Heat transfer in thermal engineering

HEAT TRANSFER MECHANISMS
 Heat as the form of energy that can be transferred from one system
to another as a result of temperature difference.
 A thermodynamic analysis is concerned with the amount of heat
transfer as a system undergoes a process from one equilibrium state
to another.
 The science that deals with the determination of the rates of such
energy transfers is the heat transfer.
 The transfer of energy as heat is always from the higher-
temperature medium to the lower-temperature one, and heat
transfer stops when the two mediums reach the same temperature.
 Heat can be transferred in three basic modes:
 conduction
 convection
 radiation
 All modes of heat transfer require the existence of a temperature
difference.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

Heat conduction
through a large plane
wall of thickness ∆x
and area A.
CONDUCTION
Conduction: The transfer of energy from the more
energetic particles of a substance to the adjacent less
energetic ones as a result of interactions between the
particles.
In gases and liquids, conduction is due to the
collisions and diffusion of the molecules during their
random motion.
In solids, it is due to the combination of vibrations of
the molecules in a lattice and the energy transport by
free electrons.
The rate of heat conduction through a plane layer is
proportional to the temperature difference across the
layer and the heat transfer area, but is inversely
proportional to the thickness of the layer.

When x → 0 Fourier’s law of
heat conduction
Thermal conductivity, k: A measure of the ability
of a material to conduct heat.
Temperature gradient dT/dx: The slope of the
temperature curve on a T-x diagram.
Heat is conducted in the direction of decreasing
temperature, and the temperature gradient becomes
negative when temperature decreases with
increasing x. The negative sign in the equation
ensures that heat transfer in the positive x direction
is a positive quantity.
The rate of heat conduction
through a solid is directly
proportional to its thermal
conductivity.
In heat conduction
analysis, A represents
the area normal to the
direction of heat
transfer.A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

Thermal
Conductivity
Thermal conductivity:
The rate of heat transfer
through a unit thickness
of the material per unit
area per unit
temperature difference.
The thermal conductivity
of a material is a
measure of the ability of
the material to conduct
heat.
A high value for thermal
conductivity indicates
that the material is a
good heat conductor,
and a low value indicates
that the material is a
poor heat conductor or
insulator.
A simple experimental setup
to determine the thermal
conductivity of a material.

The range of
thermal
conductivity of
various
materials at
room
temperature.

The mechanisms of heat
conduction in different
phases of a substance.
The thermal conductivities of gases such
as air vary by a factor of 104
from those of
pure metals such as copper.
Pure crystals and metals have the highest
thermal conductivities, and gases and
insulating materials the lowest.

The variation of
the thermal
conductivity of
various solids,
liquids, and gases
with temperature.

Thermal Diffusivity
cp Specific heat, J/kg · °C: Heat capacity
per unit mass
ρcp Heat capacity, J/m3
·°C: Heat capacity
per unit volume
α Thermal diffusivity, m2
/s: Represents
how fast heat diffuses through a material
A material that has a high thermal
conductivity or a low heat capacity will
obviously have a large thermal diffusivity.
The larger the thermal diffusivity, the faster
the propagation of heat into the medium.
A small value of thermal diffusivity means
that heat is mostly absorbed by the
material and a small amount of heat is
conducted further.

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.
Heat transfer from a hot surface to air
by 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.

Newton’s law of cooling
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.
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

RADIATION
• Radiation: The energy emitted by matter in the form of electromagnetic
waves (or photons) as a result of the changes in the electronic
configurations of the atoms or molecules.
• Unlike conduction and convection, the transfer of heat by radiation does
not require the presence of an intervening medium.
• In fact, heat transfer by radiation is fastest (at the speed of light) and it
suffers no attenuation in a vacuum. This is how the energy of the sun
reaches the earth.
• In heat transfer studies we are interested in thermal radiation, which is
the form of radiation emitted by bodies because of their temperature.
• All bodies at a temperature above absolute zero emit thermal radiation.
• Radiation is a volumetric phenomenon, and all solids, liquids, and
gases emit, absorb, or transmit radiation to varying degrees.
• However, radiation is usually considered to be a surface phenomenon
for solids.

Stefan–Boltzmann law
σ = 5.670 × 10−8
W/m2
· K4
Stefan–Boltzmann constant
Blackbody: The idealized surface that emits radiation at the maximum rate.
Blackbody radiation represents the maximum
amount of radiation that can be emitted from
a surface at a specified temperature.
Emissivity ε : A measure of how closely
a surface approximates a blackbody for
which ε = 1 of the surface. 0≤ ε ≤ 1.
Radiation emitted
by real surfaces

Absorptivity α: The fraction of the radiation energy incident on a
surface that is absorbed by the surface. 0≤ α ≤ 1
A blackbody absorbs the entire radiation incident on it (α = 1).
Kirchhoff’s law: The emissivity and the absorptivity of a surface at
a given temperature and wavelength are equal.
The absorption of radiation incident on
an opaque surface of absorptivity .

Radiation heat transfer between a surface
and the surfaces surrounding it.
Net radiation heat transfer:
The difference between the
rates of radiation emitted by the
surface and the radiation
absorbed.
The determination of the net
rate of heat transfer by radiation
between two surfaces is a
complicated matter since it
depends on
• the properties of the surfaces
• their orientation relative to
each other
• the interaction of the medium
between the surfaces with
radiation
Radiation is usually
significant relative to
conduction or natural
convection, but
negligible relative to
forced convection.
When a surface is completely enclosed by a
much larger (or black) surface at temperature
Tsurr separated by a gas (such as air) that
does not intervene with radiation, the net rate
of radiation heat transfer between these
two surfaces is given by

Combined heat transfer coefficient hcombined
Includes the effects of both convection and radiation
When radiation and convection occur
simultaneously between a surface and a gas:

INSULATING MATERIALS
INSULATING MATERIALS, GENERAL
PROPERTIES
 PHYSICAL PROPERTIES
ELECTRIAL PROPERTIES
THERMAL PROPERTIES
CHEMICAL PROPERTIES
MECHANICAL PROPERTIES

• INSULATING MATERIALS AND THEIR
APPLICATIONS
PLASTICS
NATURAL INSULATING
MATERIALS
GASEOUS MATERIALS

INTRODUCTION
The materials which have very high resistivity i.e. offers
a very high resistance to the flow of electric current.
Insulating materials plays an important part in
various electrical and electronic circuits. In domestic
wiring insulating material protect us from shock and
also prevent leakage current.
So insulating material offers a wide range of uses in
engineering applications.

FACTORS AFFECTING SELECTION OF AN
INSULATING MATERIAL
1. Operating condition : Before selecting an insulating
material for a particular application the selection should
be made on the basis of operating temperature, pressure
and magnitude of voltage and current.
2. Easy in shaping : Shape and size is also important affect.
3. Availability of material : The material is easily available.
4. Cost : Cost is also a important factor.

CLASSIFICATION OF
SUBSTANCES
Conductors
Insulators
Semiconductors

CONDUCTORS
The substances through which electric
current can flow easily are called
conductors.
e.g. Silver, gold, copper, aluminum etc.
Conductors have a large number of free
electrons. Generally metals have a large
number of free electrons, So all metals are
good conductors.

INSULATORS
Those substances through which
electric current cannot pass easily
are called insulators. e.g. Glass,
Mica, dry Air, Bakelite etc.

SEMICONDUCTORS
The substances whose resistivity
lies between the resistivity of
conductors and insulators are called
semiconductors. e.g. Germanium,
Silicon, Carbon etc.

RESISTIVITY
Resistivity is the resistance between
the two opposite faces of a cube having
each side equal to one meter.
Resistivity of
CONDUCTORS 10-8
to 10-3
ohm-m
INSULATORS 1010-20
ohm-m
SEMICONDUCTORS 100-0.5 ohm-m

HEAT EXCHANGERS
• Recognize numerous types of heat exchangers, and
classify them
• Develop an awareness of fouling on surfaces, and
determine the overall heat transfer coefficient for a heat
exchanger
• Perform a general energy analysis on heat exchangers
• Obtain a relation for the logarithmic mean temperature
difference for use in the LMTD method, and modify it
for different types of heat exchangers using the
correction factor
• Develop relations for effectiveness, and analyze heat
exchangers when outlet temperatures are not known
using the effectiveness-NTU method
• Know the primary considerations in the selection of
heat exchangers.

TYPES OF HEAT EXCHANGERS

Compact heat exchanger: It has a large heat
transfer surface area per unit volume (e.g., car
radiator, human lung). A heat exchanger with the
area density β > 700 m2
/m3
is classified as being
compact.
Cross-flow: In compact heat exchangers, the two fluids
usually move perpendicular to each other. The cross-
flow is further classified as unmixed and mixed flow.

Shell-and-tube heat exchanger: The most common type of heat
exchanger in industrial applications.
They contain a large number of tubes (sometimes several hundred)
packed in a shell with their axes parallel to that of the shell. Heat
transfer takes place as one fluid flows inside the tubes while the other
fluid flows outside the tubes through the shell.
Shell-and-tube heat exchangers are further classified according to the
number of shell and tube passes involved.

Regenerative heat exchanger:
Involves the alternate passage of the
hot and cold fluid streams through the
same flow area.
Dynamic-type regenerator: Involves a
rotating drum and continuous flow of
the hot and cold fluid through different
portions of the drum so that any
portion of the drum passes periodically
through the hot stream, storing heat,
and then through the cold stream,
rejecting this stored heat.
Condenser: One of the fluids is cooled
and condenses as it flows through the
heat exchanger.
Boiler: One of the fluids absorbs heat
and vaporizes.

Plate and frame (or just plate) heat exchanger: Consists of a series of plates
with corrugated flat flow passages. The hot and cold fluids flow in alternate
passages, and thus each cold fluid stream is surrounded by two hot fluid streams,
resulting in very effective heat transfer. Well suited for liquid-to-liquid applications.
A plate-and-frame
liquid-to-liquid heat
exchanger.

THE OVERALL HEAT TRANSFER COEFFICIENT
• A heat exchanger typically involves two
flowing fluids separated by a solid wall.
• Heat is first transferred from the hot fluid to
the wall by convection, through the wall by
conduction, and from the wall to the cold
fluid again by convection.
• Any radiation effects are usually included in
the convection heat transfer coefficients.
Thermal resistance network
associated with heat transfer in
a double-pipe heat exchanger.A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

U the overall heat transfer
coefficient, W/m2
⋅°C
When
The overall heat transfer coefficient U is dominated by the smaller convection
coefficient. When one of the convection coefficients is much smaller than the other
(say, hi << ho), we have 1/hi >> 1/ho, and thus U ≈ hi. This situation arises frequently
when one of the fluids is a gas and the other is a liquid. In such cases, fins are
commonly used on the gas side to enhance the product UA and thus the heat
transfer on that side.

The overall heat transfer coefficient
ranges from about 10 W/m2
⋅°C for
gas-to-gas heat exchangers to about
10,000 W/m2
⋅°C for heat exchangers
that involve phase changes.
For short fins of high
thermal conductivity, we
can use this total area in
the convection
resistance relation
Rconv = 1/hAs
To account for fin efficiency
When the tube is finned on one
side to enhance heat transfer, the
total heat transfer surface area on
the finned side is

Fouling Factor
The performance of heat exchangers usually deteriorates with time as a result of
accumulation of deposits on heat transfer surfaces. The layer of deposits represents
additional resistance to heat transfer. This is represented by a fouling factor Rf.
The fouling factor increases with the operating temperature and the length of
service and decreases with the velocity of the fluids.

THE LOG MEAN TEMPERATURE DIFFERENCE
METHOD
Variation of the fluid
temperatures in a
parallel-flow double-pipe
heat exchanger.
log mean
temperature
difference

The arithmetic mean temperature difference
The logarithmic mean temperature
difference ∆Tlm is an exact representation
of the average temperature difference
between the hot and cold fluids.
Note that ∆Tlm is always less than ∆Tam.
Therefore, using ∆Tam in calculations
instead of ∆Tlm will overestimate the rate of
heat transfer in a heat exchanger between
the two fluids.
When ∆T1 differs from ∆T2 by no more than
40 percent, the error in using the arithmetic
mean temperature difference is less than 1
percent. But the error increases to
undesirable levels when ∆T1 differs from
∆T2 by greater amounts.

Counter-Flow Heat Exchangers
In the limiting case, the cold fluid will be
heated to the inlet temperature of the hot
fluid.
However, the outlet temperature of the cold
fluid can never exceed the inlet
temperature of the hot fluid.
For specified inlet and outlet temperatures,
∆Tlm a counter-flow heat exchanger is
always greater than that for a parallel-flow
heat exchanger.
That is, ∆Tlm, CF > ∆Tlm, PF, and thus a
smaller surface area (and thus a smaller
heat exchanger) is needed to achieve a
specified heat transfer rate in a counter-
flow heat exchanger.
When the heat capacity rates
of the two fluids are equal

Multipass and Cross-Flow Heat Exchangers:
Use of a Correction Factor
F correction factor depends on the
geometry of the heat exchanger and the
inlet and outlet temperatures of the hot
and cold fluid streams.
F for common cross-flow and shell-and-
tube heat exchanger configurations is
given in the figure versus two
temperature ratios P and R defined as
1 and 2 inlet and outlet
T and t shell- and tube-side temperatures
F = 1 for a condenser or boiler

Correction factor
F charts for
common shell-
and-tube heat
exchangers.

Correction
factor F charts
for common
cross-flow heat
exchangers.

The LMTD method is very suitable for determining the size of a heat
exchanger to realize prescribed outlet temperatures when the
mass flow rates and the inlet and outlet temperatures of the hot
and cold fluids are specified.
With the LMTD method, the task is to select a heat exchanger that
will meet the prescribed heat transfer requirements. The
procedure to be followed by the selection process is:
1. Select the type of heat exchanger suitable for the application.
2. Determine any unknown inlet or outlet temperature and the heat
transfer rate using an energy balance.
3. Calculate the log mean temperature difference ∆Tlm and the
correction factor F, if necessary.
4. Obtain (select or calculate) the value of the overall heat transfer
coefficient U.
5. Calculate the heat transfer surface area As .
The task is completed by selecting a heat exchanger that has a heat
transfer surface area equal to or larger than As.

THE EFFECTIVENESS–NTU METHOD
A second kind of problem encountered in heat exchanger analysis is the
determination of the heat transfer rate and the outlet temperatures of the hot and
cold fluids for prescribed fluid mass flow rates and inlet temperatures when the type
and size of the heat exchanger are specified.
Heat transfer effectiveness
the maximum possible heat transfer rate
Cmin is the smaller of Ch and Cc

Actual heat transfer rate

The effectiveness of a
heat exchanger depends
on the geometry of the
heat exchanger as well
as the flow arrangement.
Therefore, different types
of heat exchangers have
different effectiveness
relations.
We illustrate the
development of the
effectiveness e relation
for the double-pipe
parallel-flow heat
exchanger.

Effectiveness relations of the heat exchangers typically involve the
dimensionless group UAs /Cmin.
This quantity is called the number of transfer units NTU.
For specified values of U and Cmin, the value
of NTU is a measure of the surface area As.
Thus, the larger the NTU, the larger the heat
exchanger.
capacity
ratio
The effectiveness of a heat exchanger is a function of the
number of transfer units NTU and the capacity ratio c.

Effectiveness
for heat
exchangers.

When all the inlet and outlet temperatures are specified, the size of
the heat exchanger can easily be determined using the LMTD
method. Alternatively, it can be determined from the effectiveness–
NTU method by first evaluating the effectiveness from its definition
and then the NTU from the appropriate NTU relation.A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

(e.g., boiler, condenser)

52A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

Heat transfer in thermal engineering

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