Heat Transfer By Eng.

Abdulraof Habibullah
1

heat transfer
Heat Transfer By Eng. Abdulraof Habibullah
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Introduction

It is well known that a hot plate of metal will cool faster when placed in front of a fan than when
exposed to still air. We say that the heat is convected away, and we call the process convection
heat transfer. The term convection provides the reader with an intuitive motion concerning the
heat-transfer process; however, this intuitive motion must be expanded to enable one to arrive at
anything like an adequate analytical treatment of the problem. For example, we know that the
velocity at which the air blows over the hot plate obviously influences the heat-transfer rate. But
does it influence the cooling in a linear way; i.e., if the velocity is doubled, will the heat-transfer
rate doubled? We should suspect that the heat transfer rate might be different if we cooled the
plate with water instead of air, but, again, how much difference would there be? These questions
may be answered with the aid of some rather basic analyses presented in later chapters.
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CONVECTION
Convection: The mode of energy transfer between a solid surface and the adjacent liquid or gas
that is in motion, and it involves the combined effects of conduction and fluid motion.
The faster the fluid motion, the greater the convection heat transfer.
In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid
is by pure conduction.
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CONVECTION
Forced convection: If the fluid is forced to flow over the surface by external means such as a
fan, pump, or the wind.
Natural (or free) convection: If the fluid motion is caused by buoyancy forces that are induced
by density differences due to the variation of temperature in the fluid.

The cooling of a boiled egg by

forced and natural convection.

Heat transfer processes that involve change of phase of a fluid are also considered to be
convection because of the fluid motion induced during the process, such as the rise of the
vapor bubbles during boiling or the fall of the liquid droplets during condensation.
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Newton s law of cooling

Regardless of the reason for the motion in the fluid, whether forced or natural, we call this
mechanism convective heat transfer

h convection heat transfer coefficient, W/m2 C

As the surface area through which convection heat transfer takes place
Ts the surface temperature
T the temperature of the fluid sufficiently far from the surface.

Note that this equation only serves to define this heat transfer coefficient h, and we must have
some way of knowing its value to use the equation for the heat flux. Later, we ll learn about
correlations that are used to calculate h values of in a variety of flow situations.
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Convective Heat Transfer Coefficient

The convection heat transfer coefficient h is not a property

of the fluid.

It is an experimentally determined parameter whose value

depends on all the variables influencing convection such as

- the surface geometry

- the nature of fluid motion
- the properties of the fluid
- the bulk fluid velocity
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Thermal resistance in convective heat transfer

For the present h may be considered as a constant in a given problem. From Newton's Law
of Cooling, we see that the thermal resistance between the fluid and the wall is
Heat Transfer By Eng. Abdulraof Habibullah
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THE OVERALL HEAT-TRANSFER COEFFICIENT

Consider the plane wall shown in the Figure exposed to a hot fluid A on one side and a cooler
fluid B on the other side. The heat transfer is expressed by

The heat-transfer process may be represented by the resistance

network as shown in the Figure, and the overall heat transfer is
calculated as the ratio of the overall temperature difference to
the sum of the thermal resistances
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Example 1

A house wall may be approximated as two 1.2 cm layers of fiber insulating board (k = 0.038
W/mK), an 8.0 cm layer of loosely packed asbestos (k = 0.16 W/mK), and a 10 cm layer of
common brick (k = 0.72 W/mK). Assuming convection heat-transfer coefficients of 12W/m2
oC on both sides of the wall, calculate the overall heat-transfer coefficient for this
arrangement.
Heat Transfer By Eng. Abdulraof Habibullah
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Class work

An insulation system is to be selected for a furnace wall at 1000 oC using first a layer of mineral
wool blocks (km=0.09 W/m oC) followed by fiberglass boards (kf=0.042 W/m oC) . The outside of
the insulation is exposed to an environment with h=15 W/m2 oC and T =40 oC. calculate the
thickness of each insulating material such that the interface temperature is not greater than 400 oC
and the outside temperature is not greater than 55 oC. What is the heat loss in this wall in watts
per square meter? [q/A= 225 W/m2, xm=0.24 m, xf=0.0644 m]

[Li= 0.195 m]
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Homework # 2

The rear window of an automobile is defogged by passing warm air at 40 C over its inner
surface, and the associated convection coefficient is 30 W/m2 K. Under conditions for which the
outside ambient air temperature is -10 C and the associated convection coefficient is 65 W/m2 K,
what are the inner and outer surface temperatures of the window? The window glass is 4 mm
thick and the thermal conductivity of it k= 1.4 W/m K [Ti=7.73 oC, To= 4.89 oC]

The rear window of an automobile is defogged by attaching a thin, transparent, film-type heating
element to its inner surface. By electrically heating this element, a uniform heat flux may be
established at the inner surface. What is the electrical power that must be provided per unit
window area to maintain an inner surface temperature of 15 C when the interior air temperature
and convection coefficient are 25 C and 10 W/m2 K and the exterior (ambient) air temperature
and convection coefficient are -10 C and 65 W/m2 K? The window glass is 4 mm thick and the
thermal conductivity of it k= 1.4 W/m K.
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Cylinders with convective heat transfer boundary conditions

Consider a pipe containing an internal fluid at temperature TFi that is surrounded by an
external fluid at TFo.
Heat is convected from the internal fluid to the inside surface of the pipe.
It is then conducted through the pipe wall. Finally, it is convected from the outer surface of
the pipe to the surrounding fluid.
In cylindrical coordinates Newton's Law of Cooling at the inner surface is written:

ro

k ri
TFi , hi TFo , ho
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For steady conditions, this must be the same as the heat transfer rate through the pipe wall and
the heat transfer rate to the surrounding fluid. Thus, with

ro

ri
k
TFi , hi TFo , ho
Heat Transfer By Eng. Abdulraof Habibullah
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ro

ri
k
TFi , hi TFo , ho
Heat Transfer By Eng. Abdulraof Habibullah
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THE OVERALL HEAT-TRANSFER COEFFICIENT

Consider the plane wall shown in the Figure exposed to a hot fluid A on one side and a cooler
fluid B on the other side. The heat transfer is expressed by
Heat Transfer By Eng. Abdulraof Habibullah
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The heat-transfer process may be represented by the resistance network in the Figure, and the
overall heat transfer is calculated as the ratio of the overall temperature difference to the sum of
the thermal resistances
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The overall heat transfer by combined conduction and convection is frequently expressed in
terms of an overall heat-transfer coefficient U, defined by the relation

where A is some suitable area for the heat flow.

The overall heat-transfer coefficient would be:
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Example 1

Water flows at 50 oC inside a 2.5-cm-inside-diameter tube such that hi =3500 W/m2 oC. The tube
has a wall thickness of 0.8 mm with a thermal conductivity of 16 W/m oC. The outside of the
tube loses heat by free convection with ho =7.6 W/m2 oC. Calculate the overall heat-transfer
coefficient and heat loss per unit length to surrounding air at 20 oC.

ro

ri
k
TFi , hi TFo , ho
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Class work

A 5 cm diameter steel pipe is covered with a 1 cm layer of insulating material having k = 0.22 W/m oC
followed by a 3 cm thick layer of another insulating material having k = 0.06 W/m oC . The entire
assembly is exposed to a convection surrounding condition of h = 60 W/m2 oC and T =15 oC. The
outside surface temperature of the steel pipe is 400 oC. Calculate the heat lost by the pipe-insulation
assembly for a pipe length of 20 m. Express in Watts.

A domestic hot water pipe is made of copper and has an internal diameter of 25 mm and a thickness of
2 mm. The pipe is exposed to atmospheric air at 10 oC and the hot water flowing inside the pipe is at 60
oC. The thermal conductivity of copper is k = 385 W/m K. The convective heat transfer coefficient h

has values of 3500 W/m2 K and 6.5 W/m 2K at the internal and external tube surfaces, respectively.
Calculate the overall thermal resistance between the hot water and the atmosphere for a unit length of
tube, based on the internal surface of the tube calculate the rate at which heat is lost to the atmosphere
per unit length of the tube.
[R = 1.693 K/W] [Ui = 0.591 W/K] [ = 29.5 W/m]
Heat Transfer By Eng. Abdulraof Habibullah
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HW# 2 Q2
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Heat Transfer from Extended Surfaces

The term extended surface is commonly used to depict an important special case involving
heat transfer by conduction within a solid and heat transfer by convection (and/or radiation)
from the boundaries of the solid. Until now, we have considered heat transfer from the
boundaries of a solid to be in the same direction as heat transfer by conduction in the solid.
In contrast, for an extended surface, the direction of heat transfer from the boundaries is
perpendicular to the principal direction of heat transfer in the solid.
Although there are many different situations that involve such combined conduction
convection effects, the most frequent application is one in which an extended surface is
used specifically to enhance heat transfer between a solid and an adjoining fluid. Such an
extended surface is termed a fin
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Heat Transfer By Eng. Abdulraof Habibullah
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Heat Transfer from Extended Surfaces

Consider the plane wall of next Figure. If Ts is fixed,
there are two ways in which the heat transfer rate
may be increased. The convection coefficient h
could be increased by increasing the fluid velocity,
and/or the fluid temperature T could be reduced.
However, there are many situations for which
increasing h to the maximum possible value is either
insufficient to obtain the desired heat transfer rate or the associated costs are prohibitive. Such costs
are related to the blower or pump power requirements needed to increase h through increased fluid
motion. Moreover, the second option of reducing T is often impractical. however, we see that there
exists a third option. That is, the heat transfer rate may be increased by increasing the surface area
across which the convection occurs. This may be done by employing fins that extend from the wall
into the surrounding fluid. The thermal conductivity of the fin material can have a strong effect on
the temperature distribution along the fin and therefore influences the degree to which the heat
transfer rate is enhanced.
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Heat Transfer from Extended Surfaces

b
Typical application areas of Fins are:
Radiators for automobiles
Air-cooling of cylinder heads of Internal Combustion engines (e.g., scooters, motorcycles,
aircraft engines etc.), air compressors etc.
Economizers of steam power plants
Heat exchangers of a wide variety, used in different industries
Cooling of electric motors, transformers etc.
Cooling of electronic equipment, chips,
I.C. boards etc.
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Heat Transfer from Extended Surfaces

Fin configurations.
(a) Straight fin of uniform cross
section.
(b) Straight fin of nonuniform cross
section.
(c) Annular fin.
(d) Pin fin.
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Heat Transfer from Extended Surfaces

As engineers we are primarily interested in knowing the extent to which particular extended
surfaces or fin arrangements could improve heat transfer from a surface to the surrounding fluid. To
determine the heat transfer rate associated with a fin, we must first obtain the temperature
distribution along the fin. As we have done for previous systems, we begin by performing an energy
balance on an appropriate differential element. Consider the extended surface of figure. The
analysis is simplified if certain assumptions are made. We choose to assume one-dimensional
conditions in the longitudinal (x-) direction, even though conduction within the fin is two-
dimensional.
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Heat Transfer from Extended Surfaces

The rate at which energy is convicted to the fluid from any point on the fin surface must be
balanced by the net rate at which energy reaches that point due to conduction in the transverse
(y-, z-) direction. However, in practice the fin is thin, and temperature changes in the transverse
direction within the fin are small compared with the temperature difference between the fin and
the environment. Hence, we may assume that the temperature is uniform across the fin thickness,
that is, it is only a function of x. We will consider steady-state conditions and also assume that
the thermal conductivity is constant, that radiation from the surface is negligible, that heat
generation effects are absent, and that the convection heat transfer coefficient h is uniform over
the surface.
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Heat Transfer from Extended Surfaces

where dAs is the surface area of the differential element. Substituting the foregoing rate
equations into the energy balance

To simplify the form of this equation, we transform the dependent variable by defining an
excess temperature as
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Heat Transfer from Extended Surfaces

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Heat Transfer from Extended Surfaces

O
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Fin Performance
Recall that fins are used to increase the heat transfer from a surface by increasing the
effective surface area. However, the fin itself represents a conduction resistance to heat
transfer from the original surface. For this reason, there is no assurance that the heat transfer
rate will be increased through the use of fins. An assessment of this matter may be made by
evaluating the fin effectiveness f. It is defined as the ratio of the fin heat transfer rate to the
heat transfer rate that would exist without the fin. Therefore

Hence the fin effectiveness may be interpreted as a ratio of thermal resistances, and to
increase f it is necessary to reduce the conduction/convection resistance of the fin. If the fin
is to enhance heat transfer, its resistance must not exceed that of the exposed base.
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Fin Performance
Another measure of fin thermal performance is provided by the fin efficiency f. The maximum
driving potential for convection is the temperature difference between the base (x=0) and the
fluid, ( b =Tb T ) Hence the maximum rate at which a fin could dissipate energy is the rate
that would exist if the entire fin surface were at the base temperature. However, since any fin is
characterized by a finite conduction resistance, a temperature gradient must exist along the fin
and the preceding condition is an idealization. A logical definition of fin efficiency is therefore

s
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Fin Performance
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Efficiency of straight fins (rectangular, triangular, and parabolic profiles)

ix s
I
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Efficiency of annular fins of rectangular profile

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eaggooeta
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Example 1

A very long rod 5 mm in diameter has one end maintained at 100 C. The surface of the rod is
exposed to ambient air at 25 with a convection heat transfer coefficient of 100 W/m2 .
Determine the temperature distributions along rods constructed from pure copper k= 398 W/m

Calculate the effectiveness and the efficiency of the fin?

Heat Transfer By Eng. Abdulraof Habibullah
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O 2

Gt
Example 2
A circumferential fin of rectangular profile has a thickness of 0.7mm and is installed on a tube
having a diameter of 3 cm that is maintained at a temperature of 200 C. The length of the fin is
2 cm and the fin material is copper. Calculate the heat lost by the fin to a surrounding
convection environment at 100 C with a convection heat-transfer coefficient of 524 W/m2 C.
0
r1= 0.015m f= 0.55
r2= r1+L = 0.015+ 0.02=0.035 m I
r2c= r2+t/2 = 0.035+ 0.00035 = 0.03535 m Qf = f hA b

Lc=L+t/2 = 0.02+0.00035 = 0.02035 m Qf = 0.55 524 A (200-100)

r2c/r1=0.03535/0.015= 2.357 = 186 W

Ap=Lct=0.02035*0.0007= 0.14 10-4 m2

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