heat transfer (for d..

Physical process by which thermal energy is
exchanged between material bodies or inside
the same body as a result of a temperature
Heat transfer is the study of the mechanism
and rate of this process.
Energy is the ability or capacity to do work on some form
of matter.
There are several forms of energy, including the following:
• Potential energy is the energy which a body possesses as a
consequence of its position in a gravitational field
• Kinetic energy is the energy which a body possesses as a
consequence of its motion (e.g., wind blowing across a wind
generator). It is dependent upon an object's mass and velocity
• Internal energy is the total energy (potential and kinetic) stored in
• Heat (or thermal) energy is kinetic energy due to motion of atoms
and molecules. It is energy that is in the process of being
transferred from one object to another because of their
temperature difference.
• Radiant energy is the energy that propagates through space or
through material media in the form of electromagnetic radiation.
Conduction- thermal energy is transferred by the
direct contact of molecules, not by the movement
of the material
Convection- thermal energy is transferred by the
mass motion of groups of molecules resulting in
transport and mixing of properties
Radiation- thermal energy is transferred by
electromagnetic radiation (waves)
Conduction heat transfer: the flow of heat from
one part of a body to another, or from one body
to another, without appreciable displacement of
the particles.
This mode of heat transfer is also called
molecular heat transfer, because it involves the
transfer of kinetic energy from one molecule to
the one adjacent to it.
Heat can be conducted through solids, liquids
and gases.
In gases heat transfer by conduction is effected
by means of molecular and atomic diffusion.
Conduction in the bulk of fluids is normally
overshadowed by convection but it assumes
great importance at fluid boundaries.
In metals heat transfer is mainly due to the
diffusion of free electrons.
The mechanism of conduction is most easily
understood by the study of conduction
through solids, because in this case
convection is not present.
Conduction is the transfer of heat within a substance, molecule
by molecule. If you put one end of a metal rod over a fire, that
end will absorb the energy from the flame. The molecules at
this end of the rod will gain energy and begin to vibrate faster.
As they do their temperature increases and they begin to bump
into the molecules next to them. The heat is being transferred
Fourier's law is an empirical law based on
observation. It states that the rate of heat
flow, Q/t, through a homogeneous solid is
directly proportional to the area, A, of the
section at right angles to the direction of heat
flow, and to the temperature difference along
the path of heat flow, dT/x i.e
A is the cross-sectional surface area,
ΔT is the temperature difference between the ends,
Δx is the distance between the ends.
Consider an area A of a wall of thickness x. Let
temperature be uniform over the area A on one
face of the wall (T1) and uniform but lower over
the same area on the opposite face (T2).
Then the heat flow will be at right angles to the
plan of A.
Fourier’s law states that, the rate of heat flow
through a uniform material is proportional to the
area A, the temperature drop (Δ T) and inversely
proportional to the length of the path of flow (x).
K= the proportionality constant known as
thermal conductivity of conducting medium
The basic low of heat transfer by conduction
can be written in the form of the rate
Rate = driving force / resistance
Driving force is the temperature drop across
the solid
Resistance is equal to (x/KA)
Thermal conductivity:
K= BTU/ hr . ft. F˚
Thermal conductivities vary considerably,
ranging from metals that have high values,
through non-metallic solids and liquids, to
gases that have the lowest values.
Thermal conductivity values
0.001- 0.1
0.01 - 1.0
1.00 – 100
As you can see air does not conduct heat
very well. This is the idea behind a
styrofoam coolers, the air pockets between
the styrofoam beads do not conduct heat
very well. On the other hand, metals do
conduct heat very well. This is why metal
seems cold when you touch it. The metal
molecules are conducting your body heat
Thermal conductance (K/x) is the amount of heat
energy per area of material per degree difference
between the outside and inside.
Q/t= K A dT/x
K/x = Q/t /AdT
K/x = Q/t A dT
So its units is Btu/ square ft. hr. F˚. In the
English system and Watt/ square meters. C˚
Thermal resistance is the reciprocal of thermal
conductance (x/K) so its units is square ft. hr.
F˚/ Btu, and square meters. C ˚/Watts.
Thermal resistance is known as the R-value
The R-value of a material is its resistance to
heat flow and is an indication of its ability to
insulate. It is used as a standard way of telling
how good a material will insulate. The higher the
R-value, the better the insulation.
Suppose a composite wall made up of three
materials with thermal conductivities K1, K2
and K3, thickness of x1, x2 and x3 and
temperature of T1,T2, T3 and T4 at the face.
Applying Fourier’s equation for each section
in turn and as the same quantity of heat Q
per unit time must pass through each area A
we get:
For the first wall:
q = K1 A. T1-T2/ x1
T1-T2= q x1/K1A
eq. 1
For the second wall:
q = K2 A T2-T3/x2
T2-T3 = qx2/K2A
For the third wall:
q= K3A T3-T4/x3
T3-T4= qx3/K3A
T1-T4= (T1-T2)+(T2-T3)+(T3-T4)
By substitution:
T1-T4 = q[ x1/K1A +x2/K2A + x3/K3A]
q = T1-T4/Σ x/KA
q= ΔT/ Σ x/KA= Total driving force/total
Pipes and tubes are common barriers over which heat
exchange takes place. Conduction is complicated in this case
by changing area over which heat is transferred. If Fourier’s
eq. is to be used, some value of A must be derived from the
length of the pipe, N, and the internal and external radii r1
and r2 respectively.
When the pipe is thin walled and the ratio r2/r1 is less than
1.5, the heat transfer area can be based on an arithmetic
mean of the two radii.
A = 2π ra N
A = 2 π ( r2+r1/2) N,
if r2/r1 < 1.5
q = K 2π ra N (T1-T2)/r2-r1
r2-r1 is the thickness of the wall and is the pass length
across which the heat flows (x).
For thick walled pipes, with a ratio r2/r1 of
more than 1.5, the previous derivation of
Fourier’s eq. will be found inaccurate. This is
because the arithmetic mean radius will not
lead to calculation of the actual surface area.
A logarithmic mean radius, rm is, in such a
case, necessary, which is:
rm = r2-r1 / 2.303 log r2/r1
Fourier’s eq. becomes:
q= K 2π rm N (T1-T2)/ r2-r1
It is the process of heat transfer through the motion of a
liquid or gas..
By convection is meant the process of heat transport
occurring through the movement of the macroparticles of the
liquid or gas in space from a region of one atmosphere to
that of another.
Convection is possible only in a fluid medium. When the
motion of the fluid arises only from the density difference
associated with the temperature field is known as natural
convection. When the fluid motion arises artificially by an
agitator or pump, and is known as forced convection.
Heat is transferred simultaneously during the process of
convection and conduction
When heat is being conducted from one fluid to another through a solid
barrier e.g. pipe wall both conduction and convection operate. it is
sometimes important to consider the conductance of the thin film of
fluid which remains stationary next to the barrier. This thin film of fluid
is difficult to quantify, its characteristics depending upon complex
conditions of turbulence and viscosity, but when dealing with thin highconductance barriers it can sometimes be quite significant
How this thin film of fluid is formed?
If a fluid flows in turbulent motion parallel to a solid surface, the velocity
increases rapidly from zero at the wall to an almost constant value at a
short distance away. The friction between the wall and the flowing fluid
reduces its velocity to zero. This leads to the formation of stagnant layer
(laminar sub-layer) besides the wall. The major resistance to the flow of
heat lies in the laminar sub-layer. Its thickness is therefore, of critical
importance in determining the rate of heat transfer from the fluid to the
boundary. Increasing flow velocity will decrease the thickness of the
layer and the resistance to heat flow. Heat is transferred only by
conduction through this layer.
If on the hot side of the wall, the film layer has a thickness of
x1, the eq. of heat transfer to the wall
q = K1 A T1-T2/x1
Writing K1/x1 = h1
Where K is the thermal conductivity of the fluid.
h is conductance of the thin film since it is equal to K/x and
has a unit of ……………..
Its reciprocal would denote
the thermal resistance of the film.
also known as film coefficient or heat transfer
coefficient of the film.
The eq. can be written as:
q= h1 A (T1-T2)
Heat transfer across the solid barrier will be expressed by:
q= Kw A (T2-T3)/xw
Using the film coefficient h2 to describe the heat
transfer from the barrier to the colder fluid:
q= h2 A (T3-T4)
q= AΔT/ 1/h1 + xw /Kw+ 1/h2
For simplicity:
The term U which is called the overall heat transfer
coefficient and is equal to
1/ 1/h1 + xw/Kw + 1/h2
So q= U A ΔT
Radiation allows heat to be transferred through wave energy. These
waves are called Electromagnetic Waves, because the energy travels in a
combination of electric and magnetic waves. This energy is released
when these waves are absorbed by an object.
For example, energy traveling from the sun to your skin, you can feel
your skin getting warmer as energy is absorbed.
 The energy a wave carries is related to its wavelength (measured
from crest to crest). Shorter wavelengths carry more energy than
longer wavelengths. Wavelengths are measured in terms of meters:
 1 (millimeter) mm = .001 m = 10-3 m
 1 (micrometer) μm = .000001 m = 10-6 m
 1 μm is 1 millionth of a meter. One-hundredth the diameter of a
human hair.
 1 (nanometer) nm = .000000001 m = 10-9 m
* When talking about electromagnetic waves it
sometimes easier to give them characteristics
particles, we call these particles photons. A photon
x-ray radiation carries more energy than a photon
visible light.
* All things with a temperature above absolute zero
emit radiation. Everything, your body, your desk, your
house, grass, snow, the atmosphere, the moon, they
all emit a wide range of radiation. The source of this
electromagnetic radiation are vibrating electrons that
exist in every atom that makes an object.
Absorbed Increasing the internal energy of the gas molecules.
This fraction is called absorptivity (a).
Reflected Radiation is not absorbed or emitted from an object
but it reaches the object and is sent backward. This fraction
is called reflectivity (r)
Scattered Scattered light is deflected in all directions,
forward, backward, sideways. It is also called diffused light.
Transmitted Radiation not absorbed, reflected, or scattered
by a gas, the radiation passes through the gas unchanged.
This fraction is called transmissivity.
Most industrial solids are opaque, so that the transmissivity is
zero and
Reflectivity and absorptivity, depend greatly on the nature of
the surface. A black body : a body which absorbs all and
reflects none of the incident radiation, so it is a perfect
The radiation of all bodies depends on
The intensity of radiation increases with
rising temperature, because a rise in
temperature is accompanied by an increase in
the internal energy of the substance.
Radiation depends considerably more on
temperature than the processes of heat
conduction and convection.
The Stefan-Boltzmann law tells us that as the
temperature of an object increases, more radiation
is emitted each second.
E = σT4
where σ is a constant, T is the temperature of an
object in Kelvin and E is the maximum rate of
radiation emitted per meter2 .
In other word, the law states that the rate of
energy emission from a black body is proportional
to the fourth power of the absolute temperature.
This figure describe what is going on and how each
method of heat transfer works in this example:
Like all other substances, water can exist in
several states— solid, liquid, or vapor—
pressure. Steam is the name for water in its
vapor state. Steam is created by heating liquid
water to a point where the intermolecular forces
between the molecules are broken, allowing the
molecules to move apart. The temperature at
which the first water molecule transforms to
vapor is called the boiling point. As more heat is
added to the liquid/vapor mixture, the
temperature remains at the boiling point until all
of the liquid is transformed to saturated steam
steam as a heating medium has superior
properties not offered by other heat
mediums. Among those, the following two
are the most notable:
1- Provides even heating
2- Provides rapid heating
In the case of saturated steam, if the steam
pressure is known then the steam temperature may
be determined. Pressure changes instantaneously
within a space. When saturated steam condenses, it
condenses at the saturation temperature, and the
saturated water (condensate) formed is of the same
temperature as the saturated steam. This means
that if the pressure at the heat transfer surface (the
jacket or coil interior of the equipment) is held at a
constant, continuous heating will be able to take
place at the same temperature at every part of the
heat transfer surface.
The transfer of heat is caused by the process
of condensing steam.
The latent heat contained in steam is released
in the instant the steam condenses into liquid
phase. The amount of latent heat released is
2 – 5 times greater than the amount of
sensible heat in the hot water (saturated
water) after condensation. This latent heat is
released instantaneously and is transferred by
means of a heat exchanger to the product
being heated
Steam Benefits:
Steam is the most commonly used heating medium in thermal
maintenance applications because of three key benefits:
Significant energy storage. A significant amount of heat energy is
required to transform liquid water to steam. This energy is stored in
the steam. When saturated steam comes into contact with a cooler
object, heat is transferred from the steam, and very large heat
transfer rates are produced as the steam condenses into liquid water
Constant temperature. The steam/condensate temperature remains
at the boiling point until all of the steam is transformed back into
liquid water. So, for a given steam pressure, the heating medium
remains at a constant temperature. This preserves a maximum
temperature difference between the heating medium and process,
Process by-product. Often, steam is created as a by-product of a
heat exchange operation designed to cool a process stream. This is
the case with a waste heat boiler. Since this steam is already
available, it is usually more economical to use it rather than another
as a heating medium/technology
1- Saturated steam (wet):
Steam directly arising from boiling water,
whether under atmospheric or higher
pressures, is said to be saturated. When
steam is generated in a boiler, the water
surface is turbulent and droplets of water are
thrown up into the steam. The movement of
the steam towards the outlet will carry these
droplets away into the steam system. Steam
which contains these particles of water in a
finely divided state is called wet steam.
In a boiler, if steam is taken away faster than it is being
generated, the surface of water will be below atmospheric
pressure. The effect of this will be lowering the boiling point
of water, lower the sensible heat and increase the latent heat.
T. of water and steam
S. H
Total heat
(15 in. Hg v)
179 ˚F
Atm. P
212 ˚F
200 psig
388 ˚F
If one pound of wet steam is made up of 95% dry steam and 5%
water particles, it is said to have a dryness fraction of 0.95.
The total heat of one pound of wet steam is less than the total heat
of dry steam, because the water particles have escaped without
receiving any latent heat.
The total heat of wet steam will be made up of h (sensible heat), f
(dryness fraction) and L (latent heat).
For example: the total heat of one pound of steam at 200 p.s.i.g.
having a dryness fraction of 0.94 is:
H = 362 + 0.94 X 838
H = 1.149 Btu/lb
This is 51 Btu/lb less than the total heat of dry steam from the
previous table (1200 Btu/lb)
In other words, the better the quality of steam, the less water it
contains, the higher will be the possible rate of production. The
simplest method of obtaining dry steam is by the use of steam
dryers or steam separators.
Steam Dryer:
The presence of water in steam pipes should never be permitted.
Water being a better conductor of heat than dry steam, will act as a
conductor between the steam and the metallic pipe, setting up
active condensation and preventing economical working of boiler.
The steam dryers separate water particles from flowing steam by
two distinct methods, both of which operate by the difference in
density of steam and water. The water separator is always fitted near
the boiler to separate water carried forward mechanically from the
How insulation works
Insulation is a barrier that minimizes the transfer of heat energy from
one material to another by reducing the conduction, convection and/or
radiation effects.
Insulating materials:
Most insulation is used to prevent the conduction of heat. In some cases
radiation is a factor. A good insulator is obviously a poor conductor.
Less dense materials are better insulators. The denser the material, the
closer its atoms are together. That means the transfer of energy of one
atom to the next is more effective. Thus, gases insulate better than
liquids, which in turn insulate better than solids.
An interesting fact is that poor conductors of electricity are also poor
heat conductors. Wood is a much better insulator than copper. The
reason is that metals that conduct electricity allow free electrons to roam
through the material. This enhances the transfer of energy from one
area to another in the metal. Without this ability, the material--like
wood- does not conduct heat well.
Insulation from conduction:
Conduction occurs when materials—
especially solids—are in direct contact with
each other. High kinetic energy atoms and
molecules bump into their neighbors,
increasing the neighbor's energy. This
increase in energy can flow through materials
and from one material to another.
Solid to solid
To slow down the transfer of heat by conduction from
one solid to another, materials that are poor
conductors are placed in between the solids.
Examples include:
Fiberglass is not a good conductor nor is air. That is
why bundles of loosely packed fiberglass strands are
often used as insulation between the outer and inner
walls of a house.
Conductive heat cannot travel through a vacuum.
That is why a thermos bottle has an evacuated lining.
This type of heat cannot be transferred from one
layer to the other through the thermos bottle
Thermal Insulation:
A hot storage vessel or a steam pipe will lose heat to the
atmosphere by radiation, conduction and convection. The loss by
radiation is a function of the fourth power of the absolute
temperatures of the body and surroundings and will be small for
low temperature differences but will increase rapidly as the
temperature difference increases. Air is a very poor conductor
and heat loss by conduction will, therefore, be small. On the
other hand, since convection currents form very easily, the heat
loss from an unlagged surface is considerable. The conservation
of heat and hence usually of steam is an economic necessity and
some form of lagging should normally be applied to hot
The two main requirements of a good lagging material are that it
should have a low thermal conductivity (High R- value) and that
it should suppress convection currents.
The materials that are frequently used are cork, asbestos and
For a circular pipe with length very large compared to outer
diameter, it may be assumed that the heat flows only in radial
directions. If a layer of insulation installed around the circular
pipe to reduce the amount of heat transfer, then it is assumed
that the heat transfer will be decreased by adding more
insulation. By adding the insulation around the pipe the outside
surface area is increased, which will increase the heat transfer.
The determination of critical thickness of an insulation-layer is
very important to minimize the heat transfer particularly in
circular hot water pipes. For this the heat loss from an
insulated pipe is considered as a function of the insulation
thickness (t). The critical thickness (rc) is determined analytically
in terms of thermal conductivity
critical = K /h
(h= heat transfer coefficient including radiation
Increasing the thickness of the lagging will
reduce the loss of heat and thus give a saving in
the operating costs. The cost of the lagging will
increase with thickness and there will be an
optimum thickness when further increase does
not save sufficient heat to justify the cost..
Generally, the smaller the pipe, the smaller the
thickness used e.g. for temperature of 100150C˚, and for pipes up to 6 in. diameter it is
recommended to use one inch thickness of
lagging and 2 inch thickness if the pipe is over 9
inch diameter.
They are classified as:
Single- pass tubular heater
Fixed-head heat exchanger
Floating-head heat exchanger
“R-value” as used in classifying performance of
insulation in commercial practice is
R= ΔT/(q/A)
The units of R-value are m2˚C /W.
Note: “R-value” differs from the resistance. In Rvalue we use heat flow per unit area.
Furthermore, “R-value” is always expressed for a
certain thickness of the insulating layer. For
example: 3.8 cm thickness of extruded
polystyrene has an “R-value” of 1.3.
Factors to be considered in the design of heat exchangers:
In an exchange, the shell-side and tube-side transfer
coefficients are of comparable importance, and both must be
large if a satisfactory overall coefficient is to be obtained.
The shell-side heat transfer can be improved by the installation
of alternating segmental baffles in the shell which will
multiplicate the path of the heating liquid or steam by making it
flow first in one sense then in the opposite sense across the tube
bundle rather than parallel to it (perpendicular to the tubes).
These baffles are frequently of the segmental form with about 25
% cut for the free space and are perforated to receive the tubes,
thus helping their support. The presence of baffles in the shell
serves also to increase the velocity of flow of the shell fluid or
gas across the tubes, thus improving further the heat transfer.
The advantages of the baffles can be
summarized as follows:
They support the long tubes and the tube
sheets and prevent their weakening.
They lengthen the path of the fluid for
maximum heating efficiency.
Increasing the velocity of the entering fluid by
decreasing the cross-section of the shell,
thus decreasing the thickness of the resistant
The tube-side: heat transfer is increased, in view
of Fourier’s law, by increasing K, and A, and
decreasing x. Thus, the tubes should be
constructed of a metal of high thermal
conductivity K, and should be made as long as
possible and as thin as practicable. Within certain
limits, the higher the number of the tubes in the
bundle, the greater will be the total surface area
offered for heat transfer. However, it is
recommended to space theses tubes so closely
that the area of the path outside the tubes is very
Different patterns of flow:
If the hot and cold fluid flow in one direction parallel
to each other, it is referred to as a parallel-flow
apparatus as in the following figure (a).
If the two fluids flow parallel to one another but in
opposite directions, the heat exchanger is known as a
counterflow device (b).
If the fluids cross each other, the pattern is referred
to as cross –flow (c).
In addition to these simple flow arrangements, more
complex ones are encountered in practice:
simultaneous parallel and cross-flow (d), and
multiple cross-flow (e).

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