mech CHAPTER.docx

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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http://en.wikipedia.org/wiki/Fennec_Fox

http://en.wikipedia.org/wiki/Jackrabbit

http://en.wikipedia.org/wiki/Hydrogen_fuel_cell

http://en.wikipedia.org/wiki/Hydrogen_fuel_cell

http://en.wikipedia.org/wiki/Power_plant

http://en.wikipedia.org/wiki/Heat_exchanger

http://en.wikipedia.org/wiki/Heat_exchanger

http://en.wikipedia.org/wiki/Radiator

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


Fig. 4.2 Drafting of triangular fin

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3) Rectangular fin profile:

i) Units: mm


iii) Length: 77.52 mm


Fig. 4.3 Drafting of rectangular fin

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4) Spline ( Random) fin profile :

i) Units: mm


iii) Length: 126.19 mm (measured by hit and trail)


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






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5.3.2 Spline fin:

Fig. 5.3 Analysis of randomly selected fin profile







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5.3.3 Parabolic fin:

Fig. 5.4 Analysis of Parabolic profile fin







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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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