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CHAPTER-1
INTRODUCTION
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1.1 GENERAL:
Heat conducted through solids, walls or boundaries has to be continuously dissipated to the
surroundings or environment to maintain the system in a steady condition. In many
engineering applications large quantities of heat have to be dissipated from small areas. Heat
transfer by convection between a surface and the fluid surrounding it can be increased by
attaching to the surface thin strips of metals called fins. The fins increase the effective area of
the surface thereby increasing the heat transfer by convection. The fins are also referred to as
“extended surfaces”. Fins are manufactured in different geometries, depending upon the
practical applications. The ribs attached along the length of a tube are called longitudinal fins.
Pin fins or spines are rods protruding from a surface.
The fins may be uniform or variable cross-section. They have many different
practical applications, viz., cooling of electronic components, cooling of engines,
compressors, electric motors, transformers, refrigerators, high-efficiency boiler superheated
tubes, etc.
1.2 OBJECTIVE:
The aim is to design different fin profiles using CAD software and further, using these
designs to analyze their temperature gradient using CAE. The softwares to be used are Pro-
engineer Creo-elements 5.0 as CAD and ANSYS 12.0 as CAE. The project will help in
deciding the optimum fin profile, for maximum heat transfer, keeping the initial cross-section
and total length constant. Using the conclusion of this project, we can maximize the overall
performance of any heat generating devices.
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1.3 BASICS OF THE PROJECT:
It has been observed that there is a variation in the temperature gradient or rate of heat transfer
in different profiles of fin. Thus it is necessary to use appropriate parameters for better
functioning of the devices. Our main aim is to find the best fin profile by analyzingand then
comparing three different profiles (Rectangular, Tapered and parabolic; selected randomly).
Using CAE, we can observe the overall pattern of heat transfer and thereby obtain the
maximum temperature gradient.
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CHAPTER-2
LITERATURE REVIEW
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2.1 FINS:
In the study of heat transfer, 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.
2.2 Types of fin generally used:
(a) (b) (c)
(d) (e)
Fig 2.1(a)External longitudinal fin, (b) Internal longitudinal fin, (c)plate fin,(d) Circular or
annular fins, (e) pin fins or spines.
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To create a simplified equation for the heat transfer of a fin, many assumptions need to be
made:
Steady state
Constant material properties (independent of temperature)
No internal heat generation
One-dimensional conduction
Uniform cross-sectional area
Uniform convection across the surface area
With these assumptions, the conservation of energy can be used to create an energy balance
for a differential cross section of the fin.
Fourier’s law states that
,
where is the cross-sectional area of the differential element.[2] Therefore the conduction
rate at x+dx can be expressed as
Hence, it can also be expressed as
.
Since the equation for heat flux is
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then is equal to
where is the surface area of the differential element. By substitution it is found that
This is the general equation for convection from extended surfaces. Applying certain
boundary conditions will allow this equation to simplify.
Uniform cross-sectional area
For all four cases, the above equation will simplify because the area is constant
and
where P is the perimeter of the cross-sectional area. Thus, the general equation
for convection from extended surfaces with constant cross-sectional area
simplifies to
.
The solution to the simplified equation is
where
and
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The constants and can be found by applying the proper boundary
conditions. All four cases have the boundary condition for the
temperature at the base. The boundary condition at , however, is different
for all of them, where L is the length of the fin.
For the first case, the second boundary condition is that there is free convection
at the tip. Therefore,
which simplifies to
Knowing that
,
the equations can be combined to produce
and can be solved to produce the temperature distribution, which is in the
table below. Then applying Fourier’s law at the base of the fin, the heat transfer
rate can be found.
Similar mathematical methods can be used to find the temperature distributions
and heat transfer rates for other cases. For the second case, the tip is assumed to
be adiabatic or completely insulated. Therefore at x=L,
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because heat flux is 0 at an adiabatic tip. For the third case, the temperature at
the tip is held constant. Therefore the boundary condition is:
For the fourth and final case, the fin is assumed to be infinitely long. Therefore
the boundary condition is:
The temperature distributions and heat transfer rates can then be found for each
case.
Table number 2.1
2.3 Fin performance
Fin performance can be described in three different ways. The first is fin effectiveness. It is
the ratio of the fin heat transfer rate to the heat transfer rate of the object if it had no fin. The
formula for this is
,
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where is the fin cross-sectional area at the base. Fin performance can also be
characterized by fin efficiency. This is the ratio of the fin heat transfer rate to the heat transfer
rate of the fin if the entire fin were at the base temperature.
The fin efficiency is defined as
in this equation is equal to the surface area of the fin. Fin efficiency will always be less
than one. This is because assuming the temperature throughout the fin is at the base
temperature would increase the heat transfer rate.
The third way fin performance can be described is with overall surface efficiency.
,
where is the total area and is the sum of the heat transfer rates of all the fins. This is the
efficiency for an array of fins.
2.4 Fin Applications
Fins are most commonly used in heat exchanging devices such as radiators in cars and heat
exchangers inpower plants. They are also used in newer technology such as hydrogen fuel
cells. Nature has also taken advantage of the phenomena of fins. The ears
of jackrabbits and Fennec Foxes act as fins to release heat from the blood that flows through
them.They have many different practical applications, viz., cooling of electronic components,
cooling of engines, compressors, electric motors, transformers, refrigerators, high-efficiency
boiler superheated tubes, etc.
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CHAPTER-3
PROBLEM
IDENTIFICATION
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3.1 INTRODUCTION
The thermal resistance of a cooling fin depends not only on its size, but also its shape,
composition, surface configuration (surface finish, painted or bare, etc.) and orientation.
Other factors influencing the thermal resistance are the temperature differences between
cooling fin and ambient temperature, the speed of the air striking the cooling fin surface, the
air-current, and the temperatures of surrounding objects. A simple fact of the internal
combustion engine is that it generates heat in order to produce power. As it turns out only a
small percentage of the heat generated actually gets converted to mechanical force and the
rest is discarded either through the exhaust, the cylinder walls, cylinder head, crankcase walls
or the engine oil. The challenge is to remove the waste heat in the most efficient and reliable
manner possible.
Air-cooled engines dissipate waste heat directly through the cylinder head and walls to the
outside air and also through the engine oil. In fact the engine oil plays a very significant role
in heat dissipation in an air-cooled engine. The problem is that a healthy percentage of heat
must be dissipated directly from the cylinder head and walls to the outside air. Air is not a
good conductor of heat because it is a gas - in fact it is often used for its insulation properties.
Fluids however have much better thermal conductivity because by their nature they are denser
than a gas. A few drops of water or oil will carry away several times more heat than several
cubic feet of air and the same is true for water. So in order to transfer heat into air there needs
to be a large amount of exposed surface area from which to radiate the heat and a substantial
volume of air is required to pass over that surface.
Fins are added to the cylinder heads and walls in order to increase the surface area that can
radiate the heat to the air passing by. The problem is that there is only so much surface area
physically available on a cylinder head in which to have fins and the fins must be of a
practical size in order for the engine components to fit together and for the entire engine to fit
comfortably in an aircraft. So we arrive at the major compromise of an air-cooled engine..
For lower powered air cooled engines - that is engines that have a relatively low power to
cubic inch displacement ratio - air cooling works reasonably well. The problem of heat
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dissipation gets compounded significantly as the power per cubic inch of displacement
increases. As more power is made from the same number of cubic inches (whether that
additional power is created by the use of a turbo charger or higher compression ratios) the
heat dissipation requirements increase significantly simply because there isn't any more
surface area radiating the excess heat away. The only solution is to increase the volume of
airflow past the cooling fins and attempt to restrict that airflow so as to both compress it
(increasing its density and thus thermal conductivity) and slow it down giving it more time to
absorb the heat from the surfaces it is passing by.
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CHAPTER-4
METHODOLOGY
ADOPTED
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4.1 INTRODUCTIONS
As per the theory of extruded surfaces, surface profile is an important parameter, which
decides its effectiveness. For deciding the best profile of fin, it is necessary to make some
assumptions and then comparing some basic profiles. Comparison can be done by various
methods. We have opted constant volume method, i.e. by keeping the net volume constant we
are going to compare the four different profiles.
Some additional assumptions for this method are as follows
1. Constant Base area
2. Constant Material property
3. Constant temperature regions ( base area region and surroundings)
4. Constant convective heat transfer coefficient for whole surface
5. Steady state heat transfer
6. Material is isotropic
The procedure to be carried out for the project can be divided into two segments.
1. Design
2. Analysis
4.2 DESIGN
Drafting or technical drawing is the means by which mechanical engineers design products
and create instructions for manufacturing parts. A technical drawing can be a computer model
or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well
as assembly notes, a list of required materials, and other pertinent information. Instructions
for manufacturing a part must be fed to the necessary machinery, either manually, through
programmed instructions, or through the use of a computer-aided manufacturing (CAM) or
combined CAD/CAM program. Optionally, an engineer may also manually manufacture a
part using the technical drawings, but this is becoming an increasing rarity, with the advent of
computer numerically controlled (CNC) manufacturing.
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Designing is used in nearly every sub discipline of mechanical engineering, and by many
other branches of engineering and architecture. Three-dimensional models created using CAD
software are also commonly used in finite element analysis (FEA).
In this project, we are using Pro-engineer Creo-elements 5.0, for designing purpose.
We are using 4 different profiles for analysis, therefore its required to design the profiles
using CAD. These profiles have been selected randomly, as they are most commonly used.
The four different profiles are
1. Parabolic
2. Triangular
3. Rectangular
4. Spline (randomly selected)
4.2.1 DESIGN PARAMETERS
Following are the design parameters selected
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1) Parabolic fin profile
i) Units: mm
ii) Base area: 40mm x 40 mm
iii) Length: 232.55mm
iv) Volume: 124028 mm3
v) Parabolic equation used: y=at2 and x=2at, where a=675.993 mm
Fig. 4.1 Drafting of parabolic fin
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2) Triangular fin profile:
i) Units: mm
ii) Base area: 40 mm x 40 mm
iii) Length: 155.04 mm
iv) Volume: 124028 mm3
Fig. 4.2 Drafting of triangular fin
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3) Rectangular fin profile:
i) Units: mm
ii) Base area: 40 mm x 40 mm
iii) Length: 77.52 mm
iv) Volume: 124028 mm3
Fig. 4.3 Drafting of rectangular fin
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4) Spline ( Random) fin profile :
i) Units: mm
ii) Base area: 40 mm x 40 mm
iii) Length: 126.19 mm (measured by hit and trail)
iv) Volume: 124028 mm3
Fig. 4.4 Drafting of splined fin
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4.3 ANALYSISSoftware tools that have been developed to support these activities are considered CAE tools.
CAE tools are being used, for example, to analyze the robustness and performance of
components and assemblies. The term encompasses simulation, validation, and optimization
of products and manufacturing tools. In the future, CAE systems will be major providers of
information to help support design teams in decision making.
In regard to information networks, CAE systems are individually considered a single node on
a total information network and each node may interact with other nodes on the network. This
is achieved by the use of reference architectures and their ability to place information views
on the business process. Reference architecture is the basis from which information model,
especially product and manufacturing models. The term CAE has also been used by some in
the past to describe the use of computer technology within engineering in a broader sense than
just engineering analysis.
We are using Ansys v-12.0 to analyze these designed fins.
4.3.1 ANALYSIS PARAMETERS Thermal analysis is done to analyze and compare the temperature gradient and heat flux of the
different fin profiles designed.
Parameters assumed to be constant during analysis are:
1) Material conductivity = 0.0536 W/mm0C
Material selected: Carbon Steel (approx. 0.5% Carbon)
2) Base temperature = 5000C
3) Ambient temperature=300C
4) Convective heat transfer coefficient = .00004 W/mm2 0C
5) Meshing Parameters
(a) Mesh size = 5 (b)Number of divisions = 5
6) Steady state heat conduction
7) Isotropic material
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CHAPTER-5
EXPECTED RESULT AND
DISCUSSIONS
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5.1 EXPECTED RESULT
According to “Fundamentals of ENGINEERING HEAT AND MASS TRANSFER” by R.C.
Sachdeva (fourth edition), there is a unique condition for parabolic profile of the fin, by which
it becomes the best economical section for a given material volume. We expect that by
designing a parabolic fin according to that condition and comparing it with the other fin
profiles, keeping some parameters constant such as: volume, material, convection coefficient,
base temperature, etc. We may obtain minimum temperature at the tip of the fin.
The condition which is discussed above is as follows:
t2l
=√B /2
Where,
t→ base height of fin
l→ length of fin
B→ Biot number ( ht /2 k)
h→ Convection coefficient
k→ conductivity
5.2 DISCUSSION:
There may be infinite number of parabolic profiles possible to be designed for a fin. But an
important point to be noted here is that there may be variation in the expected outcome. The
condition mentioned above should be satisfied while designing the profile for best
performance. This can be easily verified using various CAE softwares.
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5.3 OBSERVATIONS THROUGH ANSYS:
5.3.1 Rectangular fin:
Fig. 5.1 Analysis of rectangular profile finTemperature at base = 5000C
Temperature at tip = 389.750C
Temperature gradient at base = 3.048 0C/mm
Temperature gradient at tip = 0.319219 0C/mm
Flux at base = 0.01711 W/mm2
Flux at tip = 0.163362 W/mm2
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5.3.2 Triangular fin:
Fig. 5.2 Analysis of triangular profile fin
Temperature at base = 5000C
Temperature at tip = 216.880C
Temperature gradient at base = 1.096 0C/mm
Temperature gradient at tip = 3.169 0C/mm
Flux at base = 0.164483 W/mm2
Flux at tip = 0.058746 W/mm2
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5.3.2 Spline fin:
Fig. 5.3 Analysis of randomly selected fin profile
Temperature at base = 5000C
Temperature at tip = 286.9850C
Temperature gradient at base = 0.288492 0C/mm
Temperature gradient at tip = 2.981 0C/mm
Flux at base = 0.015463 W/mm2
Flux at tip = 0.1598 W/mm2
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5.3.3 Parabolic fin:
Fig. 5.4 Analysis of Parabolic profile fin
Temperature at base = 5000C
Temperature at tip = 30.9640C
Temperature gradient at base = 3.131 0C/mm
Temperature gradient at tip = 1.149 0C/mm
Flux at base = 0.161561 W/mm2
Flux at tip = 0.167803 W/mm2
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CHAPTER-6
CONCLUSION AND
SCOPE OF FURTHER
WORK
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6.1 CONCLUSION:
By following the above methodology and the mentioned assumptions we can conclude that,
out of the four basic profiles of fin, parabolic fin is the most efficient and economic profile
for the same amount of material as well as same base area. For this result, it is necessary to
fulfill the condition shown below,
ht2k
=√B /2
Tabulation of the above result:
Sr.
no.
profile Base
temp
(0C)
Tip temp
(0C)
Base temp
gradient
(0C/mm)
Tip
temp
gradient
(0C/mm)
Base flux
(W/mm2)
Tip flux
(W/mm2)
1 Rectangular 500 389.75 3.048 3.069 0.01711 0.163362
2 Triangular 500 216.88 1.096 3.069 0.058746 0.164483
3 Spline 500 286.985 0.288492 2.981 0.015463 0.1598
5 Parabolic 500 30.964 3.131 1.149 0.061561 0.167803
Table number 6.1
From our analysis through CAE (Ansys) it can be easily observed that the tip temperature of
the four fins varies due to their shape although the volume and the base area is kept constant.
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BIBLIOGRAPHY/REFRENCES
www.ces.clemson.edu/tcl/honors.ppt
www2.latech.edu/~dehall/.../19_transient_thermal_fin_solid87.pdf
ipac.kacst.edu.sa/edoc/2011/191411_1.pdf
en.wikipedia.org/wiki/Fin_(extended_surface)
http://www.google.co.in/imghp?hl=en&tab=wi
http://144.206.159.178/ft/490/72440/1237883.pdf
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