Heat transfer for Semester-2 students of GTU

2. INTRODUCTION
Heat transfer is a physical process
involving the transfer of heat from hot area
to cold area.
 Heat transfer occurs due to temperature
difference i.e. driving force between the points
where heat is received and where heat is
originating.
 Heat always tend to flow from point of high
temperature to point of low temperature.

3. INTRODUCTION
 It is a unit operation.
 It is always accompanied by another unit
operation in practice such as…
Heating & cooling of liquid/solid/air
Refrigeration
Evaporation
Drying
Distillation

4. MECHANISM OF HEAT TRANSFER
There are 3 basic mechanisms of heat
transfer.
 Conduction
 Convection
 Radiation

5. CONDUCTION
“When heat flow in a body is achieved by
the transfer of the momentum of individual
atoms or molecules without mixing, such
process is known as conduction.”
 It takes place in solids and fluids whose
movement is restricted.
 e.g. - iron rod such as metal wall of an
evaporator.

6. CONDUCTION
 There is no actual movement of molecules.
On receiving energy from surface of heat,
molecules vibrates and pass on energy to
adjacent molecule.
 When both end have same temperature,
heat transfer is stopped.
 Driving force: Difference of temperature
between two end

7. CONVECTION
“When heat flow is achieved by actual
mixing of warmer portions and cooler
portions of the same material, the process
is known as convection.”
 There is actual physical movement of
molecules.
 It takes place in some fluids (i.e. liquids and
gases).

8. CONVECTION
e.g. If hot and cold liquids are mixed, the heat
can transfer from hot liquid to cold liquid by
physical movement of molecules. This
method of heat transfer is called as
convection.

9. RADIATION
“When heat flows through space by
means of electromagnetic waves, such
energy transfer is known as radiation.”
E.g. Black surface absorbs most of the
radiation received by it & simultaneously
the absorbed energy is quantitatively
transferred into heat.

10. RADIATION
 In short…
The hot body emits radiant energy in all
direction. If this radiation strikes a receiver
then part of it may be absorbed and part of
it may be refracted. This method of heat
transfer is called as radiation.

11. RADIATION
Few examples in which radiation is utilized
for producing heat…
 Solar water heaters
 Solar cookers
 Microwave ovens
 Microwave cookers

12. In general, all 3 mechanisms may operate
simultaneously.
For example…
In ovens air circulate by fan, so as to transfer heat
by forced convection.
Simultaneously, heat is transferred by conduction
from the shelf to the material in contact.
Heat also radiates from hot walls of the oven.

13. CONDUCTION – Fourier’s law
Heat can flow only when there is a temp. gradient i.e.
heat flow from a hot surface to a cold surface.
Thus, basic law of heat transfer by conduction can be
written in the form of a rate equation as follows:
Resistance
forceDriving
Rate
surfacetheofareaconstantalityproportionMean
surfacetheofThickness
Resistance



14. A
Conduction – Fourier‟s law
dx
X
t1
t2

15. FOURIER’S LAW
The rate of heat transfer through
homogenous solid body by conduction is..
- directly proportional to the temperature
difference across the body & cross sectional
area at right angle to the direction of heat
flow and
- inversely proportional to the length of the
path of flow.

16. FOURIER’S LAW
 The Fourier‟s law may be mathematically expressed
as:
or
Where Km = mean proportionality constant (W / m.k)
thickness
differencetemp.area
flowheatofRate


X
tA
q

 α
X
tAK
q
m 

xd
dtAK-
dθ
dQ


17. xd
dtAK-
dθ
dQ

Where,
dQ/d = rate of heat transfer (J/sec)
K = thermal conductivity of material (Btu/ hour.ft.ºF)
A = cross sectional area (m2)
-dt/dx = the rate change of temp (t) with respect to
length at path of heat flow (x)
The minus sign indicates the decrease in
temperature in the direction of flow.

18. Thermal conductivity (K)
Thermal conductivity is the reciprocal of
thermal resistance.
Definition: It is the quantity of heat that flows
across a unit surface area in unit time, when the
temperature drop is unity.
Value of K mainly depends upon…..
- Temperature
- Nature of material
For a given range of temperature & material K is
constant.
Unit : 1 Btu/ hour.ft.ºF (SI unit)
3.154591 J/ m.s. ºK
( 1 Btu = 1.055 KJ)

19. Thermal conductivities of liquid (water = 0.62) and
gases are very small (air =0.03) compared to most
of the solids (copper =379.0).
This is because the resistance offered by liquids
and gases is high as far as the conduction is
concerned.
In case of steam jacket vessels, the kettle (inner
surface) is usually made up of copper and jacket
(outer surface) is usually made up of iron (???.....)

20. FOURIER’S LAW UNDER STEADY
STATE CONDITIONS
 When the heat transfer (in most of the industrial
processes) is stabilized, there is no change in
temp. from one end to the another end. This is
called as steady state condition.
 Under the steady state condition the Fourier‟s
law is expressed as:
xd
dtAK-
constant
dθ
dQ


21. Resistance to the flow of heat
 When heat flows through a solid by conduction,
there is certain resistance to the flow
determined by the thermal conductivity, cross
sectional area and thickness of the particular
substance.
surfacetheofareaconstantalityproportionMean
surfacetheofThickness
Resistance


.Ak
x
R 

22. TYPES OF RESISTANCE
With the reference to the direction of
heat flow:
 Resistance in series
 Resistance in parallel

23. Compound resistance in series
 If one solid is placed is placed in series with another
solid so that heat must pass through both of these, the
resistance to the flow of heat will be greater than it would
be for one of the solid alone.
If 3 solids of equal cross sectional area, designated as
1,2 and 3 are placed in series, and if condition of steady
heat flow exists, than exactly same amount of heat per
unit time must be transferred through each of the solids.
 This can be expressed mathematically as…..
eq – (1)




















QQQ
θ
Q
1 2
1
3
3

24. Direction of heat flow
Hot side
Cool side
R1
R2
R3

25. Thus, the characteristics are:
Thickness of the 3 layers = L1,L2, amd L3 (m).
Conductivities of materials of which layers are made = K1, K2,
and K3 (W /m.k)
Area of the entire wall = A (m2)
Temperature drop across three layers = t1, t2, and t3 (K)
Resistances of 3 layers = R1, R2 and R3
So, for the above description, the total temperature drop may be written
as:
Driving force, ttotal = t1 + t2 + t3
The rate of flow of heat through several resistances in series is
exactly analogous to the current flowing through several electrical
resistances in series. Therefore, the overall resistance (R) is equal to
the sum of individual resistances.
R = R1, R2 and R3

26. 1 1
ttotal = t1 + t2 + t3
332211total
QQ
R
Q
t RR 



















Now using eq –(1):
)RR(R
Q
t 321total 





 total

total









Q
)RR(R
t
321
total

27. Resistance in parallel
When several solids are placed side by side with their edges
touching in such a manner that the direction of heat flow is
perpendicular to the plane of the exposed face surfaces, the
solids are said to be placed in parallel.
Total cross-sectional area available for heat transfer with
parallel resistance is greater than it would be for any one of
the resistance alone.

28. When the resistances are in parallel, the total amount of heat
transfer is equal to the sum of heat transfer by all individual
resistances in the same time of period, i.e.




















QQQ
θ
Q
1 2 3
3
K1
R1
A1
K2
R2
A2
K3
R3
A3
x1

29. 321total
x
tKA
x
tKA
x
tKA
θ
Q





 





 





 






321total
QQQ
θ
Q

























Now, assuming that t is same for each of the 3 solids;
t





























321total
x
KA
x
KA
x
KA
θ
Q
t





























321total
R
1
R
1
R
1
θ
Q
Substituting value of R i.e. R = x / KA

30. Average area:
A1 = D1L
A2 = D2L
Where, D = diameter, L = Length
When area is not constant, we take average area.
These are two method to take average area.
(1) Arithmetic mean:
(2) Log mean value:
A1
A2
2
AA
A
21
A.M.


 12
12
L.M.
/AAlog2.3
AA
A



31. Average Temperature:
When temperature is not constant, we have to take average
temperature.
These are two method to take average temperature.
(1) Arithmetic temperature:
(2) Log mean temperature difference (LMTD):
If A2/A1 or t2/t1 is more than 2, we have to take LMTD.
If this value is less than 2, we have to take arithmetic mean value.
2
tt
t
21
A.M.


 12
12
t/tlog2.3
tt
t
10
L.M.




32. CONVECTION
 e.g. liquids and gases.
 There is actual physical movement of
molecules.
 It is always accompanied by conduction.
 Film concept: In convection heat transfer, mass
of hot fluid that transfers the heat through a
static film of fluid, is known as film concept.
H
Film of fluidHot fluid

33. The rate of heat flow is directly proportional to area between
two films and temperature difference across the film.
fAα
θ
Q
ftα
θ
Q

ff tAα
θ
Q

ff thA
θ
Q

“h” is called as film co-efficient
Af is area between two films
tf is the temperature difference across the film
Therefore,
and

34. (1) Rate of heat transfer through steam film (convection)
't'Ah'
θ
Q
ff1 





1
θ
Q
Af'h'
1
'tf 





 (1)
(2) Rate of heat transfer through glass wall (conduction)
w
www
2
X
tAK
θ
Q 






2
ww
w
w
θ
Q
AK
X
t 





 (2)

35. (3) Rate of heat transfer through cooling water film (convection)
"t"Ah"
θ
Q
ff3 





3
θ
Q
"Ah"
1
"t
f
f 





 (3)
and
(4) total heat transfer
totaltota tUA
θ
Q
l 





Where, U= overall heat transfer co-efficient
totaltotal
θ
Q
UA
1
t 





 (4)

36. U is called as overall co-efficient of heat transfer which
combines conduction and convection heat transfer co-
efficient.
The value of U is based on whether, we have chosen inside
or outside pipe diameter for calculation of area.
The equation for deriving „U‟:
Now, with the respect to the direction of heat flow, all three
resistances i.e.
(1) Steam film
(2) Glass wall
(3) Cooling water film
are placed in series, therefore:

























QQQ
θ
Q
t ot al
1 2 3
(5)

37. Now, ttotal = tf + tw + tf
Putting the value from equation – (1), (2), (3), and (4)
From equation – (5)
321
θ
Q
"Ah"
1
θ
Q
AK
X
θ
Q
'Ah'
1
t
fww
w
f
total 


















321
θ
Q
"Ah"
1
θ
Q
AK
X
θ
Q
'Ah'
1
A
Q
UA
1
fww
w
f
Total 
























"Ah"
1
AK
X
'Ah'
1
UA
1
fww
w
f


38. Now multiplying both the sides by A:
For pipes having less thickness:
A  Af  Aw  Af
"Ah"
A
AK
AX
'Ah'
A
U
1
fww
w
f

h"
1
K
X
h'
1
U
1
w
w


39. For prolonged use of pipelines, dirt-films are
formed on the either side of pipe. They also offer
resistance to heat-transfer, so final equation will
be:
"h
1
'h
1
h"
1
K
X
h'
1
U
1
ddw
w

U is called as overall co-efficient of heat transfer
which combines conduction and convection
heat transfer co-efficient.

40. Radiation
The hot body continuously emits radiation in all
direction. When this radiant energy strikes a
receiver body,
- some of the energy will be absorbed by the receiver (a),
- some may be reflected (b),
- some may pass through without affecting cold body when
substance is transparent (c).
c
a
b
Heat
transfer

41.  The flow of heat from hot body to cold body
in this manner is known as heat transfer by
thermal radiation.
Radiation

42. Black body
 Imagine a surface or small body, where all the
radiant energy striking on a surface is absorbed
and none is reflected or transmitted. Such
receiver is known as black body.
e.g. piece of rough black cloth
 No physical substance is a perfect black body.
 Thus,
Black body is defined as a body that radiates
maximum possible amount of energy at a given
temperature.

43. Rate of Radiation
 A good absorber of heat is a good emitter too.
Conversely a poor absorber is a poor emitter.
 Normally, hot bodies emit radiation.
 Stefan Boltzmann law gives the total amount of
radiation emitted by a black body.







100
T
0.173AQ
4

44. RADIATION – Stefan Boltzmann’s law
The amount of heat radiation emitted by
a body increases rapidly with increase in its
temperature.
As per this law, “the radiation heat
energy emitted by a body is directly
proportional to the fourth power of the
absolute temp (T) of total body.”

45. Qradiation  T4
Where, T is expressed in R (Rankin)
R = F + 460
100
T
Ax0.173Qradiation





4
For two black body, where one is HOT and other is COLD.
Black
body
(HOT)T2,
A2
Black
body
(COLD)T1,
A1
T2 > T1

46. Radiation heat absorbed by cold black body is Q1(net);
Radiation heat absorbed by cold black body is Q2(net);
100
T
100
T
Ax0.173Q
12
11(net)



















44
AE
12
22(net) F
100
T
100
T
Ax0.173Q 


















44
Where, FAE = Correction factor

47. Absortivity: Fraction of the insident radation which is
absorbed by a material is called absorptivity (A).
Emmisivity: It is the radio of radiation heat emitted by 1 sq.ft.
of a body per unit time at a particular temperature to radiation
heat emitted by 1 sq.ft. of black body per unit time of same
temperature.
As per above equation, emissivity is 1 for black body.
For actual bodies,  is less than one, because a fraction of
the radation is absorbed, which appears as heat.
A good absorber of heat is also a good emitter at a given
temperature.
bodyblackbyemittedenergy
bodyactualbyemittedenergy
Emmisivity

48. Grey Body
Absorption of energy by a substance depends on
its properties. Fairly high amount of energy will be
absorbed by dark coloured, opaque and rough
surface bodies. Least energy is absorbed by light
coloured, transparent and smooth surfaced
substances.
At a given temperature, the value of  varies
somewhat with the wavelength of the radiation
falling on it. To solve the problems in practice,
concept of grey body has been introduced.
“A grey body is defined as that body whose
absorptivity is constant at all wavelengths of
radiation, at a given temperature.”

49. Steam as heating media
Steam is used most commonly for heating pharmaceutical
materials in operations such as drying, evaporation, etc.
In addition, steam has important use in pharmacy for
sterilisation.
Steam is commonly used as heating media because…
(1) It has very high heat content.
(2) The heat is given at constant temperature.
(3) The raw material is cheap and plentiful.
(4) Steam is clear, odourless, and tasteless, so that the results
of accidental contamination of a product are not likely to be
serious. On other-hand, heating media such as oils could be
very dangerous if entered in product.
(5) Steam is easy to generate, distribute and control.

50. (6) Steam has three different types of heat (properties):
(a) Sensible heat of water
(b) Latent heat
(c) Superheated steam