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MODULE 1
HEAT TRANSFER
Course Objectives
• To cover the basic principles of heat transfer.
• To present a wealth of real-world engineering applications to give students a feel for engineering
practice.
• To develop an intuitive understanding of the subject matter by emphasizing the physics and physical
arguments.
Topics
• Introduction to Heat Transfer
• Modes of Heat Transfer
• Convection
• Conduction
• Radiation
• Conduction through multilayered plane wall
• Conduction through cylindrical pipes
• Conduction through multilayered cylindrical pipes
• Heat transfer from fluid to fluid separated by composite plane wall
• Heat transfer from fluid to fluid through an insulated cylindrical pipes
• Overall Coefficient of heat transfer
• Heat Transfer Equipment or Heat Exchangers
• Log Mean Temperature Difference (LMTD)
• Arithmetic Mean Temperature Difference (AMTD)
• Design of Surface Condensers
Introduction
This course is an introduction to the principal concepts and methods of heat transfer. The objectives of this
integrated subject are to develop the fundamental principles and laws of heat transfer and to explore the
implications of these principles for system behavior; to formulate the models necessary to study, analyze and
design heat transfer systems through the application of these principles; to develop the problem-solving skills
essential to good engineering practice of heat transfer in real-world application
Objectives
In this lecture you will learn the following
• The science of thermodynamics deals with the amount of heat transfer as a system undergoes a process
from one equilibrium state to another, and makes no reference to how long the process will take. But
in engineering, we are often interested in the rate of heat transfer, which is the topic of the science of
heat transfer.
• The objective of this lecture is to extend the thermodynamic analysis through study of the modes of
heat transfer and through development of relations to calculate heat transfer rates.
MODES OF HEAT TRANSFER : There are three modes of heat transfer namely conduction, convection
and radiation.
• Conduction : Conduction refers to the heat transfer that occurs across the medium. Medium can be
solid or a fluid.
• Convection : Convection refers to the heat transfer that will occur between a surface and a moving
fluid when they are at different temperatures.
• Radiation : In radiation, in the absence of intervening medium, there is net heat transfer between two
surfaces at different temperatures in the form of electromagnetic waves.
PHYSICAL ORIGINS AND RATE EQUATIONS:
It is important to understand the physical mechanisms which underlie the heat transfer modes and that we are
able to use the rate equations that quantify the amount of energy being transferred per unit time.
Conduction:
It is the transfer of heat from one point to another point within a body or the transfer of heat from one point of
a body to another point of another body , when they are in physical contact with each other.
Conduction can be imagined as a atomic or molecular activity which involves the transfer of energy from the
more energetic to the less energetic particles of a substance due to interactions between the particles.
From Fourier’s Law: The conductive heat flow through a material varies directly as the product of the surface
area A and the temperature gradient dt/dx. (where negative sign is used because, temperature decreases in the
direction of heat flow.
L
t
kA
Q
Kelvin
in
)
T
-
T
(
T
T
t
but
t
t
t
L
x
t
kA
x
Q
dt
kA
dx
Q
kAdt
Qdx
dx
dt
kA
Q
dx
dt
A
-
Q
1
2
1
2

−
=
=


=

−
=

=


−
=

−
=
−
=
−
=

 
)
W
K
or
W
C
,
resistance
(thermal
3
kA
L
R
potential)
re
(temperatu
2
t
t
t
1
R
t
Q
conduction
thermal
to
relating
R
V
I
conductor)
electric
an
(For
Law
s
Ohm'
From
kA
L
t
Q
2
1


→
=
→
−
=

−
→

−
=
=

−
=
Figure 1
Where
Q – conductive heat flow, Watts
A – surface area, m
L – thickness, m
R – thermal resistance,
W
K
or
W
C 

k – thermal conductivity,
K
m
W
or
C
m
W
−

−
Thermal Circuit Diagram
Convection
It is the transfer of heat from one point to another point with in a fluid (Liquid or Gas)
Natural convection results from the tendency of most fluids to expand when heated—i.e., to become less
dense and to rise as a result of the increased buoyancy. Circulation caused by this effect accounts for the
uniform heating of water in a kettle or air in a heated room: the heated molecules expand the space they move
in through increased speed against one another, rise, and then cool and come closer together again, with
increase in density and a resultant sinking.
Forced convection involves the transport of fluid by methods other than that resulting from variation of
density with temperature. Movement of air by a fan or of water by a pump are examples of forced convection.
Atmospheric convection currents can be set up by local heating effects such as solar radiation (heating and
rising) or contact with cold surface masses (cooling and sinking). Such convection currents primarily move
vertically and account for many atmospheric phenomena, such as clouds and thunderstorms.
Figure 3: Fluid in contact with a material of cross sectional area A.
From Newton’s Law of Cooling, the effect of convection between the wall and fluid as shown in the figure
above is given by the equation
Figure 2: Thermal Circuit Diagram
2
1
2
1
t
t
where
4
)
t
t
(
hA
Q

→
−
=
Here the heat-transfer rate is related to the overall temperature difference between the wall and fluid and the
surface area A
Watt
C
,
resistance
convective
R
hA
1
R
6
R
t
Q
as
equation
the
rewriting
by
process
convection
for the
drawn
be
also
can
analogy
resistance
-
electric
An
5
hA
1
t
Q
hA
1
)
t
t
(
hA
1
)
t
t
(
Q
)
t
t
(
hA
Q
1
2
2
1
2
1

−
=
→

−
=
→

−
=
−
−
=
−
=
−
=
Radiation
Radiation is the transfer of heat from a body with a high temperature to a body with a lower temperature, when
bodies are not in direct physical contact with each other or when they are separated by a distance in space, is
called heat radiation. All physical substances in solid, liquid, or gaseous states can emit energy via a process
of electromagnetic radiation because of vibrational and rotational movement of their molecules and atoms.
The intensity of such energy flux depends upon the temperature of the body and the nature of its surface. The
radiation occurs at all temperatures, with the rate of emission increasing with the temperature.
Unlike conduction and convection, heat transfer by thermal radiation does not necessarily need a material
medium for the energy transfer. In the case of thermal radiation from a solid surface, the medium through
which the radiation passes could be vacuum, gas, or liquid. Molecules and atoms of the medium can absorb,
reflect, or transmit the radiation energy. If the medium is a vacuum, since there are no molecules or atoms,
the radiation energy is not attenuated and, therefore, fully transmitted. Therefore, radiation heat transfer is
more efficient in a vacuum. In the case of a gas (e.g., air), energy can be slightly absorbed or reflected by air
molecules and the balance is transmitted. For liquid medium, most of the radiation is absorbed is a thin layer
close to the solid surface and nothing is transmitted.
In the context of heat radiation, a surface that absorbs all incident radiation and reflects none is called a black
surface or black body. The Stefan–Boltzmann Law of thermal radiation for a black body states that the rate
of radiation energy from the surface is proportional to the surface or body area A, times the absolute surface
temperature to the fourth power. A blackbody or black surface is one that absorbs all the radiation incident
upon it.
4
4
AT
Q
AT
Q

=

If we consider a black body with surface temperature T1 which radiates to another black body with surface
temperature T2 that completely surrounds it, the second black body completely absorbs the incident energy
and emits radiant energy that is proportional to
4
2
T . The net rate heat transfer by thermal radiation is then
given by:
K
re,
temperatu
surface
other
or
g
surroundin
absolute
-
T
K
re,
temperatu
surface
absolute
-
T
Constant
Boltzmann
-
Stefan
K
-
m
W
,
10
x
5.678
δ
where
Watts
T
T
A
δ
Q
2
1
4
2
8
-
4
2
4
1
→
=





 −
=
Emissivity ()
A black body is a perfect radiator. Real bodies, however, do not act like a perfect radiator and emit at a lower
rate. To take into account the real nature of the radiant bodies, a factor ε, called emissivity, is introduced. is
the ratio of the actual body (or surface) radiation at temperature T to the black body (or black surface) radiation
at the same temperature T.
Watts
T
T
A
Q
:
by
given
is
,
T
ture
at tempera
body
black
a
by
surrounded
is
which
T
ture
at tempera
body
real
a
from
fer
heat trans
radiation
of
rate
the
Then,
T
@
radiation
Surface
Black
T
@
radiation
Surface
Actual
4
2
4
1
2
1





 −

=
=

( )
( )
( ) ( )
( )( )
( )
( ) t
coefficien
radiation
T
T
T
T
h
T
-
T
T
-
T
T
T
T
T
T
-
T
T
T
T
T
T
-
T
T
T
h
T
-
T
h
T
T
T
-
T
A
h
T
T
A
Q
Convection
to
Radiation
Relating
T
T
where
2
1
2
2
2
1
r
2
1
2
1
2
1
2
2
2
1
2
1
2
2
2
1
2
2
2
1
2
1
4
2
4
1
r
2
1
r
4
2
4
1
2
1
r
4
2
4
1
2
1
→
+





 +

=
+





 +

=





 −





 +

=





 −

=
=





 −

=





 −

=

Combined Radiation and Convection heat transfer
Actual surface exposed to the surrounding air involves convection and radiation simultaneously, the total heat
transfer Q
Convection
Radiation
combined
2
1
c
h
h
h
)
t
t
(
A
h
Q
+
=
−
=
Thermal Conductivity of Common Materials
SAMPLE PROBLEMS
1. The inner and outer surface temperatures of a glass window 5 mm thick are 15C and 5C, respectively.
What is the heat loss through a window that 1 m x 3 m on a side. The thermal conductivity of the glass
is 1.4 W
m K
−
2. The roof of an electrically heated home is 6 m long, 8 m wide, and 250 mm thick, and is made of a flat
layer of concrete whose thermal conductivity is k = 0.8 W/m-°C. The temperatures of the inner and
the outer surfaces of the roof one night are measured to be 15°C and 4°C, respectively, for a period of
10 hours. Determine (a) the rate of heat loss through the roof that night and (b) the cost of that heat
loss to the home owner if the cost of electricity is P 80/KW-hr.
- t (15-4)
Q 1,689.6 W
L 0.25
kA 0.8(6)(8)
1,689.6(10)(80)
Cos t P 1,351.7
1000

= = =
= =
3. Air at 300C flows over a flat plate of dimensions 50 cm by 25 cm. If the convection heat transfer
coefficient is 250
C
m
W
2

−
, determine the heat transfer rate from the air to one side of the plate when
the plate is maintained at 40C.
4. A surface area of 0.5 m2, emissivity 0.8, and temperature 150C is placed in a large evacuated chamber
whose walls are maintained at 25C. What is the rate at which radiation is emitted by the surface?
What is the net rate at which radiation is exchanged between the surface and the chamber walls.
END OF MODULE 1

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Fuels and Combustion

  • 1. MODULE 1 HEAT TRANSFER Course Objectives • To cover the basic principles of heat transfer. • To present a wealth of real-world engineering applications to give students a feel for engineering practice. • To develop an intuitive understanding of the subject matter by emphasizing the physics and physical arguments. Topics • Introduction to Heat Transfer • Modes of Heat Transfer • Convection • Conduction • Radiation • Conduction through multilayered plane wall • Conduction through cylindrical pipes • Conduction through multilayered cylindrical pipes • Heat transfer from fluid to fluid separated by composite plane wall • Heat transfer from fluid to fluid through an insulated cylindrical pipes • Overall Coefficient of heat transfer • Heat Transfer Equipment or Heat Exchangers • Log Mean Temperature Difference (LMTD) • Arithmetic Mean Temperature Difference (AMTD) • Design of Surface Condensers Introduction This course is an introduction to the principal concepts and methods of heat transfer. The objectives of this integrated subject are to develop the fundamental principles and laws of heat transfer and to explore the implications of these principles for system behavior; to formulate the models necessary to study, analyze and design heat transfer systems through the application of these principles; to develop the problem-solving skills essential to good engineering practice of heat transfer in real-world application Objectives In this lecture you will learn the following • The science of thermodynamics deals with the amount of heat transfer as a system undergoes a process from one equilibrium state to another, and makes no reference to how long the process will take. But in engineering, we are often interested in the rate of heat transfer, which is the topic of the science of heat transfer. • The objective of this lecture is to extend the thermodynamic analysis through study of the modes of heat transfer and through development of relations to calculate heat transfer rates.
  • 2. MODES OF HEAT TRANSFER : There are three modes of heat transfer namely conduction, convection and radiation. • Conduction : Conduction refers to the heat transfer that occurs across the medium. Medium can be solid or a fluid. • Convection : Convection refers to the heat transfer that will occur between a surface and a moving fluid when they are at different temperatures. • Radiation : In radiation, in the absence of intervening medium, there is net heat transfer between two surfaces at different temperatures in the form of electromagnetic waves. PHYSICAL ORIGINS AND RATE EQUATIONS: It is important to understand the physical mechanisms which underlie the heat transfer modes and that we are able to use the rate equations that quantify the amount of energy being transferred per unit time. Conduction: It is the transfer of heat from one point to another point within a body or the transfer of heat from one point of a body to another point of another body , when they are in physical contact with each other. Conduction can be imagined as a atomic or molecular activity which involves the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions between the particles. From Fourier’s Law: The conductive heat flow through a material varies directly as the product of the surface area A and the temperature gradient dt/dx. (where negative sign is used because, temperature decreases in the direction of heat flow. L t kA Q Kelvin in ) T - T ( T T t but t t t L x t kA x Q dt kA dx Q kAdt Qdx dx dt kA Q dx dt A - Q 1 2 1 2  − = =   =  − =  =   − =  − = − = − =    ) W K or W C , resistance (thermal 3 kA L R potential) re (temperatu 2 t t t 1 R t Q conduction thermal to relating R V I conductor) electric an (For Law s Ohm' From kA L t Q 2 1   → = → − =  − →  − = =  − = Figure 1
  • 3. Where Q – conductive heat flow, Watts A – surface area, m L – thickness, m R – thermal resistance, W K or W C   k – thermal conductivity, K m W or C m W −  − Thermal Circuit Diagram Convection It is the transfer of heat from one point to another point with in a fluid (Liquid or Gas) Natural convection results from the tendency of most fluids to expand when heated—i.e., to become less dense and to rise as a result of the increased buoyancy. Circulation caused by this effect accounts for the uniform heating of water in a kettle or air in a heated room: the heated molecules expand the space they move in through increased speed against one another, rise, and then cool and come closer together again, with increase in density and a resultant sinking. Forced convection involves the transport of fluid by methods other than that resulting from variation of density with temperature. Movement of air by a fan or of water by a pump are examples of forced convection. Atmospheric convection currents can be set up by local heating effects such as solar radiation (heating and rising) or contact with cold surface masses (cooling and sinking). Such convection currents primarily move vertically and account for many atmospheric phenomena, such as clouds and thunderstorms. Figure 3: Fluid in contact with a material of cross sectional area A. From Newton’s Law of Cooling, the effect of convection between the wall and fluid as shown in the figure above is given by the equation Figure 2: Thermal Circuit Diagram
  • 4. 2 1 2 1 t t where 4 ) t t ( hA Q  → − = Here the heat-transfer rate is related to the overall temperature difference between the wall and fluid and the surface area A Watt C , resistance convective R hA 1 R 6 R t Q as equation the rewriting by process convection for the drawn be also can analogy resistance - electric An 5 hA 1 t Q hA 1 ) t t ( hA 1 ) t t ( Q ) t t ( hA Q 1 2 2 1 2 1  − = →  − = →  − = − − = − = − = Radiation Radiation is the transfer of heat from a body with a high temperature to a body with a lower temperature, when bodies are not in direct physical contact with each other or when they are separated by a distance in space, is called heat radiation. All physical substances in solid, liquid, or gaseous states can emit energy via a process of electromagnetic radiation because of vibrational and rotational movement of their molecules and atoms. The intensity of such energy flux depends upon the temperature of the body and the nature of its surface. The radiation occurs at all temperatures, with the rate of emission increasing with the temperature. Unlike conduction and convection, heat transfer by thermal radiation does not necessarily need a material medium for the energy transfer. In the case of thermal radiation from a solid surface, the medium through which the radiation passes could be vacuum, gas, or liquid. Molecules and atoms of the medium can absorb, reflect, or transmit the radiation energy. If the medium is a vacuum, since there are no molecules or atoms, the radiation energy is not attenuated and, therefore, fully transmitted. Therefore, radiation heat transfer is more efficient in a vacuum. In the case of a gas (e.g., air), energy can be slightly absorbed or reflected by air molecules and the balance is transmitted. For liquid medium, most of the radiation is absorbed is a thin layer close to the solid surface and nothing is transmitted. In the context of heat radiation, a surface that absorbs all incident radiation and reflects none is called a black surface or black body. The Stefan–Boltzmann Law of thermal radiation for a black body states that the rate of radiation energy from the surface is proportional to the surface or body area A, times the absolute surface temperature to the fourth power. A blackbody or black surface is one that absorbs all the radiation incident upon it. 4 4 AT Q AT Q  = 
  • 5. If we consider a black body with surface temperature T1 which radiates to another black body with surface temperature T2 that completely surrounds it, the second black body completely absorbs the incident energy and emits radiant energy that is proportional to 4 2 T . The net rate heat transfer by thermal radiation is then given by: K re, temperatu surface other or g surroundin absolute - T K re, temperatu surface absolute - T Constant Boltzmann - Stefan K - m W , 10 x 5.678 δ where Watts T T A δ Q 2 1 4 2 8 - 4 2 4 1 → =       − = Emissivity () A black body is a perfect radiator. Real bodies, however, do not act like a perfect radiator and emit at a lower rate. To take into account the real nature of the radiant bodies, a factor ε, called emissivity, is introduced. is the ratio of the actual body (or surface) radiation at temperature T to the black body (or black surface) radiation at the same temperature T. Watts T T A Q : by given is , T ture at tempera body black a by surrounded is which T ture at tempera body real a from fer heat trans radiation of rate the Then, T @ radiation Surface Black T @ radiation Surface Actual 4 2 4 1 2 1       −  = =  ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) t coefficien radiation T T T T h T - T T - T T T T T T - T T T T T T - T T T h T - T h T T T - T A h T T A Q Convection to Radiation Relating T T where 2 1 2 2 2 1 r 2 1 2 1 2 1 2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 1 4 2 4 1 r 2 1 r 4 2 4 1 2 1 r 4 2 4 1 2 1 → +       +  = +       +  =       −       +  =       −  = =       −  =       −  =  Combined Radiation and Convection heat transfer Actual surface exposed to the surrounding air involves convection and radiation simultaneously, the total heat transfer Q Convection Radiation combined 2 1 c h h h ) t t ( A h Q + = − =
  • 6. Thermal Conductivity of Common Materials SAMPLE PROBLEMS 1. The inner and outer surface temperatures of a glass window 5 mm thick are 15C and 5C, respectively. What is the heat loss through a window that 1 m x 3 m on a side. The thermal conductivity of the glass is 1.4 W m K − 2. The roof of an electrically heated home is 6 m long, 8 m wide, and 250 mm thick, and is made of a flat layer of concrete whose thermal conductivity is k = 0.8 W/m-°C. The temperatures of the inner and the outer surfaces of the roof one night are measured to be 15°C and 4°C, respectively, for a period of 10 hours. Determine (a) the rate of heat loss through the roof that night and (b) the cost of that heat loss to the home owner if the cost of electricity is P 80/KW-hr.
  • 7. - t (15-4) Q 1,689.6 W L 0.25 kA 0.8(6)(8) 1,689.6(10)(80) Cos t P 1,351.7 1000  = = = = = 3. Air at 300C flows over a flat plate of dimensions 50 cm by 25 cm. If the convection heat transfer coefficient is 250 C m W 2  − , determine the heat transfer rate from the air to one side of the plate when the plate is maintained at 40C. 4. A surface area of 0.5 m2, emissivity 0.8, and temperature 150C is placed in a large evacuated chamber whose walls are maintained at 25C. What is the rate at which radiation is emitted by the surface? What is the net rate at which radiation is exchanged between the surface and the chamber walls. END OF MODULE 1