Experimentation and analysis of heat transfer through perforated fins of different geometry

1
VISVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAVI
“EXPERIMENTATION AND ANALYSIS OF HEAT TRANSFER
THROUGH PERFORATED FINS OF DIFFERENT GEOMETRY”
Submitted in partial fulfillment of the requirements for the award of the degree of
Bachelor of Engineering in
Mechanical Engineering
Submitted by
ABHIJATH H B 4VV11ME002
AKSHAY MOHANRAJ 4VV11ME012
DASHARATHA H S 4VV11ME024
M S SHARATH KUMAR 4VV11ME039
Under the valuable guidance of
Prof. GANESH B.B
Assistant professor
Mechanical engineering, VVCE

EXPERIMENTATION AND ANALYSIS OF HEAT TRANSFER THROUGH
PERFORATED FINS OF DIFFERENT GEOMETRY
VIDYAVARDHAKA COLLEGE OF ENGINEERING, MYSOORU Page 2
DEPARTMENT OF MECHANICAL ENGINEERING
VIDYAVARDHAKA COLLEGE OF ENGINEERING
GOKULAM III STAGE, MYSORE-570002, KA, INDIA
2014-2015
VIDYAVARDHAKA COLLEGE OF ENGINEERING,
GOKULAM III STAGE, MYSORE

CERTIFICATE
Certified that the project work entitled “EXPERIMENTATION AND ANALYIS OF
HEAT TRANSFER THROUGH PERFORATED FINS OF DIFFERENT GEOMETRY” is
carried out by
ABHIJATH H B 4VV11ME002
AKSHAY MOHANRAJ 4VV11ME012
DASHARATHA H S 4VV11ME048
M S SHARATH KUMAR 4VV11ME039
Bonafide students of vidyavardhaka college of engineering in partial fulfillment
for the award of “Bachelor of engineering” in Mechanical engineering of the
Visvesvaraya technological university, Belgavi during the year 2014-2015.It is
certified that all corrections and suggestions indicated for Internal Assessment
have been incorporated in the report deposited in the department library. The
project report has been approved as it satisfies the academic requirements in
respect of project work prescribed for this degree.
Mr B B GANESH Dr. G B KRISHNAPPA Dr. B
SADASHIVE GOWDA
B.E, M.TECH M.E., PhD, MISTE, FIE, MICC M.E., Ph.D.,
MISTE, FIE
PROJECT GUIDE HOD
PRINCIPAL

CHAPTER
NO.
CONTENTS PAGE
NO.
1 INTRODUCTION 1-28
2 LITERATURE REVIEW 29-32
3 EXPERIMENTATION
3.1 EXPERIMENTAL SETUP 33-39
3.2 EXPERIMENTAL PROCEDURE 39-40
3.3 EXPERIMENTAL READINGS 41-58
3.4 CALCULATION 59-60
4 RESULTS AND DISCUSSIONS
4.1 GRAPHICAL RESULTS AND DISCUSSION 61-74
4.2 ANALYTICAL RESULTS 75-76
4.3 COST ESTIMATION 77
5 CONCLUSION AND SUGGESTIONS 78
REFERENCES 79

CHAPTER 1
INTRODUCTION
The removal of excessive heat from system components is essential to avoid damaging
effects of burning or overheating. Therefore, the enhancement of heat transfer is an important
subject of thermal engineering. 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. Various types of heat exchanger fins, ranging from relatively simple shapes,
such as rectangular, square, cylindrical, annular, tapered or pin fins, to a combination of
different geometries, have been used. Among the all geometrical variations, rectangular fins are
the most commonly encountered because of their simple construction, cheaper cost and
effective cooling capability. Two common orientations of fin configurations, horizontally based
vertical fins and vertically based vertical fins, have been widely used in the applications. There
are many techniques which are available for enhancement for single or two-phase heat transfer
in natural or forced convection. The heat transfer improvement may in general be achieved by
either of increasing the heat transfer coefficients, or the heat transfer surface area or by both.
The basic equation describing such heat losses is given by Qc = hA∆T As seen from this
equation, the rate of heat dissipation from the surface can be increased by increasing either the
heat transfer coefficient h, For the surface area A. Since the use of extended surfaces is often
more economical, convenient and trouble free, most proposed application of increasing surface
area is adding fins to the surface in order to achieve required rate of heat transfer.
Heat transfer is a discipline of thermal engineering that concerns the generation, use,
conversion, and exchange of thermal energy and heat between physical systems. Heat transfer is
classified into various mechanisms, such as thermal conduction, thermal convection, thermal
radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass
of differing chemical species, either cold or hot, to achieve heat transfer. While these
mechanisms have distinct characteristics, they often occur simultaneously in the same system.

However, the designer should optimize the spacing or the number of fins on base
carefully, otherwise fin additions may cause the deterioration of the rate of heat transfer.
Although adding numerous fins increase the surface area, they may resist the air flow and cause
boundary layer interferences which affect the heat transfer adversely.
1.1 HEAT TRANSER MODES
Heat transfer processes are classified into three types: Conduction, Convection and
Radiation.
1.1 CONDUCTION HEAT TRANSFER
When heat is transferred via conduction, the substance itself does not flow; rather, heat is
transferred internally, by vibrations of atoms and molecules. Electrons can also carry heat,
which is the reason metals are generally very good conductors of heat. Metals have many free
electrons, which move around randomly; these can transfer heat from one part of the metal to
another.
Copper, a good thermal conductor, which is why some pots and pans have copper bases, has a
thermal conductivity of 390 J / (s m °C). Styrofoam, on the other hand, a good insulator, has a
thermal conductivity of 0.01 J / (s m °C).
Steady state conduction: is a form of conduction that happens when the temperature difference
driving the conduction is constant, so that after an equilibration time, the spatial distribution of
temperatures in the conducting object does not change any further, in steady state conduction,
the amount of heat entering a section is equal to amount of heat coming out.
Transient conduction: occurs when the temperature within an object changes as a function of
time. Analysis of transient systems is more complex and often calls for the application of
approximation theories or numerical analysis by computer.

Q = -kA (T2-T1)/L
• A = wall surface area normal to heat flow (m2
)
• T1 = temperature of one surface of the wall (K)
• T2 = temperature of the other surface of the wall (K)
• K= thermal conductivity of the material (W/mK)
1.1.1 Thermal conductivity Thermal conductivity is the quantity of heat transmitted
through a unit thickness in a direction normal to a surface of unit area, due to a unit temperature
gradient under steady state conditions. It is measured in watts per degree Kelvin.
The law which governs the phenomenon of conduction is called Fourier’s law of conduction. It
states that the rate of heat flow by conduction in a given direction is proportional to the area
normal to the direction of heat flow and the temperature gradient in that direction.
Thermal Conductivity = heat × distance / (area × temperature gradient)
K= Q × L / (A × ΔT)
Where,
➢ Q – Rate of heat flow (W)
➢ A – Effective area of heat transfer (m2
)
➢ K – thermal conductivity of the material
(W/mK)
➢ ∆T – Temperature gradient (K/m)
Fig.1 Conduction through a Plane Wall

1.2 CONVECTION HEAT TRANSFER
Heat transfer in fluids generally takes place
via convection. Convection currents are set
up in the fluid because the hotter part of the
fluid is not as dense as the cooler part, so
there is an upward buoyant force on the
hotter fluid, making it rise while the cooler, denser, fluid sinks. Birds and gliders make use of
upward convection currents to rise, and we also rely on convection to remove ground-level
pollution. Forced convection, where the fluid does not flow of its own accord but is pushed, is
often used for heating (e.g., forced-air furnaces) or cooling (e.g., fans, automobile cooling
systems).
1.2.1 Natural convection: Natural or “Buoyant” or “Free” convection is a very important
mechanism that is operative in a variety of environments from cooling electronic circuit boards
in computers to causing large scale circulation in the atmosphere as well as in lakes and oceans
that influences the weather. It is caused by the action of density gradients in conjunction with a
gravitational field. This is a brief introduction that will help you understand the qualitative
features of a variety of situations you might encounter.
There are two basic scenarios in the context of natural convection. In one, a density gradient
exists in a fluid in a direction that is parallel to the gravity vector or opposite to it. Such
situations can lead to “stable” or “unstable” density stratification of the fluid. In a stable
stratification, less dense fluid is at the top and denser fluid at the bottom. In the absence of other
effects, convection will be absent, and we can treat the heat transfer problem as one of
conduction. In an unstable stratification, in which less dense fluid is at the bottom, and more
dense fluid at the top, provided the density gradient is sufficiently large, convection will start
spontaneously and significant mixing of the fluid will occur.
Fig 1.2.1 Natural Convection

1.2.2 Forced convection is a mechanism, or type of transport in which fluid motion is
generated by an external source (like a pump, fan, suction device, etc.). Heat transfer by forced
convection generally makes use of a fan, blower, or pump to provide high velocity fluid (gas or
liquid). The high-velocity fluid results in a decreased thermal resistance across the boundary
layer from the fluid to the heated surface. This, in turn, increases the amount of heat that is
carried away by the fluid
1.2.3 Heat-transfer coefficient: The amount of heat which passes through a unit area of a
medium or system in a unit time when the temperature difference between the boundaries of the
system is one degree
1.2.4 Newton's law of cooling: "The rate of heat loss of a body is proportional to the difference
in temperatures between the body and its surroundings."
Fig 1.2.4 Experimental set up of Newton’s Law of Cooling
Newton’s law of cooling expresses the overall effect of convection:
q = hA(Tw
- T∞
)
Fig 1.2.2 Forced Convection

Where,
➢ A - surface area (m2
)
➢ h- Convection heat transfer coefficient (W/m
2
K)
➢ T
w
-wall surface temperature (K)
➢ T∞
- fluid temperature (K)
The heat transfer co-efficient varies with the type of flow (laminar or turbulent). It also depends
on the physical properties of the fluid, the body geometry and the flow passage area, the average
temperature position along the surface of the body and forced (or) natural convection.
As in the case of conduction, thermal resistance is also associated with the convection heat
transfer and can be expressed as:
Rconv= (Tw
- T∞
)/q
Rconv== 1/ (hA)
The convection heat transfer may be classified according to the nature of fluid flow. Forced
convection occurs when the flow is caused by external means, such as a fan, a pump and
similar.
1.3 RADIATION HEAT TRANSFER
Heat transfer through radiation takes place in form of electromagnetic waves mainly in the
infrared region. Radiation emitted by a body is a consequence of thermal agitation of its
composing molecules. Radiation heat transfer can be described by a reference to the so-
called 'black body'.

A black body is defined as a body that absorbs all radiation that falls on its surface. Actual black
bodies don't exist in nature - though its characteristics are approximated by a hole in a box filled
with highly absorptive material.
Fig 1.2.5
A black body is a hypothetic body that completely absorbs all wavelengths of thermal radiation
incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures
are low enough so as not to be self-luminous. All blackbodies heated to a given temperature
emit thermal radiation.
1.3.1 Emissivity: The emissivity of a material (usually written ε or e) is the relative ability of its
surface to emit energy by radiation. It is the ratio of energy radiatedby a particular material to
energy radiated by a black body at the same temperature. A true black body would have ε = 1
while any real object would have ε < 1. Emissivity is a dimensionless quantity.
Fig 1.3.1 Emissivity

1.3.2 Stefan Boltzmann law: the total radiant heat energy emitted from a surface is
proportional to the fourth power of its absolute temperature.
Eb = ЄσT4
Where,
➢ Eb – Emissive power of black body (W/m2)
➢ T – Absolute temperature (K)
➢ σ - Stefan-Boltzmann constant = 5.6697*10-9
W/m2
K4
➢ Є- emissivity
Fig 1.3.2 Radiation from surfaces vs Heat emission
1.4 Thermal contact resistance: When two solid bodies come in contact, such as A and
B in Figure 1, heat flows from the hotter body to the colder body. From experience,
the temperature profile along the two bodies varies, approximately, as shown in the figure. A
temperature drop is observed at the interface between the two surfaces in contact. This
phenomenon is said to be a result of a thermal contact resistance existing between the

contacting surfaces. Thermal contact resistance is defined as the ratio between this temperature
drop and the average heat flow across the interface.
1.5 FINS: 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.
Fig 1.5 Heat Sink Fins
Fins are used to enhance convective heat transfer in a wide range of engineering applications,
and offer a practical means for achieving a large total heat transfer surface area without the use
of an excessive amount of primary surface area. Fins are commonly applied for heat

management in electrical appliances such as computer power supplies or substation
transformers. Other applications include IC engine cooling, such as _ns in a car radiator. It is
important to predict the temperature distribution within the _fin in order to choose the
configuration that offers maximum effectiveness.
The fins may be uniform or variable cross section. They also find applications in cooling of
electric motors, compressors, refrigerators and transformers.
1.5.1 Classification of extended surfaces:
Extended surfaces or fins are available in a number of different geometries. They are generally
classified as
• Longitudinal fins.
• Transverse fins and
• Pin or spine fins.
Longitudinal fins are the long metal strips (ribs) attached to the outside of the pipe/tube
along the length of the pipe/tube. Longitudinal fins are commonly used in double type heat
exchangers or in an unbaffled shell and heat exchanger when the flow proceeds along the axis
of the tube. These are commonly used in problems involving gases and viscous liquids.
Fig 1.5.1 cylindrical fin

Transverse fins are made in a variety of types and are used primarily for cooling and heating
of gases in cross flow. Helical fins and disc type fins are the transverse fin. Disc type
circumferential fins are the concentric annular disc attached to a tube around the tube.
Fig 1.5.2 specifications of fin
Longitudinal fins are used when the direction of flow is parallel to the axis of the tube
whereas transverse fins are used when the direction of flow is across the tubes.
Pin fins or spine are rods/bars protruding from the surface of a tube. These can be employed for
either longitudinal flow or cross flow.
Fig 1.5.1 Types of Fins
Types of perforations included in the Fins:
1. Circular Perforations.
2. Rectangular Perforations.
3. Triangular Perforations.

Applications of fins:
• Automobiles internal combustion engine.
• Microprocessor cooling.
• In the battery used for electric vehicles.
• They also find applications in electric motors, Refrigerators, transformers.
1.5.2 Fin efficiency: It is defined as the ratio of the actual heat transferred by the fin to the
maximum heat transferred by the same fin, if all the fin area were at base temperature. The heat
transfer from a fin would be maximum if the fin were made of a material with an infinite
thermal conductivity(so that the temperature of the extended surface becomes equal to the base
temperature at all the points).
ɳ = qf/qmax
ɳ = qf/hAƟb
Here, qf is the rate of heat transfer from this area if no fins are attached to the surface,
qmaxis the maximum rate of heat transfer.
1.5.3 Effectiveness of fin: It is defined as the ratio of the actual heat transfer rate from a
surface with the fin to the heat transfer rate that would be obtained without fin. The performance
of fins expressed in terms of the fin effectiveness Єfin defined as
Єfin= qf/hAcƟb
Here, Ac is the cross sectional area of the fin at the base and qf represents the rate of heat
transfer from this area if no fins are attached to the surface. The physical significance of
effectiveness of fin can be summarized below

• An effectiveness of Єfin = 1 indicates that the addition of fins to the surface does not
affect heat transfer at all. That is, heat conducted to the fin through the base area Abis
equal to the heat transferred from the same area Abto the surrounding medium
• An effectiveness of Єfin< 1 indicates that the fin actually acts as insulation, slowing
down the heat transfer from the surface. This situation can occur when fins made of low
thermal conductivity materials are used.
• An effectiveness of Єfin> 1 indicates that the fins are enhancing heat transfer from the
surface, as they should. However, the use of fins cannot be justified unless Єfin is
sufficiently larger than 1. Fin surfaces are designed on the basis of maximizing
effectiveness of a specified cost or minimizing cost for a desired effectiveness.
Fig 1.5.3 Circular Perforated Fins

Fig 1.5.4 Rectangular Perforated Fins
1.6 Dimensionless numbers
1.6.1 Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of
inertial forces to viscous forces. Re = ρVD/µ
Re = VD/ν
Re = QD/νA
Where,
➢ V is the mean fluid velocity.

➢ D is the diameter.
➢ Q is the volumetric flow rate.
➢ μ is the dynamic viscosity of the fluid.
➢ v is the kinematic velocity of the fluid.
In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a
measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative
importance of these two types of forces for given flow conditions. These definitions generally
include the fluid properties of density and viscosity, plus a velocity and a characteristic
length or characteristic dimension.
This dimension is a matter of convention – for example a radius or diameter are equally
valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or
width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is
generally used today.
The Reynold’s number can be used to determine if a flow is laminar, transient or turbulent
• Laminar when Re < 2300
• Turbulent when Re > 4000
• Transient when 2300 < Re < 4000.
1.6.2 Nusselt number (Nu) In heat transfer at a boundary (surface) within a fluid, the Nusselt
number is the ratio of convective to conductive heat transfer across (normal to) the boundary. In
this context, convection includes both advection and diffusion. Named after Wilhelm Nusselt, it
is a dimensionless. The conductive component is measured under the same conditions as the
heat convection but with a (hypothetically) stagnant (or motionless) fluid.
A Nusselt number close to one, namely convection and conduction of similar magnitude, is
characteristic of "slug flow" or laminar flow. A larger Nusselt number corresponds to more
active convection, with turbulent flow typically in the 100–1000 range.
The convection and conduction heat flows are parallel to each other and to the surface normal of
the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.

NuL = Convective heat transfer/Conductive heat transfer
NuL= hL/kf
Where,
➢ L = characteristic length
➢ Kf = thermal conductivity of the fluid
➢ h = convective heat transfer coefficient of the fluid
1.6.3 Prandtl number (Pr) is a dimensionless numberused in the study of diffusion in
flowing systems; It is equal to the kinematic viscosity divided by the molecular diffusivity. It is
defined as:
Pr = ν/α = viscous diffusion rate/thermal diffusivity = cPµ/k
The Prandtl number controls the relative thickness of the momentum and thermal boundary
layers. If Pr is small, the heat diffuses very quickly compared to the velocity (momentum). This
means that for liquid metals the thickness of the thermal boundary layer is much bigger than the
velocity boundary layer. It is also known as Schmidt number 1 (Nsc).
1.6.4 Grashoff number (Gr) is one of a dimensionless number in fluid dynamics and heat
transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It
frequently arises in the study of situations involving natural convection.
Gr = gβ(Ts-T∞)L3
/ν2
It frequently arises in the study of situations involving natural convection. It is named
after the German engineer Franz Grashof. The transition to turbulent flow occurs in the
range 108
<GrL < 109
for natural convection from vertical flat plates. At higher Grashof
numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is
laminar.

1.6.5 Rayleigh number is the ratio of buoyancy and viscosity forces times the ratio of
momentum and thermal diffusivities.
The Rayleigh number for a fluid is a dimensionless number associated with buoyancy
driven flow (also known as free convection or natural convection). When the Rayleigh number
is below the critical value for that fluid, heat transfer is primarily in the form of conduction;
when it exceeds the critical value, heat transfer is primarily in the form of convection.
The Rayleigh number is named after Lord Rayleigh and is defined as the product of
the Grashoff number, which describes the relationship between buoyancy and viscosity within a
fluid, and the Prandtl number, which describes the relationship between momentum diffusivity
and thermal diffusivity. For free convection near a vertical wall, the Rayleigh number is defined
as
Rax = GrxPr = (gβ/να)*(Ts-T∞)*x3
Where,
➢ x = Characteristic length (in this case, the distance from the leading edge)
➢ Rax = Rayleigh number at position x
➢ Grx = Grashoff number at position x
➢ Pr = Prandtl number
➢ g = acceleration due to gravity
➢ Ts = Surface temperature (temperature of the wall)
➢ T∞ = Quiescent temperature (fluid temperature far from the surface of the object)
➢ ν = Kinematic viscosity
➢ α = Thermal diffusivity
➢ β = Thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute
temperature)
1.7 Types of flow
➢ Laminar flow
➢ Turbulent flow

➢ Transient flow
1.7.1 Laminar flow
Laminar flow generally happens when dealing with small pipes and low flow velocities.
Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost
parts flow the fastest, and the cylinder touching the pipe isn't moving at all. Shear stress depends
almost only on the viscosity and is independent of density
1.7.2 Turbulent flow
In turbulent flow vortices, eddies and wakes make the flow unpredictable. Turbulent flow
happens in general at high flow rates and with larger pipes. Shear stress for turbulent flow is a
function of the density
1.7.3 Transitional flow
Transitional flow is a mixture of laminar and turbulent flow, with turbulence in the center of the
pipe, and laminar flow near the edges. Each of these flows behave in different manners in terms
of their frictional energy loss while flowing, and have different equations that predict their
behavior. Turbulent or laminar flow is determined by the dimensionless Reynolds Number.
The flow is
• laminar when Re < 2300
• transient when 2300 < Re < 4000
• turbulent when 4000 < Re

Fig 1.7.1 Type of Flows Fig 1.7.2 Nature of flow
1.7.4 Characteristics of Laminar Flow in Ducts
As a result of the development of the hydrodynamic and thermal boundary layers, four types of
laminar flows occur in ducts, namely, fully developed, hydro-dynamically developing,
thermally developing (hydro-dynamically developed and thermally developing), and
simultaneously developing (hydro-dynamically and thermally developing). In this chapter, the
term fully developed flow refers to fluid flow in which both the velocity profile and temperature
profile are fully developed (i.e., hydro-dynamically and thermally developed flow). In such
cases, the velocity profile and dimensionless temperature profile are constant along the flow
direction. The friction factor and Nusselt number are also constant.
Hydro-dynamically developing flow is isothermal fluid flow in which the velocity profile varies
in the flow direction. Fluid flow from the entrance of the duct to the location at which the fully
developed velocity profile forms is referred to as hydro-dynamically developing flow. The
distance over which the velocity distribution changes and the hydro-dynamic boundary layer
developed is referred to as the hydro-dynamic entrance length. The friction factor in the hydro-
dynamic entrance is a function of the axial location.
The term thermally developing flow refers to fluid flow in which the temperature profile is
developing and the velocity profile has already developed (i.e., the velocity distribution is
invariant with axial length, and the non-dimensional temperature profile changes with axial
length). In other words, the hydro-dynamic boundary layer is already developed while the
thermal boundary is developing. This kind of flow is alternately termed thermal entrance flow.
The distance over which the non-dimensional temperature distribution changes or the thermal
boundary layer develops is termed thermal entrance length, corresponding to hydro-dynamic
entrance length in hydro-dynamically developing flow. The Nusselt number for thermally
developing flow changes with axial location.

Simultaneously developing flow is fluid flow in which both the velocity and the temperature
profiles are developing. The hydrodynamic and thermal boundary layers are developing in the
entrance region of the duct. Both the friction factor and Nusselt number vary in the flow
direction.
Fig 1.7.3 Laminar flow in Ducts
1.7.5 Characteristics of Turbulent Flow in Ducts
In turbulent flow, the fluid particles do not travel in a well-ordered pattern. These particles
possess velocities with macroscopic fluctuations at any point in the flow field. Even in steady
turbulent flow, the local velocity components transverse to the main flow direction change in
magnitude with respect to time. Instantaneous velocity consists of time-average velocity and its
fluctuating component. When heat transfer is involved in turbulent flow, the instantaneous
temperature is composed of the time-average temperature and its fluctuating components.
Similar to laminar flow in ducts, turbulent flow can be divided into four types, fully developed,
hydro-dynamically developing, thermally developing, and simultaneously developing.
Nevertheless, the hydrodynamic and thermal entrance lengths in turbulent duct flow are
characteristically much shorter than their corresponding lengths in laminar duct flow.

Consequently, the results of fully developed turbulent flow and heat transfer are frequently used
in design calculations without reference to the hydro-dynamic and thermal entrance regions.
However, caution must be taken in using the fully developed results for low Prandtl number
fluids such as liquid metals inasmuch as entrance effects are very important for these fluids.
Table below illustrates the relationships between the types of flow, boundary layers, velocity
and temperature distributions, the friction factor, and the Nusselt number.
1.7.5 Design factors
1.7.5.1 Thermal resistance
For semiconductor devices used in a variety of consumer and industrial electronics, the idea
of thermal resistance simplifies the selection of heat sinks. The heat flow between the
semiconductor die and ambient air is modeled as a series of resistances to heat flow; there is a
resistance from the die to the device case, from the case to the heat sink, and from the heat sink
to the ambient air. The sum of these resistances is the total thermal resistance from the die to the
ambient air. Thermal resistance is defined as temperature rise per unit of power, analogous to
electrical resistance, and is expressed in units of degrees Celsius per watt (°C/W). If the device
dissipation in watts is known, and the total thermal resistance is calculated, the temperature rise
of the die over the ambient air can be calculated.
The idea of thermal resistance of a semiconductor heat sink is an approximation. It does not
take into account non-uniform distribution of heat over a device or heat sink. It only models a
system in thermal equilibrium, and does not take into account the change in temperatures with
time. Nor does it reflect the non-linearity of radiation and convection with respect to
temperature rise. However, manufacturers tabulate typical values of thermal resistance for heat
sinks and semiconductor devices, which allows selection of commercially manufactured heat
sinks to be simplified.
Commercial extruded aluminum heat sinks have a thermal resistance (heat sink to ambient air)
ranging from 0.4 °C/W for a large sink meant for TO3 devices, up to as high as 85 °C/W for a

clip-on heat sink for a TO92 small plastic case.[3]
The famous, popular, historic and
notable 2N3055 power transistor in a TO3 case has an internal thermal resistance from junction
to case of 1.52 °C/W.[4]
The contact between the device case and heat sink may have a thermal
resistance of between0.5 up to 1.7 °C/W, depending on the case size, and use of grease or
insulating mica washer.
1.7.5.2 Materials
The most common materials are aluminum alloys. Aluminum alloy 1050A has one of the
higher thermal conductivity values at 229 W/mK but is mechanically soft. Aluminum alloys
6061 and 6063 are commonly used, with thermal conductivity values of 166 and 201 W/mK
respectively. The values depend on the temper of the alloy.
Copper has excellent heat sink properties in terms of its thermal conductivity, corrosion
resistance, bio-fouling resistance, and antimicrobial. Copper has around twice the thermal
conductivity of aluminum and faster, more efficient heat absorption. Its main applications are in
industrial facilities, power plants, solar thermal water systems, HVAC systems, gas water
heaters, forced air heating and cooling systems, geothermal heating and cooling, and electronic
systems.
Copper is three times as denseand more expensive than aluminum. Copper heat sinks are
machined and skived. Another method of manufacture is to solder the fins into the heat sink
base. Aluminum can be extruded, but copper cannot.
Diamond is another heat sink material and its thermal conductivity of 2000 W/mK exceeds
copper five-fold. In contrast to metals, where heat is conducted by delocalized electrons, lattice
vibrations are responsible for diamond's very high thermal conductivity. For thermal
management applications, the outstanding thermal conductivity and diffusivity of diamond is an
essential. Nowadays synthetic diamond is used as sub-mounts for high-power integrated circuits
and laser diodes.
Composite materials can be used. Examples are a copper-tungsten pseudo alloy, AlSiC (silicon
carbide in aluminum matrix), Dymalloy (diamond in copper-silver alloy matrix), and E-

Material (beryllium oxide in beryllium matrix). Such materials are often used as substrates for
chips, as their thermal expansion coefficient can be matched to ceramics and semiconductors.
1.7.5.3 Fin efficiency
Fin efficiency is one of the parameters which makes a higher thermal conductivity material
important. A fin of a heat sink may be considered to be a flat plate with heat flowing in one end
and being dissipated into the surrounding fluid as it travels to the other. As heat flows through
the fin, the combination of the thermal resistance of the heat sink impeding the flow and the
heat lost due to convection, the temperature of the fin and, therefore, the heat transfer to the
fluid, will decrease from the base to the end of the fin. Fin efficiency is defined as the actual
heat transferred by the fin, divided by the heat transfer were the fin to be isothermal
(hypothetically the fin having infinite thermal conductivity).
1.7.5.4 Spreading resistance
Another parameter that concerns the thermal conductivity of the heat sink material is spreading
resistance. Spreading resistance occurs when thermal energy is transferred from a small area to
a larger area in a substance with finite thermal conductivity. In a heat sink, this means that heat
does not distribute uniformly through the heat sink base. The spreading resistance phenomenon
is shown by how the heat travels from the heat source location and causes a large temperature
gradient between the heat source and the edges of the heat sink. This means that some fins are at
a lower temperature than if the heat source were uniform across the base of the heat sink. This
no uniformity increases the heat sink's effective thermal resistance.
To decrease the spreading resistance in the base of a heat sink:
• Increase the base thickness
• Choose a different material with better thermal conductivity
• Use a vapor chamber or heat pipe in the heat sink base.
1.7.5.5 Fin arrangements

Fig 1.7.5 A pin- straight- and flared fin types
A pin fin heat sink is a heat sink that has pins that extend from its base. The pins can be
cylindrical, elliptical or square. A pin is by far one of the more common heat sink types
available on the market. A second type of heat sink fin arrangement is the straight fin. These run
the entire length of the heat sink. A variation on the straight fin heat sink is a cross cut heat sink.
A straight fin heat sink is cut at regular intervals.
In general, the more surface area a heat sink has, the better it works. However, this is not always
true. The concept of a pin fin heat sink is to try to pack as much surface area into a given
volume as possible. As well, it works well in any orientation. Kordyban has compared the
performance of a pin fin and a straight fin heat sink of similar dimensions. Although the pin fin
has 194 cm2
surface area while the straight fin has 58 cm2
, the temperature difference between
the heat sink base and the ambient air for the pin fin is 50 °C. For the straight fin it was 44 °C or
6 °C better than the pin fin. Pin fin heat sink performance is significantly better than straight
fins when used in their intended application where the fluid flows axially along the pins rather
than only tangentially across the pins.
Another configuration is the flared fin heat sink; its fins are not parallel to each other, as shown
in figure. Flaring the fins decreases flow resistance and makes more air go through the heat sink
fin channel; otherwise, more air would bypass the fins. Slanting them keeps the overall
dimensions the same, but offers longer fins. Forghan, et al. has published data on tests
conducted on pin fin, straight fin and flared fin heat sinks. They found that for low approach air
velocity, typically around 1 m/s, the thermal performance is at least 20% better than straight fin
heat sinks. Lasance and Eggink also found that for the bypass configurations that they tested,
the flared heat sink performed better than the other heat sinks tested.

1.7.5.6 Surface color
The heat transfer from the heat sink occurs by convection of the surrounding air, conduction
through the air, and radiation.
Heat transfer by radiation is a function of both the heat sink temperature, and the temperature of
the surroundings that the heat sink is optically coupled with. When both of these temperatures
are on the order of 0 °C to 100 °C, the contribution of radiation compared to convection is
generally small, and this factor is often neglected. In this case, finned heat sinks operating in
either natural-convection or forced-flow will not be affected significantly by surface emissivity.
In situations where convection is low, such as a flat non-finned panel with low airflow, radiative
cooling can be a significant factor. Here the surface properties may be an important design
factor. Matte-black surfaces will radiate much more efficiently than shiny bare metal in the
visible spectrum. A shiny metal surface has low effective emissivity due to its low surface area.
While the emissivity of a material is tremendously energy (frequency) dependent, the noble
metals demonstrate very low emissivity in the Near-Infrared spectrum. The emissivity in the
visible spectrum is closely related to color. For most materials, the emissivity in the visible
spectrum is similar to the emissivity in the infrared spectrum; however there are exceptions,
notably certain metal oxides that are used as "selective surfaces".
In a vacuum or in outer space, there is no convective heat transfer, thus in these environments,
radiation is the only factor governing heat flow between the heat sink and the environment. For
a satellite in space, a 100 °C (373 Kelvin) surface facing the sun will absorb a lot of radiant
heat, because the sun's surface temperature is nearly 6000 Kelvin, whereas the same surface
facing deep-space will radiate a lot of heat, since deep-space has an effective temperature of
only a few Kelvin.
1.8 Attachment methods
1.8.1 Thermal Tapes

As power dissipation of components increases and component package size decreases, thermal
engineers must innovate to ensure components won't overheat. Devices that run cooler last
longer. A heat sink design must fulfill both its thermal as well as its mechanical requirements.
Concerning the latter, the component must remain in thermal contact with its heat sink with
reasonable shock and vibration. The heat sink could be the copper foil of a circuit board, or else
a separate heat sink mounted onto the component or circuit board. Attachment methods include
thermally conductive tape or epoxy, wire-form z clips, flat spring clips, standoff spacers, and
push pins with ends that expand after installing.
Fig 1.8.1 Roll of thermally conductive tape.
Thermally conductive tape is one of the most cost-effective heat sink attachment materials. It is
suitable for low-mass heat sinks and for components with low power dissipation. It consists of a
thermally conductive carrier material with a pressure-sensitive adhesive on each side.
This tape is applied to the base of the heat sink, which is then attached to the component.
Following are factors that influence the performance of thermal tape:[13]
• Surfaces of the component must be clean, with no residue such as a film of silicone
grease.
• Preload pressure is essential to ensure good contact. Insufficient pressure results in areas
of non-contact with trapped air, and results in higher-than-expected interface thermal
resistance.
• Thicker tapes tend to provide better "wettability" with uneven component surfaces.
"Wettability" is the percentage area of contact of a tape on a component. Thicker tapes,

however, have a higher thermal resistance than thinner tapes. From a design standpoint,
it is best to strike a balance by selecting a tape thickness that provides maximum
"wettablilty" with minimum thermal resistance.
1.8.2 Epoxy
Epoxy is more expensive than tape, but provides a greater mechanical bond between the heat
sink and component, as well as improved thermal conductivity.[13]
The epoxy chosen must be
formulated for this purpose. Most epoxies are two-part liquid formulations that must be
thoroughly mixed before being applied to the heat sink, and before the heat sink is placed on the
component. The epoxy is then cured for a specified time, which can vary from 2 hours to 48
hours. Faster cure time can be achieved at higher temperatures. The surfaces to which the epoxy
is applied must be clean and free of any residue.
The epoxy bond between the heat sink and component is semi-permanent/permanent.[13]
This
makes re-work very difficult and at times impossible. The most typical damage caused by
rework is the separation of the component die heat spreader from its package.
1.8.3 Push pins with compression springs
For larger heat sinks and higher preloads, push pins with compression springs are very
effective.[13]
The push pins, typically made of brass or plastic, have a flexible barb at the end
that engages with a hole in the PCB; once installed, the barb retains the pin. The compression
spring holds the assembly together and maintains contact between the heat sink and component.
Care is needed in selection of push pin size. Too great an insertion force can result in the die
cracking and consequent component failure. Threaded standoffs with compression springs.

Fig 1.9 Push Pins
For very large heat sinks, there is no substitute for the threaded standoff and compression spring
attachment method. A threaded standoff is essentially a hollow metal tube with internal threads.
One end is secured with a screw through a hole in the PCB. The other end accepts a screw
which compresses the spring, completing the assembly. A typical heat sink assembly uses two
to four standoffs, which tends to make this the most costly heat sink attachment design. Another
disadvantage is the need for holes in the PCB.
1.9 ANSYS:
ANSYS Mechanical provides solutions for many types of analyses including structural, thermal,
modal, linear buckling and shape optimization studies.
ANSYS Mechanical is an intuitive mechanical analysis tool that allows geometry to be
imported from a number of different CAD systems. It can be used to verify product
performance and integrity from the concept phase through the various product design and
development phases.
The use of ANSYS Mechanical accelerates product development by providing rapid feedback
on multiple design scenarios, which reduces the need for multiple prototypes and product
testing iterations.
ANSYS WORKBENCH FEATURES
• Bidirectional, parametric links with all major CAD systems

• Integrated, analysis-focused geometry modelling, repair, and simplification via ANSYS
Design Modeler
• Highly-automated, physics-aware meshing
• Automatic contact detection
• Complete analysis system that guide the user start-to-finish through an analysis
• Complex project schematics can be saved for re-use
• Pervasive, project-level parameter management across all physics
CHAPTER 2
LITERATURE REVIEW
Comparisons of round-elliptical-square-parallel fins appear seldom in the literature. Wirtz et
al.[1] were amongst the earliest ones to measure the performance of a pin fin heatsink. In their
work, experimental results were reported on the thermal performance of model fan-
sink assemblies consisting of a small axial flow fan for impingement of air on a square array of
pin fins. Cylinder, square, and diamond shape cross-section pin fins were considered. The
overall heat sink thermal resistances, R, were evaluated at fixed applied pressure rise and fixed
fan power. They concluded that cylindrical pin fins give the best overall fan-sink performance.
Elliptical pin fin arrays were not studied in their investigation. In addition, only impinging flow
drawn through the fin arrays was considered.

Sparrow and Larson [7] performed experiments to determine per- fin heat transfer
coefficients for a pin fin array situated in an oncoming longitudinal flow that turns to a cross-
flow. They varied the geometric parameters of round fins including the fin height to diameter
ratio (H/D) and the inter-fin pitch to diameter ratio (P/D). The pressure drop across the array
was also measured and presented in dimensionless form relative to a specially defined velocity
head, which gave a universal pressure drop result for all operating conditions. Subsequent to
this study, they also compared the performance of different pin fin geometries. How- ever, the
objective was to determine which fin height and inter- fin spacing yield the lowest overall
thermal resistance for the array. The minimization of the resistance was sought under the
constraint of constant pumping power for all candidate systems (i.e. those characterized by
different H/D and P/D values) and for a uniform fin-to-airstream temperature difference for all
fins in a given array.
In the experiments of Chapman [2] et al.1 with elliptical pin-fin heat sinks, results were
obtained with aluminum heat sink made of extruded fin, crosscut rectangular fins, and elliptical
fins in laminar air flow. All three heat sinks have equal volume, and the total surface area was
also calculated to be nearly identical. The heat sink and ambient temperature difference was
used to calculate thermal resistance. They supposed that the elliptical pin fin heat sink was
designed to minimize the pressure loss across the heat sink by reducing the vortex effects and to
enhance the thermal performance by maintaining large exposed surface area available for heat
transfer. The optimal geometry of an array of fins that minimizes the thermal resistance between
the substrate and the flow forced through the fins was reported by Bejan and Morega. Both
round pin fin arrays and staggered plate fin arrays were optimized in two steps, first the optimal
fin thickness was selected and then the optimal size of fluid channel was determined. They also
compared the minimum thermal resistance of staggered plate arrays and parallel plate fins.
Furthermore, the dimensionless pressure gradient was plotted against Reynolds number. Wirtz
and Colban [1] simulated electronic packages to com- pare the cooling performance of in-
line and staggered plate arrays for both sparse and dense packaging configurations. They found
that staggered arrays exhibit higher element heat transfer coefficients and friction factors than
inline arrays at a given flow rate. However, no significant difference in performance was
observed between staggered and inline configurations when they were compared based on either

equal coolant flow pressure drop or pumping power. They did not change the element or
channel geometry and therefore the effect of these parameters on their results is not known. In-
line and staggered plate arrays were also investigated, both numerically and experimentally, by
Sathyamurthy et al. They obtained a good agreement between their numerical results and
experiments. Their results illustrated that the thermal performance of the staggered fin
configuration was better than the planar fin configuration over the power and flow ranges
examined. This enhanced thermal performance, however, was realized at the expense of an
additional pressure drop. Heat transfer enhancement mechanisms in in-line and staggered
parallel plate fin heat exchangers were also studied by Zhang et al., [5] who examined the
geometrical effects.
There are also a few reports on the thermal performance and the flow bypass effects of
parallel plate fin arrays. Barrett and Obinelostudied tip clearance and span wise spacing across a
range of approach flow rates and fin densities. Wirtz et al.[1] also studied the effect of flow
bypass on the performance of longitudinal fin heat sinks. Iwasaki et al. studied the cooling
performance of this typical heat sink by using numerical, experimental and nodal network
techniques. Keyes studied forced convection through parallel plate fins, while natural
convection in the same geometry was studied by Culham et al.
M.J. Sable, S.J. Jagtap, P.S. Patil, P.R. Baviskar& S.B. Barve,[6] heat transfer enhancing
technique was investigated for natural convection adjacent to a vertical heated plate with a
multiple v- type partition plates (fins) in ambient air surrounding. As compared to conventional
vertical fins. In this investigation work a totally new heat transfer technique is found out to
increase the rate of natural convection heat transfer on vertical heated plate. The V –type fin
array can be seen as the combination of a horizontal and vertical partition plates. For the same
surface areas, V-type partition plates gave better heat transfer performance than vertical
rectangular fin array and V- fin with bottom spacing type array.
Margarita buike and Andrisbuikil, they constructed exact analytical three-dimensional
solution for the distribution of the temperature field in the wall with rectangular fin in the form
of the 2nd kind Fredholm integral equation. The solution obtained is in the form of Fredholm
integral equation of 2nd kind and has continuous kernel. They allow passing over from
problems for individual fins to problems for fins’ arrays.

Somayyeh Sadri, Mohammad Reza Raveshi and ShayanAmiri,[3] In their study, one
type of applicable analytical method, differential transformation method (DTM), is used to
evaluate the efficiency and behavior of a straight fin with variable thermal conductivity and heat
transfer coefficient. In this study, Nonlinear heat transfer equation related to a considerable fin
is derived and dimensionalized. Using DTM, differential equations are transformed to algebraic
equations in the K domain and solved iteratively.
Raseeelo J oitsheki and Charis Harley, [6] studied Transient heat transfer through a
longitudinal ﬁn of various proﬁles. The thermal conductivity and heat transfer coefficients are
assumed to be temperature dependent. Since the governing boundary value problem is not
invariant under any Lie point symmetry, we solve the original partial differential equation
numerically.
Federico Rossi, Franco Cotana, MirkoFilipponiin this paper a new relation for the
optimum spacing between rectangular fins is proposed. The relation was been obtained keeping
into account non-unitary fin efficiency. The difference between heat dissipation rate calculated
by literature method and heat dissipation rate evaluated by the proposed method increases as fin
height grows. Application on CPU dissipater shows heat flux increase up to 3%.
H. YuÈncuÈ, G. Anbar [5] made an an experimental study of free convection heat
transfer from rectangular fin-arrays on a horizontal base. An experimental set-up was
constructed and calibrated, 15 sets of fin-arrays and a base plate without fins were tested in
atmosphere. Fin height was varied from 6 mm to 26 mm, fin spacing was varied from 6.2 mm to
83 mm. Fin length and fin thicknesses were fixed at 100 mm and 3 mm, respectively.
One of the earliest studies is that of Starner and McManus who presented free
convection data for four rectangular fin-arrays in three positions including the vertical position
for the ®n base. Welling and Wooldridge experimentally investigated the free convection heat
transfer from rectangular fins placed on a vertical plate. Jones and Smith studied the variations
of local heat transfer coefficient for isothermal vertical fin arrays on a horizontal base over a
wide range of fin spacing.
The results of experiments have shown that the convective heat transfer rate from fin
arrays depends on geometric parameters and base-to ambient temperature difference. The

separate roles of fin height, fin spacing and base-to-ambient temperature difference were
investigated. It was found that, for a given base-to-ambient temperature difference, the
convective heat transfer rate from fin arrays takes on a maximum value as a function of fin
spacing and fin height and an optimum fin spacing value which maximizes the convective heat
transfer rate from the fin array is available for every fin height.
CHAPTER 3
EXPERIMENTATION
3.1 EXPERIMENTATION SETUP
3.1.1 Air duct
The air duct is the housing where the fin and the heating coil assembly has been placed.
It is a rectangular passage made of galvanized iron sheet. It has a dimension of
150×100×600mm. It is connected to an air blower at the back side end whereas the front end is
exposed to the atmosphere.

Fig 3.1 Air duct
3.1.2 Dimmer for heating
Dimmer stator is a controller, which can be used to regulate the input voltage. As the voltage
increases, the heat generation in the heating coil also increases or vice versa.
Fig 3.2 Dimmer for Heating
3.1.3 Display unit
The display unit has three major components. One display measures the different
temperatures in the system. The other two are used to measure the voltage and current in the
circuit.

Fig 3.3.2 Current display unit Fig 3.3.2 Voltage display unit
3.1.4 Air blower assembly
These are machines whose primary function is to provide a large flow of air or gas to
various processes of many industries. This is achieved by rotating a number of blades,
connected to a hub and shaft, and driven by a motor or turbine. . It is connected to a pipe at the
other end. The air sucked in through the air duct passes over the fin arrangement and is then
dissipated to the atmosphere through this pipe.
Fig 3.4 Blower assembly
3.1.5 Heating element
A heating element converts electricity into heat through the process of resistive or Joule
heating. Electric current passing through the element encounters resistance, resulting in heating

of the element.
Unlike
the Peltier
Effect this
process is
independent of
the direction of current flow.
Fig 3.5 Heating Element
3.1.6 Fins
The rectangular fins with perforations and without perforations are used in our project. The
dimension of the rectangular fin 55×50mm, 100mm length with the fin thickness of 5mm and
spacing between the fins is 10mm.Materials used for the projects are Aluminum and Copper.
Fig 3.1.1 Fin without perforations Fig 3.1.2 Fin with perforation

Fig 3.1.3 Fin without perforations

Fig 3.1.4 Fin with rectangular perforations.
Fig 3.1.5 Fin with triangular
perforations.

Fig 3.1.5 Fin with circular perforations.
3.1.7 Thermo couples
A thermocouple is a temperature-measuring device consisting of two dissimilar conductors
that contact each other at one or more spots. It produces a voltage when the temperature of one
of the spots differs from the reference temperature at other parts of the circuit. Thermocouples
are a widely used type of sensor for measurement and control. Thermocouple of K type is
used in our experiment. The maximum temperature that can be measured in this is around
8000
c. The thermocouple has two types of lugs. Round lug is fixed to the fin and the U-shaped
lug is fixed to the selector switch
Fig 3.7 Thermocouples
3.1.8 Thermo Anemometer
A thermo anemometer is a device for measuring wind speed and also the temperature of the air.

Fig 3.8.1 Anemometer
3.2 EXPERIMENTAL PROCEDURE
The experiments have been conducted in a controlled environment inside the
laboratory. The experiment is carried out for two different fin materials. The arrangement
consists of 4 fins and are placed on a base plate with spacing of 10mm.Thermocouples are fixed
to the heating coil to measure the base temperature, freely left inside the air duct to measure
ambient temperature and to the fin to measure the fin temperatures
Fig 3.2.1 Experimental arrangement

The above figure shows the experimental arrangement. For a particular fin material , it is made
sure that all the connections are properly attached to the system. The system is then switched
on.
• The experiment is conducted by keeping the voltage constant and varying velocity of air
i.e. 4, 5, 6, 7, 8, 9, 10,11,12,13 and 14 m/s.
• Once the steady state is reached, voltmeter reading, ammeter reading and temperature
readings T1 to T6 for fins are noted down.
• The experiment is repeated for voltage value 50, 60, 70, 80, and 90 respectively.
• Same experimental procedure is repeated for both plane and perforated fin and for
different materials.
• After the experiment is conducted, suitable formulae are used to calculate the heat
transfer co-efficient and efficiency of the fin.

3.3 EXPERIMENTAL READINGS
3.3.1 Aluminium without perforations
V
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0.1
33
4
0.72
19
18.4
848
21.3
061 26.0686 0.8173
8
0.4
5
69.9
00
54.6
00
18.4
192
0
43,
43
2.9
4
0.
6
9
7
0
8
61
.3
56
53
0.
02
85
8
17
.5
36
9
2
9
.
3
3
0.
6
0
0
20
.0
85
8
1
7.
3
1
9
6
10
3.0
85
9
5.
15
43
2.
9
4
6
4
6.9
51
9
6.
9
5
1
6
0.1
42
9
0.83
47
17.1
213
25.3
383 30.8034 0.8226
10
0.4
5
66.8
50
52.3
75
18.1
922
5
54,
96
8.4
6
0.
6
9
7
5
3
69
.0
39
92
0.
02
84
3
19
.6
25
5
2
9
.
3
2
8.
9
5
0
21
.2
30
6
1
7.
3
1
9
6
10
9.3
50
0
5.
46
75
3.
1
0
8
4
7.3
13
6
7.
3
1
3
4
0.1
50
8
0.93
41
16.1
402
26.8
269 33.3599 0.8042
12
0.4
5
63.0
50
50.1
75
17.9
678
5
66,
78
5.9
5
0.
6
9
7
9
7
76
.1
16
23
0.
02
82
7
21
.5
19
8
2
9
.
3
2
5.
7
5
0
23
.8
68
9
1
7.
3
1
9
6
11
4.8
17
3
5.
74
09
3.
2
4
6
1
7.6
29
3
7.
6
2
9
2
0.1
57
4
1.02
42
15.3
715
26.1
648 34.5476 0.7574
14
0.4
5
60.3
75
48.5
38
17.8
052
1
78,
62
8.6
6
0.
6
9
8
1
5
82
.5
96
70
0.
02
81
6
23
.2
57
3
2
9
.
3
2
3.
6
7
5
25
.9
60
9
1
7.
3
1
9
6
11
9.6
05
2
5.
98
03
3.
3
6
7
8
7.9
05
8
7.
9
0
5
7
0.1
63
3
1.10
69
14.7
560
25.9
986 35.1407 0.7398
V
=
7
0
V
2
0.4
9
82.0
00
71.1
00
20.1
377
0
9,9
31.
62
0.
6
9
3
7
8
29
.2
93
75
0.
02
97
5
8.
71
46
3
4
.
3
2
1.
8
0
0
33
.0
61
5
1
7.
3
1
9
6
71.
22
89
3.
56
14
2.
1
1
9
0
5.1
11
0
5.
1
0
6
0
0.1
02
9
0.41
48
24.8
020
8.97
03 10.6985 0.8385
4
0.4
9
79.1
00
65.3
00
19.5
265
0
20,
48
4.9
8
0.
6
9
4
9
4
42
.0
94
40
0.
02
93
3
12
.3
46
7
3
4
.
3
2
7.
6
0
0
26
.1
13
8
1
7.
3
1
9
6
85.
38
49
4.
26
92
2.
5
0
4
4
5.9
29
6
5.
9
2
8
0
0.1
21
5
0.58
76
20.6
751
16.0
902 18.5970 0.8652
6
0.4
9
75.4
00
59.7
00
18.9
394
0
31,
67
9.9
9
0.
6
9
6
0
6
52
.3
75
95
0.
02
89
4
15
.1
57
1
3
4
.
3
3
1.
4
0
0
22
.9
53
5
1
7.
3
1
9
6
95.
24
34
4.
76
22
2.
7
5
6
2
6.4
99
0
6.
4
9
8
4
0.1
33
7
0.72
14
18.5
321
22.4
723 26.7663 0.8396
8
0.4
9
72.9
00
56.6
00
18.6
232
0
42,
95
7.1
7
0.
6
9
6
6
8
61
.0
07
89
0.
02
87
2
17
.5
22
7
3
4
.
3
3
2.
6
0
0
22
.1
08
6
1
7.
3
1
9
6
10
2.7
92
6
5.
13
96
2.
9
5
2
4
6.9
35
0
6.
9
3
4
6
0.1
43
2
0.83
40
17.1
702
26.9
724 31.3575 0.8602
10
0.4
9
69.9
25
54.4
13
18.4
000
8
54,
34
7.6
0
0.
6
9
7
1
2
68
.6
35
56
0.
02
85
7
19
.6
08
4
3
4
.
3
3
1.
0
2
5
23
.2
30
9
1
7.
3
1
9
6
10
9.0
29
3
5.
45
15
3.
1
1
4
8
7.2
95
1
7.
2
9
4
9
0.1
51
1
0.93
33
16.1
877
28.7
247 34.2567 0.8385
12
0.4
9
66.2
50
52.2
75
18.1
820
5
65,
99
9.1
6
0.
6
9
7
5
5
75
.6
51
38
0.
02
84
2
21
.4
99
6
3
4
.
3
2
7.
9
5
0
25
.7
86
7
1
7.
3
1
9
6
11
4.4
66
2
5.
72
33
3.
2
5
3
0
7.6
09
0
7.
6
0
8
9
0.1
57
8
1.02
33
15.4
186
28.3
735 34.9212 0.8125
14
0.4
9
62.1
50
49.9
25
17.9
425
8
78,
02
6.7
0
0.
6
9
8
0
1
82
.2
74
48
0.
02
82
5
23
.2
46
4
3
4
.
3
2
4.
4
5
0
29
.4
78
1
1
7.
3
1
9
6
11
9.3
71
7
5.
96
86
3.
3
7
2
8
7.8
92
3
7.
8
9
2
2
0.1
63
6
1.10
64
14.7
849
26.8
372 33.4779 0.8016

3.3.2 Aluminium with circular perforations
V
el
oc
ity
C
ur
re
nt Ts Tf v Re Pr Nu k h
Q
∆
T h
theo A m ml
m
k
Nu
m
De
n Qfin
Q
m
ax
Efficien
cy(%) QFin
Qunfi
n
Effectiv
eness
V=40V
2
0.
27 58.400
49.3
50
17.
885
65
11,18
2.15
0.
69
80
7
31.
14
71
3
0.0
28
21
8.7
88
0
1
0.
8
18
.1
00
12.5
380
17.
31
96
73.
447
6
3.6
724
2.
07
23
5.23
94
5.
23
53
0.10
06
0.
41
83 24.0483
7.510
5
9.875
7 0.7605
4
0.
27 53.425
46.6
63
17.
619
59
22,70
2.01
0.
69
83
3
44.
38
57
1
0.0
28
03
12.
43
97
1
0.
8
13
.5
25
16.7
792
17.
31
96
87.
677
9
4.3
839
2.
45
73
6.06
20
6.
06
08
0.11
92
0.
59
21 20.1334
7.944
2
11.45
37 0.6936
6
0.
27 50.050
44.4
75
17.
403
03
34,47
6.76
0.
69
85
5
54.
70
40
7
0.0
27
87
15.
24
78
1
0.
8
11
.1
50
20.3
532
17.
31
96
97.
337
1
4.8
669
2.
71
31
6.61
99
6.
61
94
0.13
16
0.
72
57 18.1331
8.027
6
12.52
73 0.6408
8
0.
27 47.625
42.5
63
17.
213
69
46,47
4.64
0.
69
87
4
63.
51
90
5
0.0
27
74
17.
61
98
1
0.
8
10
.1
25
22.4
137
17.
31
96
104
.88
68
5.2
443
2.
90
95
7.05
59
7.
05
56
0.14
11
0.
83
86 16.8272
8.423
6
13.56
09 0.6212
10
0.
27 45.850
41.1
25
17.
071
38
58,57
7.59
0.
69
88
9
71.
31
67
4
0.0
27
64
19.
71
11
1
0.
8
9.
45
0
24.0
146
17.
31
96
111
.13
85
5.5
569
3.
07
17
7.41
69
7.
41
67
0.14
90
0.
93
82 15.8804
8.795
2
14.05
36 0.6258
12
0.
27 44.625
40.1
63
16.
976
09
70,68
7.67
0.
69
89
8
78.
34
61
1
0.0
27
57
21.
60
11
1
0.
8
8.
92
5
25.4
273
17.
31
96
116
.48
70
5.8
244
3.
21
17
7.72
57
7.
72
56
0.15
58
1.
02
81 15.1511
9.103
0
14.48
32 0.6285
14
0.
27 42.825
38.9
13
16.
855
60
83,05
8.45
0.
69
92
2
84.
93
48
4
0.0
27
47
23.
33
32
1
0.
8
7.
82
5
29.0
017
17.
31
96
121
.28
63
6.0
643
3.
33
20
8.00
28
8.
00
28
0.16
16
1.
11
06 14.5515
8.621
1
14.87
34 0.5796
V=45V
2
0.
32 65.800
56.5
00
18.
613
00
10,74
5.18
0.
69
67
0
30.
51
26
0
0.0
28
72
8.7
61
7
1
4.
4
18
.6
00
16.2
680
17.
31
96
72.
695
6
3.6
348
2.
08
75
5.19
59
5.
19
15
0.10
13
0.
41
70 24.2985
7.694
9
10.13
57 0.7592
4
0.
32 62.025
53.9
13
18.
349
08
21,79
9.46
0.
69
72
2
43.
47
13
0
0.0
28
53
12.
40
40
1
4.
4
16
.2
25
18.6
493
17.
31
96
86.
770
1
4.3
385
2.
47
59
6.00
96
6.
00
82
0.12
01
0.
59
04 20.3444
9.502
8
13.41
22 0.7085
6
0.
32 58.225
51.3
63
18.
088
98
33,16
9.38
0.
69
77
3
53.
63
57
2
0.0
28
36
15.
20
86
1
4.
4
13
.7
25
22.0
462
17.
31
96
96.
382
0
4.8
191
2.
73
29
6.56
48
6.
56
42
0.13
26
0.
72
39 18.3130
9.856
1
14.79
31 0.6663
8
0.
32 53.825
47.9
13
17.
743
34
45,08
7.35
0.
69
82
1
62.
54
78
7
0.0
28
11
17.
58
46
1
4.
4
11
.8
25
25.5
885
17.
31
96
104
.08
19
5.2
041
2.
92
61
7.00
94
7.
00
91
0.14
19
0.
83
69 16.9574
9.818
3
15.94
18 0.6159
10
0.
32 51.575
46.5
38
17.
607
21
56,79
4.91
0.
69
83
5
70.
20
50
5
0.0
28
02
19.
66
98
1
4.
4
10
.0
75
30.0
332
17.
31
96
110
.26
89
5.5
134
3.
08
95
7.36
67
7.
36
65
0.14
98
0.
93
62 16.0056
9.357
2
15.69
60 0.5962
12
0.
32 49.075
44.4
88
17.
404
26
68,94
8.63
0.
69
85
5
77.
36
04
4
0.0
27
87
21.
56
35
1
4.
4
9.
17
5
32.9
792
17.
31
96
115
.75
19
5.7
876
3.
22
65
7.68
33
7.
68
32
0.15
65
1.
02
63 15.2473
9.341
7
17.20
71 0.5429
14
0.
32 46.900
42.5
50
17.
212
45
81,33
6.47
0.
69
87
5
84.
03
08
8
0.0
27
74
23.
30
89
1
4.
4
8.
70
0
34.7
798
17.
31
96
120
.63
91
6.0
320
3.
34
63
7.96
55
7.
96
54
0.16
23
1.
10
94 14.6296
9.575
1
17.16
91 0.5577
V=50
2
0.
35 69.250
60.9
75
19.
072
10,48
6.37
0.
69
30.
12
0.0
29
8.7
46
1
7.
16
.5
22.2
190
17.
31
72.
238
3.6
119
2.
09
5.16
95
5.
16
0.10
18
0.
41 24.4532
6.834
7
8.878
9 0.7698

38 58
1
99
9
03 2 5 50 96 4 70 48 63
4
0.
35 61.950
56.2
25
18.
584
95
21,52
2.79
0.
69
67
6
43.
18
50
1
0.0
28
70
12.
39
23
1
7.
5
11
.4
50
32.1
157
17.
31
96
86.
483
9
4.3
242
2.
48
17
5.99
31
5.
99
17
0.12
04
0.
58
98 20.4118
6.699
7
11.64
41 0.5754
6
0.
35 58.775
53.5
38
18.
310
83
32,76
7.50
0.
69
72
9
53.
29
87
4
0.0
28
51
15.
19
42
1
7.
5
10
.4
75
35.1
049
17.
31
96
96.
078
7
4.8
039
2.
73
90
6.54
73
6.
54
67
0.13
29
0.
72
32 18.3708
7.515
1
12.84
20 0.5852
8
0.
35 55.325
50.9
63
18.
048
18
44,32
5.81
0.
69
78
1
62.
00
55
3
0.0
28
33
17.
56
45
1
7.
5
8.
72
5
42.1
461
17.
31
96
103
.62
96
5.1
815
2.
93
56
6.98
33
6.
98
30
0.14
24
0.
83
60 17.0314
7.236
1
13.26
96 0.5453
10
0.
35 53.125
48.3
63
17.
787
89
56,21
8.03
0.
69
81
6
69.
84
15
2
0.0
28
15
19.
65
72
1
7.
5
9.
52
5
38.6
062
17.
31
96
109
.98
30
5.4
992
3.
09
55
7.35
02
7.
35
00
0.15
01
0.
93
56 16.0473
8.840
7
15.40
74 0.5738
12
0.
35 50.450
45.8
25
17.
536
68
68,42
8.02
0.
69
84
2
77.
06
29
1
0.0
27
97
21.
55
28
1
7.
5
9.
25
0
39.7
540
17.
31
96
115
.52
91
5.7
765
3.
23
11
7.67
04
7.
67
03
0.15
67
1.
02
58 15.2767
9.413
4
17.91
09 0.5256
14
0.
35 49.125
44.3
63
17.
391
89
80,49
7.30
0.
69
85
6
83.
58
90
4
0.0
27
87
23.
29
24
1
7.
5
9.
52
5
38.6
062
17.
31
96
120
.32
16
6.0
161
3.
35
28
7.94
71
7.
94
71
0.16
26
1.
10
86 14.6682
10.47
57
16.60
71 0.6308
V=55V
2
0.
38 73.075
64.4
38
19.
435
94
10,29
0.22
0.
69
51
1
29.
83
69
7
0.0
29
27
8.7
33
5
2
0.
9
17
.2
75
25.4
222
17.
31
96
71.
886
3
3.5
943
2.
10
42
5.14
91
5.
14
43
0.10
21
0.
41
57 24.5737
7.123
7
9.237
1 0.7712
4
0.
38 67.600
60.6
50
19.
038
25
21,01
0.33
0.
69
58
7
42.
64
97
4
0.0
29
01
12.
37
08
2
0.
9
13
.9
00
31.5
948
17.
31
96
85.
946
3
4.2
973
2.
49
29
5.96
20
5.
96
05
0.12
09
0.
58
88 20.5398
8.119
2
13.37
62 0.6070
6
0.
38 62.975
56.7
38
18.
637
23
32,19
3.63
0.
69
66
5
52.
81
38
1
0.0
28
73
15.
17
43
2
0.
9
12
.4
75
35.2
038
17.
31
96
95.
640
6
4.7
820
2.
74
79
6.52
20
6.
52
13
0.13
33
0.
72
22 18.4551
8.938
2
15.83
44 0.5645
8
0.
38 58.725
53.1
13
18.
267
48
43,79
3.68
0.
69
73
8
61.
61
95
7
0.0
28
48
17.
54
79
2
0.
9
11
.2
25
39.1
241
17.
31
96
103
.30
66
5.1
653
2.
94
20
6.96
47
6.
96
43
0.14
27
0.
83
52 17.0847
9.300
7
17.15
14 0.5423
10
0.
38 54.700
50.2
00
17.
970
40
55,64
7.06
0.
69
79
6
69.
47
92
0
0.0
28
27
19.
64
45
2
0.
9
9.
00
0
48.7
964
17.
31
96
109
.69
74
5.4
849
3.
10
16
7.33
37
7.
33
35
0.15
04
0.
93
50 16.0891
8.348
1
16.41
79 0.5085
12
0.
38 51.225
47.6
13
17.
713
64
67,74
4.41
0.
69
82
4
76.
67
04
7
0.0
28
09
21.
53
89
2
0.
9
7.
22
5
60.7
845
17.
31
96
115
.23
46
5.7
617
3.
23
73
7.65
34
7.
65
33
0.15
70
1.
02
52 15.3158
7.347
9
15.66
20 0.4692
14
0.
38 48.725
45.3
63
17.
490
89
80,04
1.68
0.
69
84
6
83.
34
81
7
0.0
27
94
23.
28
36
2
0.
9
6.
72
5
65.3
038
17.
31
96
120
.14
81
6.0
074
3.
35
64
7.93
71
7.
93
70
0.16
28
1.
10
82 14.6894
7.393
4
16.38
09 0.4513
V=60V
2
0.
42 75.650
66.9
25
19.
697
13
10,15
3.77
0.
69
46
2
29.
63
14
2
0.0
29
44
8.7
24
9
2
5.
2
17
.4
50
30.3
452
17.
31
96
71.
638
3
3.5
819
2.
10
94
5.13
47
5.
12
99
0.10
24
0.
41
53 24.6593
7.188
8
10.21
68 0.7036
4
0.
42 72.275
60.8
88
19.
063
19
20,98
2.85
0.
69
58
2
42.
62
08
7
0.0
29
02
12.
36
95
2
5.
2
22
.7
75
23.2
502
17.
31
96
85.
917
2
4.2
959
2.
49
35
5.96
03
5.
95
89
0.12
10
0.
58
87 20.5467
13.30
18
17.52
16 0.7592
6
0.
42 67.150
54.5
75
18.
416
65
32,57
9.22
0.
69
70
9
53.
14
01
2
0.0
28
58
15.
18
76
2
5.
2
25
.1
50
21.0
546
17.
31
96
95.
935
7
4.7
968
2.
74
19
6.53
90
6.
53
84
0.13
30
0.
72
29 18.3983
18.03
55
24.59
71 0.7332
8
0.
42 64.475
51.3
38
18.
086
43
44,23
2.07
0.
69
77
3
61.
93
77
1
0.0
28
35
17.
56
16
2
5.
2
26
.2
75
20.1
531
17.
31
96
103
.57
29
5.1
786
2.
93
67
6.98
00
6.
97
97
0.14
24
0.
83
58 17.0408
21.78
75
28.35
90 0.7683

10
0.
42 60.600
48.7
50
17.
826
25
56,09
7.05
0.
69
81
3
69.
76
50
4
0.0
28
17
19.
65
46
2
5.
2
23
.7
00
22.3
427
17.
31
96
109
.92
28
5.4
961
3.
09
68
7.34
67
7.
34
65
0.15
02
0.
93
55 16.0561
21.99
45
30.06
84 0.7315
12
0.
42 58.725
47.5
13
17.
703
74
67,78
2.30
0.
69
82
5
76.
69
22
7
0.0
28
09
21.
53
97
2
5.
2
22
.4
25
23.6
131
17.
31
96
115
.25
10
5.7
625
3.
23
69
7.65
44
7.
65
42
0.15
70
1.
02
52 15.3136
22.80
73
31.12
17 0.7328
14
0.
42 55.150
45.4
25
17.
497
08
80,01
3.37
0.
69
84
6
83.
33
31
9
0.0
27
94
23.
28
31
2
5.
2
19
.4
50
27.2
248
17.
31
96
120
.13
73
6.0
069
3.
35
66
7.93
65
7.
93
64
0.16
28
1.
10
82 14.6907
21.38
27
30.45
24 0.7022
V=65
2
0.
45 78.675
68.9
38
19.
908
44
10,04
5.99
0.
69
42
1
29.
46
80
6
0.0
29
59
8.7
18
3
2
9.
3
19
.4
75
31.5
597
17.
31
96
71.
440
5
3.5
720
2.
11
36
5.12
33
5.
11
83
0.10
26
0.
41
49 24.7280
8.017
0
11.36
17 0.7056
4
0.
45 75.800
63.1
50
19.
300
75
20,72
4.58
0.
69
53
7
42.
34
85
8
0.0
29
18
12.
35
75
2
9.
3
25
.3
00
24.2
935
17.
31
96
85.
642
3
4.2
821
2.
49
91
5.94
44
5.
94
29
0.12
12
0.
58
82 20.6128
14.76
23
18.84
67 0.7833
6
0.
45 72.750
57.8
75
18.
753
25
31,99
4.45
0.
69
64
3
52.
64
44
5
0.0
28
81
15.
16
75
2
9.
3
29
.7
50
20.6
597
17.
31
96
95.
487
2
4.7
744
2.
75
11
6.51
31
6.
51
25
0.13
34
0.
72
19 18.4848
21.30
61
26.06
86 0.8173
8
0.
45 69.900
54.6
00
18.
419
20
43,43
2.94
0.
69
70
8
61.
35
65
3
0.0
28
58
17.
53
69
2
9.
3
30
.6
00
20.0
858
17.
31
96
103
.08
59
5.1
543
2.
94
64
6.95
19
6.
95
16
0.14
29
0.
83
47 17.1213
25.33
83
30.80
34 0.8226
10
0.
45 66.850
52.3
75
18.
192
25
54,96
8.46
0.
69
75
3
69.
03
99
2
0.0
28
43
19.
62
55
2
9.
3
28
.9
50
21.2
306
17.
31
96
109
.35
00
5.4
675
3.
10
84
7.31
36
7.
31
34
0.15
08
0.
93
41 16.1402
26.82
69
33.35
99 0.8042
12
0.
45 63.050
50.1
75
17.
967
85
66,78
5.95
0.
69
79
7
76.
11
62
3
0.0
28
27
21.
51
98
2
9.
3
25
.7
50
23.8
689
17.
31
96
114
.81
73
5.7
409
3.
24
61
7.62
93
7.
62
92
0.15
74
1.
02
42 15.3715
26.16
48
34.54
76 0.7574
14
0.
45 60.375
48.5
38
17.
805
21
78,62
8.66
0.
69
81
5
82.
59
67
0
0.0
28
16
23.
25
73
2
9.
3
23
.6
75
25.9
609
17.
31
96
119
.60
52
5.9
803
3.
36
78
7.90
58
7.
90
57
0.16
33
1.
10
69 14.7560
25.99
86
35.14
07 0.7398
V=70V
2
0.
49 82.000
71.1
00
20.
137
70
9,931
.62
0.
69
37
8
29.
29
37
5
0.0
29
75
8.7
14
6
3
4.
3
21
.8
00
33.0
615
17.
31
96
71.
228
9
3.5
614
2.
11
90
5.11
10
5.
10
60
0.10
29
0.
41
48 24.8020
8.970
3
10.69
85 0.8385
4
0.
49 79.100
65.3
00
19.
526
50
20,48
4.98
0.
69
49
4
42.
09
44
0
0.0
29
33
12.
34
67
3
4.
3
27
.6
00
26.1
138
17.
31
96
85.
384
9
4.2
692
2.
50
44
5.92
96
5.
92
80
0.12
15
0.
58
76 20.6751
16.09
02
18.59
70 0.8652
6
0.
49 75.400
59.7
00
18.
939
40
31,67
9.99
0.
69
60
6
52.
37
59
5
0.0
28
94
15.
15
71
3
4.
3
31
.4
00
22.9
535
17.
31
96
95.
243
4
4.7
622
2.
75
62
6.49
90
6.
49
84
0.13
37
0.
72
14 18.5321
22.47
23
26.76
63 0.8396
8
0.
49 72.900
56.6
00
18.
623
20
42,95
7.17
0.
69
66
8
61.
00
78
9
0.0
28
72
17.
52
27
3
4.
3
32
.6
00
22.1
086
17.
31
96
102
.79
26
5.1
396
2.
95
24
6.93
50
6.
93
46
0.14
32
0.
83
40 17.1702
26.97
24
31.35
75 0.8602
10
0.
49 69.925
54.4
13
18.
400
08
54,34
7.60
0.
69
71
2
68.
63
55
6
0.0
28
57
19.
60
84
3
4.
3
31
.0
25
23.2
309
17.
31
96
109
.02
93
5.4
515
3.
11
48
7.29
51
7.
29
49
0.15
11
0.
93
33 16.1877
28.72
47
34.25
67 0.8385
12
0.
49 66.250
52.2
75
18.
182
05
65,99
9.16
0.
69
75
5
75.
65
13
8
0.0
28
42
21.
49
96
3
4.
3
27
.9
50
25.7
867
17.
31
96
114
.46
62
5.7
233
3.
25
30
7.60
90
7.
60
89
0.15
78
1.
02
33 15.4186
28.37
35
34.92
12 0.8125
14
0.
49 62.150
49.9
25
17.
942
58
78,02
6.70
0.
69
80
1
82.
27
44
8
0.0
28
25
23.
24
64
3
4.
3
24
.4
50
29.4
781
17.
31
96
119
.37
17
5.9
686
3.
37
28
7.89
23
7.
89
22
0.16
36
1.
10
64 14.7849
26.83
72
33.47
79 0.8016

3.3.3 Aluminium with rectangular perforations
V
el
oc
ity
C
ur
re
nt Ts Tf v Re Pr Nu k h
Q
∆
T
h
the
o A m ml
m
k
Nu
m
De
n Qfin
Q
m
ax
Efficien
cy(%) QFin
Qunfi
n
Effective
ness
V=40V
2
0.
28 54.000
47.1
50
17.
667
85
11,32
0.00
0.6
98
29
31.
341
81
0.0
28
06
8.7
94
7
1
1.
2
13
.7
00
17.
178
4
17.
31
96
73.
676
8
3.6
838
2.
06
74
5.25
27
5.
24
86
0.10
03
0.
41
86 23.9731
6.446
1
11.15
12 0.5781
4
0.
28 52.200
46.0
50
17.
558
95
22,78
0.41
0.6
98
40
44.
463
59
0.0
27
98
12.
44
25
1
1.
2
12
.3
00
19.
133
6
17.
31
96
87.
754
8
4.3
877
2.
45
57
6.06
65
6.
06
52
0.11
91
0.
59
22 20.1157
8.187
8
14.97
76 0.5467
6
0.
28 50.400
44.6
50
17.
420
35
34,44
2.48
0.6
98
54
54.
676
40
0.0
27
89
15.
24
68
1
1.
2
11
.5
00
20.
464
7
17.
31
96
97.
312
5
4.8
656
2.
71
36
6.61
85
6.
61
80
0.13
16
0.
72
57 18.1377
9.380
6
17.61
92 0.5324
8
0.
28 48.775
43.1
38
17.
270
61
46,32
1.46
0.6
98
69
63.
412
54
0.0
27
78
17.
61
58
1
1.
2
11
.2
75
20.
873
0
17.
31
96
104
.79
88
5.2
399
2.
91
13
7.05
08
7.
05
05
0.14
12
0.
83
84 16.8414
10.62
61
19.69
71 0.5395
10
0.
28 46.700
41.5
50
17.
113
45
58,43
3.57
0.6
98
85
71.
227
57
0.0
27
67
19.
70
76
1
1.
2
10
.3
00
22.
848
9
17.
31
96
111
.06
90
5.5
534
3.
07
31
7.41
29
7.
41
27
0.14
90
0.
93
80 15.8903
10.85
99
20.34
91 0.5337
12
0.
28 45.250
40.4
75
17.
007
03
70,55
9.08
0.6
98
95
78.
273
65
0.0
27
59
21.
59
82
1
1.
2
9.
55
0
24.
643
3
17.
31
96
116
.43
31
5.8
217
3.
21
28
7.72
26
7.
72
25
0.15
58
1.
02
80 15.1581
11.03
51
21.26
13 0.5190
14
0.
28 43.625
39.3
13
16.
894
00
82,86
9.66
0.6
99
14
84.
835
03
0.0
27
50
23.
33
33
1
1.
2
8.
62
5
27.
286
2
17.
31
96
121
.21
50
6.0
608
3.
33
39
7.99
87
7.
99
86
0.16
17
1.
11
06 14.5601
10.76
69
21.34
65 0.5044
V=45V
2
0.
32 62.275
54.7
38
18.
433
23
10,84
9.97
0.6
97
05
30.
666
19
0.0
28
59
8.7
68
0
1
4.
4
15
.0
75
20.
071
9
17.
31
96
72.
878
4
3.6
439
2.
08
37
5.20
65
5.
20
21
0.10
11
0.
41
73 24.2372
7.071
5
13.55
66 0.5216
4
0.
32 55.100
50.4
50
17.
995
90
22,22
7.29
0.6
97
91
43.
910
31
0.0
28
29
12.
42
29
1
4.
4
9.
30
0
32.
536
0
17.
31
96
87.
207
1
4.3
604
2.
46
72
6.03
48
6.
03
35
0.11
97
0.
59
13 20.2422
6.181
0
14.82
11 0.4170
6
0.
32 50.700
47.5
00
17.
702
50
33,89
3.52
0.6
98
25
54.
231
55
0.0
28
09
15.
23
09
1
4.
4
6.
40
0
47.
278
8
17.
31
96
96.
915
8
4.8
458
2.
72
19
6.59
56
6.
59
50
0.13
20
0.
72
49 18.2120
5.215
1
14.91
18 0.3497
8
0.
32 48.725
45.7
63
17.
530
49
45,63
4.78
0.6
98
42
62.
932
89
0.0
27
96
17.
59
82
1
4.
4
5.
92
5
51.
069
1
17.
31
96
104
.40
17
5.2
201
2.
91
94
7.02
79
7.
02
76
0.14
16
0.
83
76 16.9054
5.578
4
16.28
80 0.3425
10
0.
32 46.050
43.7
75
17.
333
73
57,69
1.00
0.6
98
62
70.
766
04
0.0
27
82
19.
69
01
1
4.
4
4.
55
0
66.
502
1
17.
31
96
110
.70
86
5.5
354
3.
08
04
7.39
21
7.
39
19
0.14
94
0.
93
72 15.9421
4.793
1
16.01
20 0.2993
12
0.
32 44.175
42.0
38
17.
161
71
69,92
3.09
0.6
98
80
77.
914
29
0.0
27
70
21.
58
43
1
4.
4
4.
27
5
70.
780
0
17.
31
96
116
.16
55
5.8
083
3.
21
81
7.70
72
7.
70
71
0.15
61
1.
02
73 15.1930
4.936
6
16.39
76 0.3011
14
0.
32 42.625
40.7
63
17.
035
49
82,18
1.39
0.6
98
92
84.
473
39
0.0
27
61
23.
32
60
1
4.
4
3.
72
5
81.
230
8
17.
31
96
120
.95
64
6.0
478
3.
34
00
7.98
38
7.
98
37
0.16
20
1.
11
02 14.5912
4.648
6
16.34
80 0.2844
V=50
2
0.
36 67.450
60.0
75
18.
977
88
10,53
8.59
0.6
95
99
30.
207
52
0.0
28
97
8.7
49
7
1
8.
0
14
.7
50
25.
642
8
17.
31
96
72.
331
3
3.6
166
2.
09
51
5.17
48
5.
17
02
0.10
17
0.
41
64 24.4216
6.904
6
8.425
9 0.8194
4
0.
36 62.025
56.2
63
18.
588
78
21,51
8.36
0.6
96
75
43.
180
41
0.0
28
70
12.
39
21
1
8.
0
11
.5
25
32.
818
3
17.
31
96
86.
479
3
4.3
240
2.
48
18
5.99
28
5.
99
14
0.12
04
0.
58
98 20.4129
7.640
8
11.93
36 0.6403
6
0.
36 58.575
53.4
38
18.
300
63
32,78
5.77
0.6
97
31
53.
314
10
0.0
28
50
15.
19
49
1
8.
0
10
.2
75
36.
810
8
17.
31
96
96.
092
6
4.8
046
2.
73
87
6.54
81
6.
54
75
0.13
28
0.
72
32 18.3682
8.352
8
13.65
71 0.6116
8
0.
36 56.150
51.3
75
18.
090
25
44,22
2.72
0.6
97
73
61.
930
94
0.0
28
36
17.
56
13
1
8.
0
9.
55
0
39.
605
3
17.
31
96
103
.56
73
5.1
784
2.
93
68
6.97
97
6.
97
94
0.14
24
0.
83
58 17.0417
8.972
5
14.28
08 0.6283
10
0.
36 53.150
48.3
75
17.
789
13
56,21
4.12
0.6
98
16
69.
839
05
0.0
28
15
19.
65
71
1
8.
0
9.
55
0
39.
605
3
17.
31
96
109
.98
11
5.4
991
3.
09
56
7.35
01
7.
34
99
0.15
01
0.
93
56 16.0475
10.04
33
17.35
23 0.5788
12
0.
36 51.425
46.3
13
17.
584
94
68,24
0.22
0.6
98
37
76.
955
30
0.0
28
00
21.
54
89
1
8.
0
10
.2
25
36.
990
8
17.
31
96
115
.44
84
5.7
724
3.
23
28
7.66
58
7.
66
56
0.15
68
1.
02
56 15.2874
11.78
81
19.36
82 0.6086

14
0.
36 48.675
44.1
38
17.
369
61
80,60
0.53
0.6
98
59
83.
643
52
0.0
27
85
23.
29
44
1
8.
0
9.
07
5
41.
678
3
17.
31
96
120
.36
08
6.0
180
3.
35
20
7.94
94
7.
94
93
0.16
26
1.
10
87 14.6634
11.30
97
23.55
41 0.4802
V=55V
2
0.
39 73.100
64.4
50
19.
437
25
10,28
9.52
0.6
95
11
29.
835
92
0.0
29
27
8.7
33
4
2
1.
5
17
.3
00
26.
053
5
17.
31
96
71.
885
0
3.5
943
2.
10
42
5.14
90
5.
14
42
0.10
21
0.
41
57 24.5742
8.083
2
11.54
08 0.7004
4
0.
39 68.450
61.0
75
19.
082
88
20,96
1.20
0.6
95
79
42.
598
11
0.0
29
04
12.
36
85
2
1.
5
14
.7
50
30.
557
6
17.
31
96
85.
894
2
4.2
947
2.
49
40
5.95
90
5.
95
75
0.12
10
0.
58
87 20.5522
9.760
3
16.27
81 0.5996
6
0.
39 62.500
56.6
00
18.
623
20
32,21
7.88
0.6
96
68
52.
834
39
0.0
28
72
15.
17
51
2
1.
5
11
.8
00
38.
197
0
17.
31
96
95.
659
3
4.7
830
2.
74
75
6.52
30
6.
52
24
0.13
33
0.
72
23 18.4515
9.580
0
14.53
24 0.6592
8
0.
39 59.200
53.3
50
18.
291
70
43,73
5.68
0.6
97
33
61.
577
35
0.0
28
49
17.
54
62
2
1.
5
11
.7
00
38.
523
5
17.
31
96
103
.27
12
5.1
636
2.
94
27
6.96
26
6.
96
23
0.14
27
0.
83
51 17.0906
10.98
30
16.80
31 0.6536
10
0.
39 56.425
51.0
63
18.
058
38
55,37
5.97
0.6
97
79
69.
304
04
0.0
28
33
19.
63
69
2
1.
5
10
.7
25
42.
025
6
17.
31
96
109
.55
90
5.4
779
3.
10
43
7.32
57
7.
32
55
0.15
06
0.
93
46 16.1094
11.26
74
16.70
41 0.6745
12
0.
39 53.350
48.6
75
17.
818
83
67,34
4.51
0.6
98
13
76.
439
97
0.0
28
17
21.
53
10
2
1.
5
9.
35
0
48.
205
9
17.
31
96
115
.06
12
5.7
531
3.
24
10
7.64
34
7.
64
33
0.15
72
1.
02
48 15.3389
10.77
04
16.93
31 0.6361
14
0.
39 50.950
46.4
75
17.
601
03
79,54
0.82
0.6
98
35
83.
082
58
0.0
28
01
23.
27
41
2
1.
5
8.
95
0
50.
360
3
17.
31
96
119
.95
65
5.9
978
3.
36
04
7.92
60
7.
92
60
0.16
30
1.
10
77 14.7128
11.14
42
20.66
98 0.5392
V=60V
2
0.
43 75.750
66.9
75
19.
702
38
10,15
1.06
0.6
94
61
29.
627
33
0.0
29
45
8.7
24
7
2
5.
8
17
.5
50
30.
890
6
17.
31
96
71.
633
3
3.5
817
2.
10
95
5.13
44
5.
12
96
0.10
24
0.
41
53 24.6611
8.191
9
11.29
59 0.7252
4
0.
43 70.425
59.9
63
18.
966
18
21,09
0.18
0.6
96
01
42.
733
52
0.0
28
96
12.
37
45
2
5.
8
20
.9
25
25.
908
3
17.
31
96
86.
030
6
4.3
015
2.
49
12
5.96
69
5.
96
54
0.12
09
0.
58
90 20.5196
13.85
31
19.79
49 0.6998
6
0.
43 67.375
54.6
88
18.
428
13
32,55
8.93
0.6
97
06
53.
123
00
0.0
28
59
15.
18
69
2
5.
8
25
.3
75
21.
364
8
17.
31
96
95.
920
2
4.7
960
2.
74
22
6.53
81
6.
53
75
0.13
30
0.
72
28 18.4012
20.61
71
27.29
99 0.7552
8
0.
43 64.150
51.2
25
18.
074
95
44,26
0.15
0.6
97
76
61.
958
03
0.0
28
35
17.
56
25
2
5.
8
25
.8
50
20.
972
2
17.
31
96
103
.58
99
5.1
795
2.
93
63
6.98
10
6.
98
07
0.14
24
0.
83
59 17.0380
24.28
85
34.01
32 0.7141
10
0.
43 60.825
48.8
63
17.
837
39
56,06
2.02
0.6
98
11
69.
742
88
0.0
28
18
19.
65
38
2
5.
8
23
.9
25
22.
659
6
17.
31
96
109
.90
53
5.4
953
3.
09
72
7.34
57
7.
34
55
0.15
02
0.
93
54 16.0586
25.15
66
34.80
39 0.7228
12
0.
43 58.375
47.3
38
17.
686
41
67,84
8.69
0.6
98
27
76.
730
47
0.0
28
07
21.
54
10
2
5.
8
22
.0
75
24.
558
6
17.
31
96
115
.27
97
5.7
640
3.
23
63
7.65
60
7.
65
59
0.15
70
1.
02
52 15.3098
25.44
02
37.80
02 0.6730
14
0.
43 54.500
45.1
00
17.
464
90
80,16
0.78
0.6
98
49
83.
411
20
0.0
27
92
23.
28
59
2
5.
8
18
.8
00
28.
836
7
17.
31
96
120
.19
35
6.0
097
3.
35
54
7.93
97
7.
93
97
0.16
27
1.
10
83 14.6838
23.42
10
34.13
48 0.6861
V=65
2
0.
46 77.475
60.5
88
19.
031
69
10,50
8.79
0.6
95
88
30.
163
30
0.0
29
00
8.7
47
7
2
9.
9
33
.7
75
18.
602
0
17.
31
96
72.
278
3
3.6
139
2.
09
62
5.17
18
5.
16
72
0.10
18
0.
41
63 24.4396
15.80
68
19.79
65 0.7985
4
0.
46 73.000
56.0
00
18.
562
00
21,54
9.40
0.6
96
80
43.
212
63
0.0
28
68
12.
39
34
2
9.
9
34
.0
00
18.
478
9
17.
31
96
86.
511
6
4.3
256
2.
48
12
5.99
47
5.
99
33
0.12
04
0.
58
99 20.4053
22.54
36
28.97
51 0.7780
6
0.
46 69.800
53.5
50
18.
312
10
32,76
5.22
0.6
97
29
53.
296
82
0.0
28
51
15.
19
41
2
9.
9
32
.5
00
19.
331
8
17.
31
96
96.
077
0
4.8
038
2.
73
90
6.54
72
6.
54
66
0.13
29
0.
72
32 18.3712
26.41
88
34.22
25 0.7720
8
0.
46 66.600
51.6
00
18.
113
20
44,16
6.69
0.6
97
68
61.
890
36
0.0
28
37
17.
55
95
2
9.
9
30
.0
00
20.
942
8
17.
31
96
103
.53
34
5.1
767
2.
93
74
6.97
78
6.
97
74
0.14
25
0.
83
58 17.0473
28.18
31
36.82
59 0.7653
10
0.
46 63.275
49.7
38
17.
924
01
55,79
1.08
0.6
98
03
69.
571
24
0.0
28
24
19.
64
80
2
9.
9
27
.0
75
23.
205
3
17.
31
96
109
.77
00
5.4
885
3.
10
01
7.33
79
7.
33
77
0.15
04
0.
93
52 16.0784
28.46
04
39.10
35 0.7278
12
0.
46 60.625
48.2
63
17.
777
99
67,49
9.20
0.6
98
17
76.
529
22
0.0
28
14
21.
53
41
2
9.
9
24
.7
25
25.
410
8
17.
31
96
115
.12
84
5.7
564
3.
23
95
7.64
73
7.
64
72
0.15
71
1.
02
49 15.3299
28.48
50
39.74
65 0.7167
14
0.
46 58.550
47.1
75
17.
670
33
79,22
8.88
0.6
98
28
82.
916
74
0.0
28
06
23.
26
83
2
9.
9
22
.7
50
27.
616
8
17.
31
96
119
.83
67
5.9
918
3.
36
29
7.91
91
7.
91
91
0.16
31
1.
10
75 14.7275
28.32
04
38.59
05 0.7339

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