1. HEAT TRANSFER
AND
HEAT EXCHANGERS

2. UNITS USED IN HEAT TRANSFER
TEMPERATURE: Temperature is the measurement of HEAT
INTENSITY, how hot or how cold, and can be measured by using
a thermometer.
Temperature is generally measured in units of oC (degrees Celsius
or Centigrade), or in o F (degrees Fahrenheit). For scientific uses,
temperature is measured in DEGREES ABSOLUTE. These are
Kelvin for the Celsius scale and degrees Rankine for the
Fahrenheit scale.
To convert degrees Celsius to Kelvin, just add 273.
0K = oC + 273
To convert degrees Fahrenheit to degrees Rankine, just add 460.
o R = o F + 460

3. oF oR oC oK
212 672 100 373
100 560 37.8 310.8
32 492 0 273
- 40 420 - 40 233
- 460 ZERO - 273 ZERO

4. HEAT.
Heat is a form of energy and is measured in units called Joules
symbol J. Fuels contain heat energy. For example, when 1 cubic
meter of natural gas is burned in air, the chemical reaction we call
combustion produces 37,000,000 joules of heat energy.
The joule is a small unit of energy.
1 kJ = 1000 J or 103 J 1 MJ = 1,000,000 J or 106 J
Energy can also be expressed in Btu, British thermal unit, or in
cal, Calorie. The calorie, abbreviated cal, is defined as the amount
of heat needed to heat 1 gram of water 1.0 oC.
Also, 1 kcal, kilocalorie = 1000 cal. The Btu is defined as the
amount of heat needed to raise 1.0 pound of water 1oF. Hence,
1 Btu = 252.16 cal 1 cal = 4.184 J 1 Btu = 1055.06 J

5. HEAT FLOW
Heat will flow from a hot to a cold area. The speed at which the
heat flows will be the number of joules that pass from the hot area
to the cold area in one second, i.e. joules per second..
In the SI system of units, 1 W = 1 JS-1
TEMPERATURE DIFFERENCE AND TEMPERATURE GRADIENT
If a temperature difference exists between two points, then heat
will flow, JS-1 or W, from the hotter to the colder point.
The temperature difference between the two points is often
thought as the DRIVING FORCE in heat transfer.
The temperature gradient between two points is :
Temp. gradient = (higher temp. – lower temp) / Distance
between points

6. 0.3 m
Hot side
900oC
(1173 K)
Cold side
60oC
(333 K)
Heat flow 1400 J s -1
Temperature 900 – 60 = 840 oC
difference or 1173 – 333 = 840 K
Temperature 840 / 0.3 = 2800 oC m –1
gradient or 840 / 0.3 = 2800 K m –1
Heat flow 1400 J s –1 or 1.4 kJ s-1
1400 W or 1.4 kW

7. TYPES OF HEAT
If heat energy is added to a substance the motion of the
molecules increases creating more heat and thereby
increasing the temperature. nearly all modern chemical
processes, heat is either:
Needed to make the reaction between the substances
happen, or
Is produced during a chemical reaction.
Heat is required to boil water to make steam or to
change any liquid into vapor. Heat is required to change
ice into water or any solid into its liquid state.

8. Latent Heat of Fusion changes solid to liquid.
Latent Heat of Vaporization changes liquid to vapor.
Latent Heat of Condensation changes vapor to liquid,
Latent Heat of Solidification changes liquid to solid.
Latent Heat of Sublimation changes solid to vapor.
If heat is given to a substance, we say the substance
becomes hotter. Conversely, if heat is taken away we say
the substance becomes colder. Heat can also cause a
change in the state of a substance without changing its
temperature. This is called LATENT HEAT.

9. HEAT CAPACITY ( specific heat capacity of a substance)
The amount of heat necessary to increase the
temperature by 1 degree. It can be expressed for 1g, 1Ib,
1 gmol, 1 kg mol or 1lb mol of the substance. For
example, a heat capacity is expressed in SI units as J/kg
mol.K; in other units as cal/g.oC,
cal/g mol.oC, kcal/kg mol . oC, Btu/lbm. oF or Btu/lb
mol.oF.
Gases have different specific heat capacity values:
 Cp = the specific heat capacity at constant pressure.
 Cv = the specific heat capacity at constant volume.
The following relations apply to ideal gases:
Cp – Cv = R = 8314.34 J/kg mol. 0K

10. For mono atomic gases: Cv = 3/2R and Cp =5/2R
For bi-atomic gases: Cv = 5/2R and Cp =7/2R
For tri atomic gases: Cv = 6/2R and Cp =8/2R
The following is a general empirical formula applies to all
multi-atomic gases:
Cp = a + bT + cT2 + dT3
Where:
T = temperature in K
a,b,c, and d are constants for the substance
concerned and can be obtained from tables.
The specific heat capacity of liquids is usually between 1.6
and 2.1 kJ/ kg.K, the specific heat will increase with rising
temperature.

11. MIXTURES.
Mixtures frequently have to be heated or cooled in the process
industry. We have to calculate an average specific heat
capacity from the composition by mass, weight percentages.
EFFECT OF PRESSURE.
 Pressure has little or no effect on solids
 The Cp of liquids increases with rising pressure.
 The Cp of gases increases as the pressure increases.
The quantity of heat which is absorbed or released can be
calculated by the following way:
Quantity of heat = mass x temperature difference ×
specific heat
The equation is:
Q == m × Δ t × c
Where: m = mass
Δt = temperature difference
c = specific heat capacity

12. Example:
2 kg of water are heated from 30oC to 60oC specific heat
capacity of water = 1 kcal/ kg.°C = 4.1868 kJ/ kg.0K
Q = 2 × 30 × 1 = 60 kcal
Q = 2 × 30 × 4.18 = 251.4 kJ

13. HEAT TRANSFER
Heat transfer is the flow of heat energy from a hot
substance to a colder substance.
METHODS OF HEAT TRANSFER.
Heat can be transferred by THREE methods:
 By CONDUCTION
 By CONVECTION
 By RADIATION

14. HEAT TRANSFER BY CONDUCTION
Heat has traveled through the metal rod by a process
known as CONDUCTION.
In metals the process is usually rapid, whereas in non-metals it
is slow.
Metals contain FREE ELECTRONS in their structure. These
electrons move about the crystal structure of the metal in a fairly
haphazard and random way. When a metal is heated, the free
electrons begin to move faster, i.e. their kinetic energy increases.
The hot electrons drift towards the colder parts of the metal taking
with them the energy they have picked up. At the same time the
slower moving, cooler, electrons drift towards the heated end, pick
up energy and in turn move towards the colder parts. This
movement of the electrons thus mixes and passes energy through
the metal rod.

15. Energy is also transmitted through the metal rod by
VIBRATION OF THE ATOMS/MOLECULES
themselves. The atoms/molecules at the hot end pick up
energy and vibrate more rapidly. Under these conditions
they collide with the colder atoms/molecules adjacent to
them and in turn cause them to vibrate at a new, faster rate.
In this way heat energy is transferred along the metal rod.
 Movement of free electrons, which have acquired more
energy.
 Heated layers of molecules colliding with other colder
molecules adjacent to them.

16. The first of the two processes is the more effective.
Non-metals do not have free electrons in their structure, and only
the second process is available for heat transfer by conduction.
This explains, to some extent, why metals are good conductors and
non-metals are usually poor conductors of heat. Copper and
aluminum are good conductors of heat, whilst substances such as
cork, wood and polystyrene are poor conductors.

17. THERMAL CONDUCTIVITY
Thermal conductivity can be defined as: The number of heat units
(Joules) flowing per unit of time (1 second) through a cross-
sectional area (1 square metre) when the temperature falls by one
degree (1 Kelvin or 1 degree Celsius) per unit length (1 metre) of
its path.
The units of thermal conductivity are, therefore, joules per second
per metre squared (area) per meter (thickness) per degree Celsius,
or Kelvin.

18. hot face
(say 25o
C)
Area (A) 1 m2
heat flow
J s-1
cold face
heat flow J s-1
thickness through which
heat flows d = 1 m
units of thermal conductivity are:
Watts per meter per oC or K (W m-1 K-1 )

19. K VALUES
The k values for most materials have been determined in the
laboratory. The thermal conductivities of some materials used in
industry are shown below.
MATERIAL THERMAL CONDUCTIVITY k (Wm-1 K-1)
 Solids – metals
Copper 390
Aluminum 202
Steel 55
 Solids – nonmetals
Magnesia 0.07
Cork 0.043
Glass 1.09
Asbestos 0.16
Brick (alumina) 3.1
 Fluids
Water 0.62
Benzene 0.16
Air 0.024

20. CONDUCTION OF HEAT THROUGH SINGLE WALLS
The rate of flow Φ (J S-1) from the hot side to the cold side will
depend on the following factors:-
The thermal conductivity k (W m-1 K-1)
The area A (m2),
 The difference in temperature T1 – T2 (K) (T1 – T2 is referred to
as ΔT).
 The thickness d (metres)
Refractory wall,
thermal conductivity, k,
(W m-1
K-1
)
Thickness of wall
d (m)
cold side temperature
T2 K
hot side temperature
T1
K
area of wall over
which heat flows
A (m2
)
heat flow by conduction through wall (J/s)

21. If Φ represents the heat flow in J S-1 (or watts), then
Φ = k A (T1 – T2) / d
Where:
Φ rate of heat flow (in J S-1)
k thermal conductivity (in W m-1 K-1)
A area over which heat is passing (in m2)
T1 hot face temperature (in K)
T2 cold face temperature (in K)
d thickness or distance between
hot face and cold face (in m)

22. Example 1.
The outer surface of a boiler is covered with insulating
material of thermal conductivity 0.04 W m-1 K-1. It is 125
mm thick and has a surface area of 50 m2. The inside edge of
the insulating material has an average temperature of 423 K
and the temperature of the outside surface is 303 K.
Calculate the heat loss through the insulation per hour.
Φ =kA (T1 – T2) / d
List the information given in the question:
Φ= this is the heat flow in JS-1, we need to calculate this
value.
K= 0.04 W m-1 K-1
A= 50 m2
T1= (423) K
T2= (303) K
d = 0.125 m

23. All of these values must be expressed in SI units before they are
substituted in the formula:
Φ =0.04 × 50 × (423 – 303) 0.125
Φ = 1920 J S-1 (or Watts)
1920 represents the number of joules of heat which pass
through the insulation in one second. To find the quantity which
will pass through the insulation per hour, we must multiply this
figure by 3600, the number of seconds in 1 hour.
Thus heat loss through insulation per hour= 1920 × 3600
= 6192000 J h-1
= 6912 kJ h-1
= 6.912 MJ h-1

24. Example 2
A horizontal steam pipe of 50 mm outside diameter is covered
with 10 mm thickness of lagging of thermal conductivity
0.12 W m-1 K-1. If the outer surface temperature of the
lagging is 308 K and the outer surface of the pipe has a
temperature of 423 K. Estimate the heat loss through the
lagging per metre length of the pipe.
Take π = 3.142. Assume the inside temperature of the lagging
is the same temperature as the outside surface of the pipe.
Heat will travel from the inside area of the lagging through to
the outside area as indicated by Φ, but in all directions along
the 1 metre length asked for in the question. The inside area of
the lagging is calculated by multiplying the inside
circumference by its length.

25. Inside area of lagging = π × 0.05 × 1 = 0.157 m2
(N.B. The circumference of a circle is π x diameter)
A similar calculation will give us the outside area of the lagging.
Outside area of lagging = π × 0.07 × 1 = 0.220 m2
Thus the heat from the hot side of the lagging will travel from
an area of 0.157 m2 through a
thickness of 0.01 m to an outside area of 0.220 m2.

26. Which area do we use in our formula?
One solution to this problem, which is accepted at this level, is to
calculate the average area and use this as A in the conductivity
equation.
Average area across which heat flows = (0.157 + 0.220) / 2 =
0.189 m2
Φ= This is the heat flow in J s-1 which we are asked to
estimate.
k = 0.12 W m-1 K-1
A = 0.189 m2 (average)
T1 = 423 K
T2 = 308 K
d = 0.01 m
Now substitute these figures into the standard formula:
Φ = k A (T1 – T2) / d
Φ = 0.12 × 0.189 × (423 – 308) / 0.01 = 261 J s-1 =261W

27. SUMMARY
The rate at which heat travels by conduction through
solids is indicated by a physical property called thermal
conductivity.
Thermal conductivities are listed in standard reference
books. A high value indicates a good conductor, a low
value a poor conductor.
The rate of heat flow Φ (in J s-1) through a solid, by
conduction, can be calculated using the standard
formula:
Φ =kA(T1 – T2) / d

28. This is the way in which heat energy travels through liquids and
gases. (FLUIDS)
CONVECTION IN LIQUIDS
When the vessel is heated at the bottom, a current of hot liquid
moves upwards and its place is taken by a cold current, moving
downwards. As heating proceeds, well defined hot upward and
cold downward moving currents can be seen. These currents are
called CONVECTION CURRENTS.

29. So how do convection currents work?
When a portion of the liquid near the bottom of the vessel
is heated, it expands. Since its mass remains the same it
must become less dense, and therefore it rises to the surface
of the liquid. Thus a warm convection current moves
upwards. Colder denser liquid falls to the base of the vessel
and in its turn is heated, becomes less dense and circulates,
taking heat with it.

30. CONVECTION IN AIR.
Hot convection currents can often be seen and felt above
a domestic water radiator. Hot air rises from the radiator
and circulates into the room thus warming it. At the same
time colder air circulates towards the base of the radiator.
In its turn it becomes heated and circulates upwards taking
and mixing the heat it contains with the rest of the air in
the room.

31. Heat transfer by convection occurs when a fluid, liquid
or gas, comes into contact with a surface hotter, or
cooler, than itself.

32. CALCULATION OF THE HEAT TRANSFER RATE
BY CONVECTION
When the fluid outside the solid surface is in forced or natural
convective motion, the expression of the rate of heat transfer from
the solid to the fluid, or vice versa, is as follows:
qc = hc A (Ts – Tf)
where:
qc =rate of heat transfer convection in J/s or W
A =Area of heat transfer, m2
Ts = The temperature of the solid surface, K
Tf =The average temperature of the fluid, K
hc =The convection heat transfer coefficient, W/m2.K

33. The coefficient hc is a function of the system
geometry, fluid properties, flow velocity, and
temperature difference. In many cases, empirical
correlation are available to predict this coefficient,
since it often cannot be predicted theoretically.

34. FACTORS AFFECTING THE RATE OF HEAT
TRANSFER BY CONVECTION.
1. DENSITY and GRAVITY.
Thus the rate of change of density with change of temperature
is an important factor to consider when predicting the speed of
heat transfer by convection.
2. COEFFICIENT OF THERMAL EXPANSION.
A fluid, which has a high coefficient of thermal expansion, will
consequently have a high change of density with change of
temperature. This, in turn, will tend to speed up the formation
and movement of convection currents.
3. VISCOSITY.
Convection currents will move slowly within fluids of high
viscosity and quickly within fluids of low viscosity. Thus the
rate of heat transfer by convection will depend upon the
viscosity of the fluid being heated.

35. 4. THERMAL CONDUCTIVITY
Most fluids have very low thermal conductivity values.
Accordingly, heat transfer by conduction is slow and far less
important than heat transfer by convection. The fluid would
need to have an uncharacteristically high thermal conductivity
for this factor to be of any importance.
5. SPECIFIC HEAT CAPACITY
A fluid with a high specific heat capacity will carry more heat
with it, as it circulates, than one with a low value. Thus the
specific heat capacity is an important factor to consider when
evaluating heat transfer by convection

36. 6. VESSEL DIMENSIONS.
The distance traveled by the convection currents and the
area of the vessel, which is heated will both affect the rate
of heat transfer by convection. So the fluid in a tall narrow
vessel may take longer to heat up than the same mass of the
same fluid in a shorter, wider vessel.
7. TEMPERATURE DISTRIBUTION.
The rate of heat transfer will depend upon the difference in
temperature between the hottest and coldest parts of the
system. For a vessel, the hottest part will be at the base and
the coldest part near the surface of the fluid. As heating
proceeds, this temperature difference gets smaller. It reaches
a minimum when the liquid begins to boil.

37. NATURALAND FORCED CONVECTION
Convection currents occur when fluids come into contact with hot
surfaces. The convection currents produced give rise to a
MIXING ACTION, which helps to transfer heat throughout the
body of the fluid. The process of heat transfer by NATURAL
CIRCULATION is called NATURAL CONVECTION.
Movement of the fluid is caused only by the differences in
density, The rate of heat transfer by convection can be improved
by agitating the fluid as it is heated.

38. The rate of heat transfer by convection will be greater if
propeller is used to mix or agitate the fluids. Heat
transfer produced in this way, i.e. by FORCING a fluid
to move over a heating surface, is referred to as
FORCED CONVECTION.
Generally speaking, with forced convection there is:
more rapid circulation.
more turbulence and,
more rapid heat transfer.
Baffles fitted to the heating vessel will produce more
turbulence, improved mixing and hence more rapid heat
transfer by convection.

39. Convection is the transfer of heat within a fluid,
or from a heated
surface to a fluid. It occurs by movement of
the fluid itself and can be either:
Natural convection, where movement of the
fluid is caused by temperature differences
(followed by density differences).
Forced convection, where movement is caused
mainly, or entirely, by mechanical means (e.g. a
propeller).

40. HEAT TRANSFER IN FLUIDS FLOWING THROUGH
PIPES AND TUBES
Heat passes through the tube wall by conduction and into the fluid
flowing through the tube by convection. If the fluid flows through
the tube in a TURBULENT way, then a mixing action will be
produced. This mixing action will improve the rate of heat transfer.
Greater turbulence will produce faster heat transfer by convection
within the fluid.

41. Fouling deposits on tubes of water tube boilers
Usually heat transfer equipment is operated with both the
process fluid and the thermal fluid flowing in a TURBULENT
manner. This procedure results in the following benefits
 Good heat transfer within the fluids, i.e. forced convection.
Static layers of fluid on the heat transfer surface are reduced to
a minimum.

42. Static layers of fluid on each side of heat exchanger tube
r

43. Resistances to the flow of heat through pipe walls

44. NATURALAND FORCED CONVECTOR HEATERS (EXAMPLE)
These are similar in principle to the domestic heater.

45. (a) shows cold air circulating over the tubes of a heat
exchanger. Heated air then moves upwards and away
from the heating surfaces. As this happens, cold air is
drawn in near the base of the exchanger and, in its turn,
becomes heated.
(b) shows a fan forcing cold air over the tubes of the
heat exchanger. This enables very much larger volumes
of air to be heated than can be heated by natural
circulation, i.e. natural convection, alone.
Fan assisted convector heaters can be fitted with a
number of smaller diameter tubes so increasing the area
of the hot surface available for heat transfer for a given
unit size. This, in turn, will increase the volume of cold
air that can be heated in a given time. The extra force
required to push the air through the bank of tubes is
provided by the fan.

46. SUMMARY
Heat transfer through fluids takes place by convection. It occurs
when cold fluids come into contact with hot surfaces.
The rate of heat transfer by convection is influenced by the
physical properties of the fluid. Some of the important ones are
viscosity, density and coefficient of expansion.
Forced convection occurs when the fluids are forced over hot
surfaces, usually by means of pumps or agitators.
Heat transfer by forced convection is more effective than heat
transfer by natural convection .Fluids are forced through tubes
of heat exchange equipment at high velocity to produce
turbulence which results in heat transfer by forced convection.

47. RADIATION consists of invisible energy waves, which are
able to pass across a space. Unlike heat transfer by conduction
and convection, heat transfer by radiation does not require any
material to be present between the hot part and the cold part of
the system. Heat can travel by radiation across a vacuum. For
example, heat energy from the sun travels across the empty
space beyond the earth’s atmosphere. Scientists call these
invisible heat waves ELECTROMAGNETIC WAVES.
Electromagnetic waves travel across a space very rapidly, 3 ×
108m s-1.

48. If you hold your hand near to an electric light bulb when the
current is switched on, you will feel radiant heat immediately.
Bulbs of this type are evacuated during manufacture so that
heat from the glowing element cannot have traveled by
conduction or convection. Energy radiated from hot surfaces
travels by means of electromagnetic waves. These have similar
properties as LIGHT WAVES and travel at the same speed, i.e.
300,000 km s-1.
When electromagnetic waves from a hot surface fall on a
cooler surface, they are partially absorbed and the cooler
surface heats up, i.e. heat energy is transferred from the hotter
surface to the cooler.

49. FACTORS AFFECTING THE RATE OF HEAT
TRANSFER BY RADIATION
The rate at which a hot surface, or object, radiates heat, J s-1,
depends upon:
its temperature (T2)
the surrounding temperature (T1)
its area (A)
its nature (ε)
1. RADIATION RATE AND SURFACE TEMPERATURE
The hotter a surface or object is, the more energy it will
radiate. The energy radiated from a surface has been shown
to be directly proportional to the fourth power of its absolute
temperature. This can be expressed mathematically as:
Energy radiated α T4
Where T is the temperature in Kelvin (i.e. o C + 273)

50. This is a difficult relationship to understand. Put in simple
terms, the heat radiated from a surface increases very
rapidly with increase in temperature. This increase in
radiant energy with increase in temperature is very much
greater than that for heat transfer by convection. At
temperatures over 500oC, most of the heat transferred
from a surface will be by radiation. For example, most of
the heat transferred from flames to water tubes in boilers
is by radiation

51. 2. RADIATION RATE AND SURROUNDING
TEMPERATURE
All surfaces, whatever their temperature, radiate energy in the
form of electromagnetic waves. A hot surface will radiate to
cold surroundings. However, at the same time, those
surroundings will radiate back to the hotter surface. The net
effect will be the transfer of heat from the hot surface to the
colder surfaces or surroundings.
If we take the temperature of the surroundings into
consideration, we must modify what we said earlier and say:
The rate of heat transfer by radiation is directly proportional
to the DIFFERENCE BETWEEN the fourth power of the
surface temperature (T2
4) and the fourth power of the
surrounding temperature (T1
4), both temperatures being
expressed in degrees absolute (K).This can be expressed
mathematically as:
Energy radiated from surface to surroundings α (T2
4 - T1
4)
Where T2 is the surface temperature (K) and
T1 is the temperature of the surroundings (K)

52. 3. RADIATION RATE AND SURFACE AREA
For a given temperature, the larger the area the greater is the
amount of energy radiated from it. Expressing it mathematically,
we can say:
Energy radiated α A
Where A is the surface area in m2.
4. RADIATION RATE AND THE NATURE OF THE
SURFACE.
Not all surfaces radiate the same amount of energy for a given
size and temperature. It is found that, for a given temperature, a
body radiates MOST HEAT when its surface is DULL BLACK
and LEAST HEAT when its surface is HIGHLY POLISHED.

53. Three surfaces are shown; all have
the same area and are held at the
same temperature. They radiate to
surroundings at constant
temperature. Detectors are placed
at the same distance in front of
each surface and measure the
radiant heat transmitted from each
of them.
It is found that the dull black
surface radiated most energy, 100 J
s-1, the polished surface the least, 6
J s-1, with the grey surface
somewhere between the two
extremes, 45 J s-1. You should note
that these figures are illustrative
and do not represent any
particular experiment,

54. The experiment can be repeated using different surfaces with different colour and textures.
It will be found that no surface radiates more energy than the dull black surface. Generally
speaking, darker surfaces radiate more energy than lighter coloured polished surfaces. Both
colour and texture of a surface affect the energy it will radiate at a given temperature. The
radiating property of a surface is referred to as its EMISSIVITY of a surface and given the
symbol ε. Since a dull black surface radiates the maximum amount of energy at a given
temperature it is used as the standard and the emissivity of a surface is defined as:
Emissivity is the ratio of the energy radiated from that surface to the energy radiated from
a dull black surface of the same size and held at the same temperature.
The dull black surface is shown to radiate 100 J s-1.
The grey surface has the same size, is held at the same temperature, and is shown to radiate
45 J s-1.
Thus the emissivity (ε) of this surface is: 45/ 100 = 0.45
The polished surface has the same size and temperature as the dull black surface and is
shown or radiate 6 Js-1
Thus the emissivity (ε) of this surface is: 6 / 100 = 0.06
(NOTE: by definition, no surface can have an emissivity greater than 1.)

55. Surface
Emissivity(ε)
Furnace interior 1.00
Iron oxide surface 0.82
Oxidized copper surface 0.79
Refractory bricks 0.78
Aluminium paints 0.50
Polished copper 0.04
Polished Aluminium 0.04
Oxidizd Aluminium 0.15

56. CALCULATING HEAT TRANSFER BY RADIATION
As you will recall, the factors which affect the rate of heat transfer by radiation
from a body are:
◦ Its temperature T2 (K)
◦ Temperature of surroundings T1 (K)
◦ Its area A (m2)
◦ Its emissivity ε
Scientists have combined these factors and produced a formula from which the
rate of heat transfer by radiation, Φ (J s-1 or W), can be calculated. This is given
below.
Φ = 5.7 × 10-8 × ε × A × (T2
4 – T1
4)
Where:
◦ Φ is the heat radiated from the hot surface (W)
◦ ε is the emissivity, from reference books.
◦ A is the surface area radiating heat (m2)
◦ T2 is the surface temperature (K)
◦ T1 is the surrounding temperature (K)
The following simplified example will be used to illustrate the use of this formula.

57. Example 3.
Calculate the rate of heat transfer by radiation, and hence the heat loss by radiation, from a
flat furnace roof at 90oC to surroundings at 20 oC. The roof measures 7 m by 3 m and has
an emissivity of 0.8.
Use the formula Φ = 5.7 × 10-8 × ε × A × (T2
4 - T1
4)
Where:
◦ ε = 0.8
◦ A = (7 × 3) = 21 m2
◦ T2 = (90 + 273) = 363 K
◦ T1 = (20 + 273) = 293 K
Substitute these figures into the formula:
Φ = 5.7 × 10-8 × 0.8 × 21 × (3634 – 2934)
Φ = 9569.3 J s-1 or W
This heat loss can be reduced by covering the roof with Aluminium sheeting, since this
would reduce the emissivity of the surface.
Assuming the emissivity of Aluminium sheeting is 0.15; calculate the new rate of heat loss
from the furnace roof.
Substituting ε = 0.15 for ε = 0.8 in the equation, we have;
Φ = 5.7 × 10-8 × 0.15 × 21 × (3634 – 2934)
Φ = 1794.2 J s-1 or W
When we compare the two answers, we can see that the use of Aluminium foil has reduced
the heat loss from 9569.3 W to 1794.2 W, a worthwhile saving.
You should not forget that other heat losses would occur by convection from the hot furnace
roof.

58. ABSORPTION OF RADIANT HEAT BY A SURFACE
When radiant heat falls onto a surface, some is absorbed and some is reflected. The portion, which is
absorbed heats up the surface. Some surfaces are good absorbers, whilst others are good reflectors.
Two sheets of tin plate have corks held onto their surfaces by thin films of wax. One of the sheets is
polished whilst the other is painted dull black. These plates are then set vertically, a short distance
apart, with a Bunsen burner midway between them. When the burner is lit, both surfaces receive equal
quantities of radiant heat. In a very short time the wax on the dull plate melts and the cork slides off.
The polished plate, however, remains cool and the wax unmelted.
waxwax
dark black surface polished surface
wax holding this cork
soon melts

59. The results of such experiments will show that darker, duller surfaces are good
absorbers of heat whilst lighter, more polished surfaces are poor absorbers of
heat. Lighter, polished surfaces, in fact, reflect heat rather than absorb it.
Vessels used for the storage of volatile liquids are often covered with
Aluminium foil, or sheeting, to reduce heat absorption on hot days. Such
absorption could result in excessive losses through evaporation, with possible
associated safety and toxic hazards.
This experiment shows that a dull black surface is a much better absorber of
radiant heat than a polished one.

60. SUMMARY
 Heat transfer by radiation takes place by means of electromagnetic
waves. These do not require a material substance for their movement.
 The rate of heat transfer by radiation from a hot surface to a cold
surface depends upon:
 The surface temperature.
 The surrounding temperature.
 The surface area.
 The emissivity of the surface.
 Duller, darker surfaces radiate more energy than lighter, smoother
surfaces. Emissivity is a measure of the ability of a surface to radiate.
 The amount of energy absorbed by a surface also depends upon its
colour and texture. Generally speaking, darker, duller surfaces absorb
radiant heat more readily than lighter, smoother surfaces.

61. HEAT TRANSMISSION (EXAMPLE)
The figure represents a heating furnace fired by natural gas. It consists of a steel
shell lines on the inside with refractory bricks and covered on the outside with
insulating material. The furnace is used to preheat cold raw material up to process
temperature.
The raw material flows through a series of heat resistant tubes, usually 18/8
stainless steel, which are suspended in the furnace space above the flame.
When natural gas burns, an exothermic chemical reaction takes place. Energy is
released at the rate of 37 MJ for each cubic metre of gas burned and a very hot
flame, about 2000oC, is produced.

62. Let us follow the progress of this energy.
Heat is transferred by RADIATION from the flame to the walls of the furnace
and from the flame to the tubes through which the process fluid is flowing. This
is a very rapid process since electromagnetic waves, energy waves, are radiated
across space, i.e. from flame to walls and from flame to tubes, at 3 x 108 m s-1
◦ Heat is transferred by CONVECTION as the hot gases, produced during
combustion, circulate over, round and between the tubes and the walls of the furnace
before they pass out through the chimney stack.
◦ The heat energy arriving at the tubes passes through the tube walls by
CONDUCTION and then by CONVECTION into the process fluid.
◦ The heat arriving at the inside walls of the furnace travels by CONDUCTION
through the refractory brick, the steel shell and then, slowly, through the insulating
material on the outside. This, unfortunately, represents a loss of energy from the
process. We shall have more to say about thermal efficiencies and energy recovery
systems in later lessons.
◦ Heat is also lost by CONDUCTION through the base and foundation of the furnace.
◦ The outside walls of industrial furnaces are usually hotter than their surroundings.
Under these conditions, the heat, which has passed through the walls, will leave the
outside surfaces by CONVECTION, as it heats up the surrounding air, and
RADIATION.

63. Heat exchangers are devices, which transfer heat from a hot fluid to
a cold fluid usually across a metal tube wall.
The most common heat exchangers used in the chemical industry are
the SHELL AND TUBE types. In their simplest form, these consist of
a bank, bundle, of small diameter tubes fitted inside a large diameter
tube, usually referred to as the SHELL.
One fluid flows through the tubes, while the other flows inside the
shell, circulating around and between the small diameter tubes. Heat
is transferred, from one fluid to the other, by CONDUCTION, across
the tube walls, and then by FORCED CONVECTION, through the
fluid.
There are several different designs of shell and tube exchangers. A
number of the more important ones are discussed in the following
sections.

64.  DOUBLE PIPE HEAT EXCHANGER
One of the simplest types of heat exchanger is the double pipe design. It consists of two
concentric pipes.
Hot fluid in
One fluid flows through the inner tube whilst the other flows through the annular space
between the tubes. Heat passes from one fluid to the other by conduction through the inner
pipe wall followed by forced convection through the fluid.
The main advantages of this type of heat exchanger are that they are simple and cheap to
make. They can often be made from standard diameter piping. Their main disadvantages
are that they have low thermal efficiencies, and cannot handle large quantities of process
fluid.

65. The performance of the Double pipe Heat Exchanger type can be
improved by connecting two or more units together.
Fluid A in
Double pipe exchangers are sometimes referred to as ANNULAR or
CONCENTRIC tube heat exchangers.

66.  SHELLAND TUBE HEAT EXCHANGER
Simple shell and tube
heat exchanger
The major features of this type of heat exchanger are:
◦ A large number of small diameter TUBES fitted into a TUBE PLATE to form a BANK or BUNDLE of tubes.
◦ A large diameter tube called a SHELL into which the bank of tubes fits.
◦ End covers or HEADERS, which are fitted over each end of the tube bundle.
◦ INLET and OUTLET pipes fitted to the shell to allow fluid into and out of the shell.
◦ INLET and OUTLET pipes fitted to each end of the cover to allow fluid to flow through the tubes.
◦ An EXPANSION JOINT, fitted to the shell. This is included to relieve stresses due to thermal expansion. It
allows the shell to expand and contract as the tube bundle expands and contracts.
◦ A set of BAFFLES, i.e. plates set at right angles to the tube bundle. Their function is to cause shell side fluid to
flow at right angles to the tubes. They also support the tubes within the bundle.
Direction of flow of fluid A
Direction of flow of fluid B

67. COUNTER CURRENT AND CO-CURRENT FLOW
Co-Current heat exchange
The heat exchanger is operating with CO-CURRENT FLOW since the two fluids flow through the
exchanger in the same direction.
Generally speaking, counter current flow provides the most efficient heat exchange since the
temperature of the cold fluid can be raised to a temperature just below the temperature of the hot
fluid. With co-current flow the heated fluid can be no hotter than the outlet temperature of the cooled
heating fluid. However, the temperature distribution within a co-current heat exchanger is more even.
For this reason co-current is often preferred when heat-sensitive fluids are being heated.
Direction of flow of fluid A
Direction of flow of fluid B