change the first two options. Adding a fin to an object,
however, increases the surface area and can sometimes be
an economical solution to heat transfer problems.
1.1 Internal Fins Concept Selection
In recent years solar energy has been strongly
promoted as a viable energy source. One of the simplest
and most direct applications of this energy is the
conversion of solar radiation into heat. Hence way that
domestic sector can lessen its impact on the environment is
by installation of solar flat plate collectors for heating
water. Although it should be said that some of these
collectors have been in service for last 40-50 years without
any real significant changes in their design and operational
principles. So, research work done and presented in this
paper is concerned with improvement of the efficiency of
solar flat plate collector using internal fins in the circular
duct or pipe of the collector to increase the heat transfer.
This is examined by the design of circular duct using
ANSYS. One of the primary goals in the design of circular
duct is the achievement of more efficient and increase heat
transfer rate of LFPC.
2. THERMOSYPHON SOLAR WATER HEATER
Natural circulation solar water heater: a natural
convection system is shown in fig.(3.a), it consists of tilt
collector, with transparent cover glasses, a separate highly
insulated water storage tank and well insulated pipe
connecting the two. The bottom of the tank is at least
1ft.(0.3m) the top of the collector, and no auxiliary energy is
required to circulate water through it. Circulation occurs
through natural convection, thermosyphon.
Fig. 2 Thermosyphon Solar Water Heater
As the water is heated in its passage through the
collector, its density decreases and hence water rises and
flows into the top of the storage tank, colder water from the
bottom of the tank has a higher density and so tends to sink
and enter the lower heater of the collector for further
heating. The density difference between the hot and cold
water thus provides the driving force for the circulation of
water through the collector and storage tank. Hot water is
drawn off from the top of the tank as required and is
replaced by cold water from the service system.
As long as the sun shines the water will quietly
circulate, getting warmer. After sunset, a thermosyphon
system can reverse its flow direction and loss heat to the
environment during the night to avoid reverse flow, the top
heater of the absorber is kept as stated above 0.3m below the
cold leg fitting on the storage tank to provide heat during
long, cloudy periods, an electrical immersion heater can be
used as a backup for the solar system.
A nonfreezing fluid may be used in the collector
circuit. The thermosyphon system is one of least expensive
solar hot water system and should be used whenever
possible. thermosyphon solar water heaters are passive
systems and do not require a mechanical pump to circulate
the water. such heaters can be used extensively in rural
areas, where electricity is expensive and there is little danger
of freezing. This solar water heating system finds useful
application and acts as a renewable energy resource in
regions where there is abundant and consistent sunlight.
The performance of the thermosyphon system
depends upon the size and capacity of the storage tank, the
thermal capacity of the collector, and the connecting pipes
including fluid flow and on the pattern of hot water use. All
components were designed for and constructed in line with
the design values obtained. The system was tested on a
normal sunny day, rainy day, and cloudy day between the
hours of 7:00 a.m. and 6:00 p.m.; and results collected
were tabulated. Principle of operation of a flat-plate solar
water heater The solar radiation passes through the glass in
front of the absorber plate and strikes the flat black surface
of the Journal of Fundamentals of Renewable Energy and
Applications 3 absorber plate where the solar energy is
absorbed as heat (i.e., by increasing the internal energy).
This causes the flat-plate collector to become very hot, and
so the water contained in the risers and headers bounded to
the plate also absorb the heat by conduction. The water
inside the tubes (risers/headers) expands and so becomes
less dense than the cold water from the storage cylinder.
On the principle of thermosyphon, hot water is pushed
through the collector and rises by natural convection to the
hot water storage tank and cold water from the cold water
tank simultaneously descends to the bottom header of the
collector by gravity pull. Therefore, there is circulation as a
result of an increase in temperature and volume of the
warmer water to the hot water storage tank. The circulation
continues as hot water goes out, while cold water comes in.
Solar water heaters based on thermosyphon principle have
the following advantages: simplicity and low cost, requires
no electrical supply, need no controller or pump, easy to
install, can withstand mild sub-zero temperature, is reliable
and long-lasting since there are no moving parts, scalable
(several collectors can be connected in parallel to increase
hot water supply), is easy to build and operate, no fuel cost,
provides heated water of about 70 °C or within the range,
and is portable. They, however, have the following
disadvantages: cannot withstand mains pressure, cannot
give higher temperature water, are affected by weather
conditions, very useful only during the dry season, and can
be more practicable and useful in the sunny regions.
3. LIQUID FLAT PLATE COLLECTOR (LFPC)
Solar collectors are the key component of active
solar-heating systems. They gather the sun's energy,
transform its radiation into heat, then transfer that heat to a
fluid (usually water or air). The solar thermal energy can be
used in solar water-heating systems, solar pool heaters, and
solar space-heating systems. There are a large number of
solar collector designs that have shown to be functional.
Flat-Plate Collector
Flat-plate collector is the most common solar
collector for solar water-heating systems in homes and
solar space heating. A typical flat-plate collector is an
insulated metal box with a glass or plastic cover (called the
glazing) and a dark-colored absorber plate. These collectors
heat liquid or air at temperatures less than 80°C.
temperature difference, is achieved by conducting the
absorbed heat to tubes that contains the heat transfer fluid.
Transferring the heat absorbed on the absorber surface into
the water give rise to heat losses. Liquid collector absorber
plates consist of a flat sheet with tubes spaced 10cm apart
and attached to it. The tubes are not spaced too apart
otherwise a much lower temperature will occur halfway
between them.
4. Calculation
4.1 Heat Transfer Rate without fins
Steady-state values of the tube and water temperature in the
duct at various locations were used to determine the values
of useful parameters.
T1 = 353 K ….[Reference 14]
T2 = 351 K,
Fig.3.a Liquid Flat Plate Collector
Flat-plate collectors are used for residential water heating
and hydronic space-heating installations.
T3 = 350 K,
T 4 = 298 K,
Ro = 0.008 m,
Ri = 0.006 m,
L=2m
ν = 0.553 × 10-6 m2/s
Cp = 4182 J/Kgk
K = 240 W/m2 K (Aluminium)
µ = 0.000547 Ns/m2
Fig.3.b Various layers of LFPC
Flat plate collectors are most common for
residential water- heating and space-heating installations. A
flat plate collector consists of an absorber, glazing covers
and an insulated box as shown in fig 1. The absorber is
sheet of high thermal conductivity metal sheet with tubes
integral attached. The insulated box provides structure and
sealing and reduces heat loss from the back and sides of the
collector. The cover sheets, called glazing, allow sunlight
to pass through to the absorber but insulate the space above
to prevent cool air from flowing into this space. The glass
reflects a small part of the sunlight, which does not reach
the absorber. The absorber plate which covers the full
aperture area of the collector performs three functions:
absorb the maximum possible amount of solar irradiance,
transfer this heat into working fluid at a minimum
temperature difference and lose a minimum amount of heat
back to the surroundings. Solar irradiance passing through
the glazing is absorbed directly onto the absorber plate. As
the second function of the absorber plate is to transfer the
absorbed energy into a heat- transfer fluid at a minimum
Fig.4.1.b Hollow cylinder without fin
QWithout =
2 ⨯ π ⨯L ⨯(T1−T4)
1
In (Ro/Ri)
+
hi ⨯Ri
K
Where, hi = Convective heat transfer co-efficient

Grashoff’s number
Grashoff number is the ratio of buoyancy force to the
viscous force acting on the fluid.
Gr. = (D3 × g × β × ∆t) / ν2
Mean temperature (K)
h = 2132.865 W/m2K
Tmean = (T2 + T4) / 2
= 324.5 K
Co-efficient of thermal expansion (k-1)
+
In (0.008/0.006)
240
Q = 8711.156 W = 8.711 KW
4.2 Heat Transfer Rate with fins
= 0.00308 K-1
As compared to Triangular, Trapezoidal, Parabolic and
circular fins, Rectangular fins provide more surface contact
with fluid. Diameter of pipe is very small and it causes
problem in designing fins of complicated structure. So we
have preferred rectangular fins.
Inner diameter of pipe (m)
D3 = 0.000001728 m3
Putting all the calculated values in equation
Gr. = [0.000001728 × 9.81 × 0.00308 × 53] / (0.553 × 10 6 2
)
= 9.0536 × 106
Steady-state values of the fin in the duct were used to
determine the values and useful parameters are given
belowb = 2m
Prandtl number
l = 0.004 m
It is the ratio of momentum diffusivity to thermal
diffusivity.
Pr =
K = 240 W/mK
ν
α
T2 = 351 K
T3 = 350 K
µ/ρ
Pr =
K/Cp ⨯ ρ
=
y = 0.001 m
T4 = 298 K
Viscous diffusion rate
Pr =
Thermal diffusion rate

0.000547 × 4182
Perimeter of fin
P=2× (b × y)
0.6405
=2 × (2 × 0.001)
Pr = 3.57

1
2132.865 ⨯ 0.006
β = 1 / Tmean

2 ⨯ π ⨯ 2 ⨯ (353 − 298)
Q=
Product of
number.
Grashoff’s number
and
= 0.004 m
Prandtl

6
Gr. × Pr. = 9.0536×10 ×3.57
6
Cross section area of fin (Acs)
Acs = b × y
9
12
= 32.321 × 10 ---------for (10 < Gr × Pr >10 )
Also the values of Nusselt number are determined
for duct by using the equation which is given below:
Nu = 0.53 (Gr. × Pr.)1/4------------{reference R.K. Rajput}
= 0.002 m

Heat transfer coefficient (h)
m=√
Nu = 39.96
The heat transfer rate is calculated in terms of
non-dimensional number i.e. Nusselt Number. The Nusselt
Number is calculated from the heat transfer coefficient as
the Nusselt number is defined as the ratio of convective to
conductive heat transfer across the boundary.
h×d
Nu. =
K
h×p
K × Acs
Where,
e-m × x =
T3−T4
T2−T4
m = 4.762
Put the value in equation.
4.762 = √
h × 0.004
h = 2721.197 W/m2K
First we consider 2 fins for calculating heat transfer
rate,

QTotal = 13.57 kW
240 × 0.002
Now we consider 4 fins for calculating heat transfer
rate,

Heat transfer rate of fin portion (4 fin)
Qfin = √𝑝 × ℎ × 𝐾 × 𝐴𝑐𝑠 × (T2 - T4) × tanh (ml)
Heat transfer rate of fin portion (2 fin)
Qfin = √𝑝 × ℎ × 𝐾 × 𝐴𝑐𝑠 × (T2 - T4) × tanh (ml)
= 2.307296 W (Single fin)
= 2.307296 × 2
= 4.614592 W (2 Fin)
= √0.004 × 2721.197 × 240 × 0.002 × (351 - 298) ×
tanh (4.762 × 0.004)
= 2.307296 W (Single fin)
= 2.307296 × 4
= 9.22918 W (4 Fin)
Fig.4.2 Hollow cylinder with 2 fins

Heat transfer rate of unfinned portion
Qunfinned = h × A × ∆t
h = 2721.197 W/m2K

Fig.4.3 Hollow cylinder with 4 fins
Area (A)
A=b×y
= 2 × 10-3 m2
Qunfinned = 2721.197 × [(π × 0.012 × l) – (2 × 2 × 10-3 × l)] ×
(351 - 298)

Qunfinned = h × A × ∆t
h = 2721.197 W/m2K

= 4860.20186 W

Qwith = 4860.20186 + 4.614592
= 2 × 10-3 m2
Qunfinned = 2721.197 × [(π × 0.012 × l) – (4 × 2 × 10-3 × l)] ×
(351 - 298)
= 4283.308 W
= 4864.816 W
4.3 Total Heat Transfer Rate
QTotal = QWithout + QWith
= 8711.156 + 4864.816
= 13575.97 W
Area (A)
A=b×y
Heat transfer rate with fin(Qwith)
Qwith = Qunfinned + Qfin
Heat transfer rate of unfinned portion

Heat transfer rate with fin(Qwith)
Qwith = Qunfinned + Qfin
Qwith = 4283.308 + 9.22918
= 4292.537 W
4.4 Total Heat Transfer Rate
QTotal = QWithout + QWith
= 13003.693 W = 13.003 kW
At end we consider 6 fins for calculating heat transfer
rate,

Heat transfer rate of fin portion (6 fin)
Qfin = √𝑝 × ℎ × 𝐾 × 𝐴𝑐𝑠 × (T2 - T4) × tanh (ml)
= √0.004 × 2721.197 × 240 × 0.002 × (351 298) × tanh (4.762 × 0.004)
= 2.307296 W (Single fin)
= 2.307296 × 6
= 13.84377 W (6 Fin)
Fig.4.4 Hollow cylinder with 6 fins

Heat transfer rate of unfinned portion
Qunfinned = h × A × ∆t
QTotal = 12431.41 W = 12.43 kW
As we calculate the heat transfer rate for 2fins, 4fins, and
6fins and we get more heat transfer rate at 2 fins
(13.57kW) and 4 fins (13.003kW). But as considering the
strength as well as heat transfer rate we are considering 4
fins in the duct.
4.6 Comparison
Without
(Qwithout)
Heat
rate
fin
With fin (Qwith)
transfer
8.711 kW
13.003 kW
7. ANALYSIS USING CATIA AND ANSYS
Fig.(7.a) shows the temperature difference
between outer and inner surface of pipe without fins,
initially pipe was designed in CATIA which is made up of
aluminum, followed in ANSYS for analysis. Thermal
conductivity (k), input temperature and heat transfer
coefficient is given to pipe. By calculation temperature
range is obtained in ANSYS.
Fig.(7.b) shows the temperature of outer surface,
inner surface and tip of the fins. Initially pipe was
designed in CATIA which is made up of aluminum,
followed in ANSYS for analysis. Thermal conductivity
(k), temperature of outer surface, inner surface and heat
transfer coefficient (h) is given to pipe. By calculation
temperature range is obtained in ANSYS.
h = 2721.197 W/m2K

Area (A)
A=b×y
= 2 × 0.1 × 10-2 = 2 × 10-3 m2
Qunfinned = 2721.197 × [(π × 0.012 × l) – (6 × 2 × 10-3 × l)] ×
(351 - 298)
= 3706.4143 W

Heat transfer rate with fin(Qwith)
Qwith = Qunfinned + Qfin
Qwith = 3706.4143 + 13.84377
= 3720.258 W
4.5 Total Heat Transfer Rate
QTotal = QWithout + QWith
= 8711.156 + 3720.258
Fig.7.a Analysis of temperature without fins
Fig.7.b Analysis of temperature with fins
5. ADVANTAGES AND DISADVANTAGES
5.1 Advantages
1. Internal finned tubes increase the internal surface area
of duct. By having a finned tube in place, it increases
overall heat transfer rate.
2. Due to this the total number of tubes required is
decreases for a given application which then also
reduced the overall equipment size and can in long run
decrease the cost of project.
3. In many application cases, one finned tube replaces six
or more bare tubes at least less than 1/3rd the cost and
1/4th the volume.
4. Up to 12 times the heat transfer area of bare tubes.
Fewer fin tubes are required for equivalent heat
transfer, Smaller and lighter package.
5. Volume to heat transfer ratio are low.
6. Lighter weight and smaller size requires less support
and easy installation.
7. More durable construction.
5..2 Disadvantages
1. The increase in frictional losses cause more power
required by the blower, hence turbulence is created
very close to the duct surface i.e. laminar sub layer.
2. Cleaning and maintenance is difficult.
3. Restrict the mass flow rate of fluid.
4. Manufacturing process of internal finned tube is hard
as compared to simple tube.
6. APPLICATIONS
1. Refrigeration and air conditioning.
2. Industrial process heating.
3. Boiler
4. Internal fins are used in compact heat exchangers.
5. Internal fins are used in phase change material storages
(PCM). PCM are used to balance the temporary
temperature alteration and to store energy in several
practical fields like automobile industries.
6. The rate of heat transfer from fluid flowing through the
micro channels can be greatly enhanced by use of
internal fins.
7. Internal fins used in Improving the thermal
performance of ventilation radiate.
7. CONCLUSION
From theoretical formulae and calculation, we
have seen that the heat transfer rate is increased by
increasing surface area contact between fluid and surface.
Surface area is increased by adding fins in tube that’s why
heat transfer rate is increased. Total heat transfer rate is
increased by 33%. Initially the heat transfer rate without
fins is 8.711kW, but after adding fins it will become
13.003kW.
In this way we are getting result of increasing
efficiency by using fins in the tube.
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