PM3125: Lectures 4 to 6

1
PM3125 Lectures 4 to 6

• Content of Lectures 1 to 6
• Heat transfer
• Source of heat
• Heat transfer
• Steam and electricity as heating media
• Determination of requirement of amount of
  steam/electrical energy
• Steam pressure
• Mathematical problems on heat transfer

2
Heat Transfer

• is the means by which energy moves from
• a hotter object to
• a colder object

3
Mechanisms of Heat Transfer

• Conduction
• is the flow of heat by direct contact between a
  warmer and a cooler body.
• Convection
• is the flow of heat carried by moving gas or
  liquid.
• (warm air rises, gives up heat, cools, then
  falls)
• Radiation
• is the flow of heat without need of an
  intervening medium.
• (by infrared radiation, or light)

4
Mechanisms of Heat Transfer
5
Conduction
HOT (lots of vibration)
COLD (not much vibration)
Heat travels along the rod
6
Conduction
Conduction is the process whereby heat is
transferred directly through a material, any bulk
motion of the material playing no role in the
transfer. Those materials that conduct heat well
are called thermal conductors, while those that
conduct heat poorly are known as thermal
insulators. Most metals are excellent thermal
conductors, while wood, glass, and most plastics
are common thermal insulators. The free electrons
in metals are responsible for the excellent
thermal conductivity of metals.
7
Conduction Fouriers Law
Cross-sectional area A
L
Q heat transferred k thermal
conductivity A cross sectional area
DT temperature difference between
two ends L length t duration of heat
transfer
What is the unit of k?
8
Thermal Conductivities
9
Conduction through Single Wall
Use Fouriers Law
T1
k A (T1 T2)
T2??? T1

x
?x
?x
10
Conduction through Single Wall
k A (T1 T2)
T1

?x
T1 T2

?x/(kA)
T2??? T1
x
?x
Thermal resistance (in k/W) (opposing heat flow)
10
11
Conduction through Composite Wall
B
C
A
T1
T2
T3
T4
kA
kB
kC
x
?xA
?xB
?xC
T1 T2
T3 T4
T2 T3



(?x/kA)A
(?x/kA)C
(?x/kA)B
11
12
Conduction through Composite Wall
T1 T4

12
13
Example 1
An industrial furnace wall is constructed of
21 cm thick fireclay brick having k 1.04 W/m.K.
This is covered on the outer surface with 3 cm
layer of insulating material having k 0.07
W/m.K. The innermost surface is at 1000oC and the
outermost surface is at 40oC. Calculate the
steady state heat transfer per area.
Solution We start with the equation
Tin Tout

(?x/kA)insulation
(?x/kA)fireclay
14
Example 1 continued
(1000 40) A

(0.03/0.07)
(0.21/1.04)
1522.6
W/m2
A
15
Example 2
We want to reduce the heat loss in Example 1
to 960 W/m2. What should be the insulation
thickness?
Solution We start with the equation
Tin Tout

(?x/kA)insulation
(?x/kA)fireclay
(1000 40)
W/m2
960

A
(?x)insulation /0.07)
(0.21/1.04)
(?x)insulation
cm
5.6
16
Conduction through hollow-cylinder
ro
Ti
ri
To
L
Ti To

ln(ro/ri) / 2pkL
17
Conduction through the composite wall in a
hollow-cylinder
r3
r2
To
Material A
Ti
r1
Material B
Ti To

ln(r3/r2) / 2pkBL
ln(r2/r1) / 2pkAL
18
Example 3
A thick walled tube of stainless steel ( k
19 W/m.K) with 2-cm inner diameter and 4-cm outer
diameter is covered with a 3-cm layer of asbestos
insulation (k 0.2 W/m.K). If the inside-wall
temperature of the pipe is maintained at 600oC
and the outside of the insulation at 100oC,
calculate the heat loss per meter of length.
Solution We start with the equation
Ti To

ln(r3/r2) / 2pkBL
ln(r2/r1) / 2pkAL
19
Example 3 continued
2 p L ( 600 100)

ln(5/2) / 0.2
ln(2/1) / 19
680 W/m
L
20
Mechanisms of Heat Transfer
?

• Conduction
• is the flow of heat by direct contact between a
  warmer and a cooler body.
• Convection
• is the flow of heat carried by moving gas or
  liquid.
• (warm air rises, gives up heat, cools, then
  falls)
• Radiation
• is the flow of heat without need of an
  intervening medium.
• (by infrared radiation, or light)

21
Convection
Convection is the process in which heat is
carried from place to place by the bulk movement
of a fluid (gas or liquid).
Convection currents are set up when a pan of
water is heated.
22
Convection
It explains why breezes come from the ocean in
the day and from the land at night
23
Convection Newtons Law of Cooling
Flowing fluid at Tfluid
Heated surface at Tsurface
Area exposed
Heat transfer coefficient (in W/m2.K)
24
Convection Newtons Law of Cooling
Flowing fluid at Tfluid
Heated surface at Tsurface
Tsurface Tfluid

1/(hA)
Convective heat resistance (in k/W)
25
Example 4
The convection heat transfer coefficient
between a surface at 50oC and ambient air at 30oC
is 20 W/m2.K. Calculate the heat flux leaving the
surface by convection.
Solution
Use Newtons Law of cooling
Flowing fluid at Tfluid 30oC
(20 W/m2.K) x A x (50-30)oC
Heated surface at Tsurface 50oC
Heat flux leaving the surface
20 x 20
400 W/m2
h 20 W/m2.K
26
Example 5
Air at 300C flows over a flat plate of
dimensions 0.50 m by 0.25 m. If the convection
heat transfer coefficient is 250 W/m2.K,
determine the heat transfer rate from the air to
one side of the plate when the plate is
maintained at 40C.
Solution
Use Newtons Law of cooling
Flowing fluid at Tfluid 300oC
Heated surface at Tsurface 40oC
250 W/m2.K x 0.125 m2 x (40 - 300)oC
- 8125 W/m2
h 250 W/m2.K A 0.50x0.25 m2
Heat is transferred from the air to the plate.
27
Forced Convection
In forced convection, a fluid is forced by
external forces such as fans.
In forced convection over external
surface Tfluid the free stream temperature
(T8), or a temperature far removed from the
surface
In forced convection through a tube or
channel Tfluid the bulk temperature
28
Free Convection
In free convection, a fluid is circulated due to
buoyancy effects, in which less dense fluid near
the heated surface rises and thereby setting up
convection.
In free (or partially forced) convection over
external surface Tfluid (Tsurface Tfree
stream) / 2
In free or forced convection through a tube or
channel Tfluid (Tinlet Toutlet) / 2
29
Change of Phase Convection
Change-of-phase convection is observed with
boiling or condensation . It is a very
complicated mechanism and therefore will not be
covered in this course.
30
Overall Heat Transfer through a Plane Wall
Fluid A at TA gt T1
T1
T2
Fluid B at TB lt T2
x
?x
31
Overall Heat Transfer through a Plane Wall
.
TA TB
Q

1/(hAA)
1/(hBA)
?x/(kA)
(TA TB)
U A
where U is the overall heat transfer coefficient
given by
1/U 1/hA
1/hB
?x/k
32
Overall heat transfer through hollow-cylinder
Fluid A is inside the pipe Fluid B is outside the
pipe TA gt TB
L
(TA TB)
U A
where
1/UA 1/(hAAi)
1/(hBAo)
ln(ro/ri) / 2pkL
33
Example 6
Steam at 120oC flows in an insulated pipe.
The pipe is mild steel (k 45 W/m K) and has an
inside radius of 5 cm and an outside radius of
5.5 cm. The pipe is covered with a 2.5 cm layer
of 85 magnesia (k 0.07 W/m K). The inside heat
transfer coefficient (hi) is 85 W/m2 K, and the
outside coefficient (ho) is 12.5 W/m2 K.
Determine the heat transfer rate from the steam
per m of pipe length, if the surrounding air is
at 35oC.
Solution Start with
(TA TB)
(120 35)
U A
U A
What is UA?
34
Example 6 continued
1/UA 1/(hAAi)
1/(hBAo)
ln(ro/ri) / 2pkL
ln(5.5/5) / 2p(45)L
1/UA 1/(85Ain)
1/(12.5Aout)
ln(8/5.5) / 2p(0.07)L
Ain 2p(0.05)L and
Aout 2p(0.08)L
1/UA (0.235 0.0021 5.35 1) / 2pL
35
Example 6 continued
UA 2pL / (0.235 0.0021 5.35 1)
(120 35)
U A
steel
air
2pL
(120 35) / (0.235 0.0021 5.35 1)
insulation
steam
81 L
81 W/m
/ L
36
Mechanisms of Heat Transfer
?

• Conduction
• is the flow of heat by direct contact between a
  warmer and a cooler body.
• Convection
• is the flow of heat carried by moving gas or
  liquid.
• (warm air rises, gives up heat, cools, then
  falls)
• Radiation
• is the flow of heat without need of an
  intervening medium.
• (by infrared radiation, or light)

?
37
Radiation
Radiation is the process in which energy is
transferred by means of electromagnetic waves of
wavelength band between 0.1 and 100 micrometers
solely as a result of the temperature of a
surface.
Heat transfer by radiation can take place through
vacuum. This is because electromagnetic waves can
propagate through empty space.
38
The StefanBoltzmann Law of Radiation
e emissivity, which takes a value between 0
(for an ideal reflector) and 1 (for a black
body). s 5.668 x 10-8 W/m2.K4 is the
Stefan-Boltzmann constant A surface
area of the radiator T temperature of the
radiator in Kelvin.
39
Why is the mother shielding her cub?
Ratio of the surface area of a cub to its volume
is much larger than for its mother.
40
What is the Suns surface temperature?
The sun provides about 1000 W/m2 at the Earth's
surface. Assume the Sun's emissivity e
1Distance from Sun to Earth  R 1.5 x 1011 m
Radius of the Sun r 6.9 x 108 m    
41
What is the Suns surface temperature?
(4 p 6.92 x 1016 m2) 5.98 x 1018 m2
(4 p 1.52 x 1022 m2)(1000 W/m2)
2.83 x 1026 W
2.83 x 1026 W
T4
(1) (5.67 x 10-8 W/m2.K4) (5.98 x 1018 m2)
e
s
T 5375 K
42
If object at temperature T is surrounded by an
environment at temperature T0, the net
radioactive heat flow is
Temperature of the radiating surface
Temperature of the environment
43
Example 7
What is the rate at which radiation is
emitted by a surface of area 0.5 m2, emissivity
0.8, and temperature 150C?
Solution
(273150) K4
0.5 m2
0.8
5.67 x 10-8 W/m2.K4
Q
(0.8) (5.67 x 10-8 W/m2.K4) (0.5 m2) (423 K)4

t
726 W
44
Example 8
If the surface of Example 7 is placed in a
large, evacuated chamber whose walls are
maintained at 25C, what is the net rate at
which radiation is exchanged between the surface
and the chamber walls?
Solution
(27325) K4
(273150) K4
Q
(0.8) x (5.67 x 10-8 W/m2.K4) x (0.5 m2)
x (423 K)4 -(298 K)4

t
547 W
45
Example 8 continued
Note that 547 W of heat loss from the surface
occurs at the instant the surface is placed in
the chamber. That is, when the surface is at
150oC and the chamber wall is at 25oC. With
increasing time, the surface would cool due to
the heat loss. Therefore its temperature, as well
as the heat loss, would decrease with increasing
time. Steady-state conditions would eventually
be achieved when the temperature of the surface
reached that of the surroundings.
46
Example 9
Under steady state operation, a 50 W
incandescent light bulb has a surface temperature
of 135C when the room air is at a temperature of
25C. If the bulb may be approximated as a 60 mm
diameter sphere with a diffuse, gray surface of
emissivity 0.8, what is the radiant heat transfer
from the bulb surface to its surroundings?
Solution
(27325) K4
(273135) K4
Q
(0.8) x (5.67 x 10-8 J/s.m2.K4) x p x (0.06) m2
x (408 K)4 -(298 K)4

t
10.2 W (about 20 of the power is dissipated
by radiation)
47
Mathematical Problems on Heat Exchanger
Tc,in
Th,out
Th,in
Tc,out
.
.
.
48
Mathematical Problems on Heat Exchanger
Tc,in
Parallel-flow heat exchanger
Th,out
Th,in
Tc,out
high heat transfer
low heat transfer
49
Mathematical Problems on Heat Exchanger
Parallel-flow heat exchanger
?Ta
?Tb
a
b
.
Q U A ?T
?Ta - ?Tb
is the log mean temperature difference (LMTD)
where ?T
ln(?Ta / ?Tb)
50
Mathematical Problems on Heat Exchanger
Tc,out
Counter-flow heat exchanger
Th,out
Th,in
Tc,in
.
.
.
51
Mathematical Problems on Heat Exchanger
Tc,out
Counter-flow heat exchanger
Th,out
Th,in
Th,in
Tc,in
Th,out
Tc,out
Tc,in
52
Mathematical Problems on Heat Exchanger
Counter-flow heat exchanger
?Ta
?Tb
a
b
.
Q U A ?T
?Ta - ?Tb
is the log mean temperature difference (LMTD)
where ?T
ln(?Ta / ?Tb)
53
Example in heat Exchanger Design
An exhaust pipe, 75 mm outside diameter, is
cooled by surrounding it by an annular space
containing water. The hot gases enters the
exhaust pipe at 350oC, gas flow rate being 200
kg/h, mean specific heat capacity at constant
pressure 1.13 kJ/kg K, and comes out at 100oC.
Water enters from the mains at 25oC, flow rate
1400 kg/h, mean specific heat capacity 4.19 kJ/kg
K. The heat transfer coefficient for gases and
water may be taken as 0.3 and 1.5 kW/m2 K and
pipe thickness may be taken as negligible.
Calculate the required pipe length for (i)
parallel flow, and for (ii) counter flow.
54
Example in heat Exchanger Design
Solution
.
.
.
(1400 kg/hr) (4.19 kJ/kg K) (Tc,out 25)oC
(200 kg/hr) (1.13 kJ/kg K) (350 100)oC
The temperature of water at the outlet Tc,out
34.63oC.
55
Example in heat Exchanger Design

• Solution continued
• Parallel flow

?Ta 350 25 325oC
?Tb 100 34.63 65.37oC
?Ta - ?Tb
325 65.37
?T
162oC

ln(?Ta / ?Tb)
ln(325 / 65.37)
.
(UA) 162oC
Q U A ?T
What is UA?
56
Example in heat Exchanger Design
Solution continued 1/U 1/hwater 1/hgases
1/1.5 1/0.3 4 (kW/m2 K)-1 Therefore,
U 0.25 kW/m2 K A p (outer diameter) (L) p
(0.075 m) (L m)
.
(0.25) p (0.075) L (162) kW
(UA) 162oC
Q
.
What is Q?
57
Example in heat Exchanger Design
Solution continued
.
.
.
(200 kg/h) (1.13 kJ/kg K) (350 100)oC
15.69 kW
Substituting the above in
.
(0.25) p (0.075) L (162) kW
(UA) 162oC
Q
we get
L 1.64 m
58
Example in heat Exchanger Design
Solution continued (ii) Counter flow
?Ta 350 34.63 315.37oC
?Tb 100 25 75oC
?Ta - ?Tb
315.37 75
?T
167.35oC

ln(?Ta / ?Tb)
ln(315.37 / 75)
.
(UA) 167.35oC
Q U A ?T
.
Q 15.69 kW U 0.25 kW/m2 K
A p (0.075) L m2
Therefore, L 1.59 m
59
Other Heat Exchanger Types
Cross-flow heat exchanger with both fluids unmixed
The direction of fluids are perpendicular to each
other. The required surface area for this heat
exchanger is usually calculated by using tables.
It is between the required surface area for
counter-flow and parallel-flow heat exchangers.
60
Other Heat Exchanger Types
One shell pass and two tube passes
Th,in
Tc,in
Tc,out
Th,out
The required surface area for this heat exchanger
is calculated using tables.
61
Other Heat Exchanger Types
Two shell passes and two tube passes
Th,in
Tc,in
Tc,out
Th,out
The required surface area for this heat exchanger
is calculated using tables.
62
Batch Sterilization (method of heating)
Steam heating
Electrical heating
Direct steam sparging
63
For batch heating with constant rate heat flow
Total heat lost by the coil to the medium
heat gained by the medium
M - mass of the medium T0 - initial
temperature of the medium T - final
temperature of the medium c - specific heat
of the medium q - rate of heat transfer
from the electrical coil to the medium t
- duration of electrical heating
.
Electrical heating
.
M c (T - T0)
q t
64
For batch heating by direct steam sparging
M - initial mass of the raw medium T0
- initial temperature of the raw medium ms
- steam mass flow rate t - duration of
steam sparging H - enthalpy of steam
relative to the enthalpy at the
initial temperature of the raw medium
(T0) T - final temperature of the mixture
c - specific heat of medium and water
.
.
.
M c T0
(M mst) c T
(ms t) (H cT0)
Direct steam sparging
.
.
(M ms t) c (T T0)
ms t H
65
For batch heating with isothermal heat source
M - mass of the medium T0 - initial
temperature of the medium TH - temperature
of heat source (steam) T - final
temperature of the medium c - specific
heat of the medium t - duration of steam
heating U - overall heat transfer
coefficient A - heat transfer area
( )
T0 - TH
Steam heating
U A t M c ln
T - TH
Could you prove the above?
66
For batch heating with isothermal heat source
( )
T0 - TH
U A t M c ln
T - TH
( )
U A t
T TH (T0 - TH) exp -
c M
Steam heating
67
Example of batch heating by direct steam sparging
A fermentor containing 40 m3 medium at 25oC is
going to be sterilized by direct injection of
saturated steam. The steam at 350 kPa absolute
pressure is injected with a flow rate of 5000
kg/hr, which will be stopped when the medium
temperature reaches 122oC. Determine the time
taken to heat the medium. Additional data
required Enthalpy of saturated steam at 350 kPa
?? Enthalpy of water at 25oC ?? The heat
capacity of the medium 4.187 kJ/kg.K The density
of the medium are 4.187 kJ/kg.K and 1000 kg/m3,
respectively.)
68
Example of batch heating by direct steam sparging
A fermentor containing 40 m3 medium at 25oC is
going to be sterilized by direct injection of
saturated steam. The steam at 350 kPa absolute
pressure is injected with a flow rate of 5000
kg/hr, which will be stopped when the medium
temperature reaches 122oC. Determine the time
taken to heat the medium. Additional data The
enthalpy of saturated steam at 350 kPa and water
at 25oC are 2732 and 105 kJ/kg, respectively. The
heat capacity and density of the medium are 4.187
kJ/kg.K and 1000 kg/m3, respectively. Solution

Use the equation below
.
.
(M ms t) c (T T0)
ms t H
69
.
.
(M ms t) c (T T0)
ms t H
(5000 kg/hr) (th) (2732-105) kJ/kg (40
m3)(1000 kg/m3) (5000 kg/hr)(th)(4.187
kJ/kg.K)(122-25)K
Taking the heating time (th) to be in hr, we get
(5000 th) (2627) kJ 40000 5000
t(4.187)(97)kJ
(5000 th) 2627 4.187 x 97 40000 x 4.187 x 97
th 1.463 hr
Therefore, the time taken to heat the medium is
1.463 hours.
70
Example of batch heating with isothermal heat
source
A fermentor containing 40 m3 medium at 25oC is
going to be sterilized by an isothermal heat
source, which is saturated steam at 350 kPa
absolute pressure. Heating will be stopped when
the medium temperature reaches 122oC. Determine
the time taken to heat the medium. Additional
data The saturated temperature of steam at 350
kPa is 138.9oC. The heat capacity and density of
the medium are 4.187 kJ/kg.K and 1000 kg/m3,
respectively. Solution
Use the equation below
( )
T0 - TH
U A t M c ln
T - TH
71
( )
T0 - TH
U A t M c ln
T - TH
(2500 kJ/hr.m2.K) (40 m2) (tc) (40 m3)
(1000 kg/m3) (4.187 kJ/kg.K) ln(25-138.9)/(122-13
8.9)
Taking the heating time (th) to be in hr, we get
(2500 kJ/K) (40) (th) (40) (1000) (4.187 kJ/K)
ln113.9/16.9
(2500 kJ/K) (40) (th) (40) (1000) (4.187 kJ/K)
(1.908)
th 3.1955 hr
Therefore, the time taken to heat the medium is
3.1955 hours.
72
Explain why heating with isothermal heat source
takes twice the time taken by heating with steam
sparging, even though we used the same steam.
73
Question from PM3125 / Jan 2010 past paper

• A steel pipeline (inside diameter 52.50 mm
  outside diameter 60.32 mm) contains saturated
  steam at 121.1oC. The line is insulated with 25.4
  mm of asbestos. Assume that the inside surface
  temperature of the metal wall is at 121.1oC and
  the outer surface of the insulation is at 26.7oC.
  Taking the average value of ksteel as 45 W/m.K
  and that of kasbestos as 0.182 W/m.K, calculate
  the following
• (a) Heat loss for 30.5 m of pipe length.
  10 marks
• (b) Mass (in kg) of steam condensed per hour in
  the pipe due to the heat loss.
  10 marks
• Additional data given on the next slide

74
Question from PM3125 / Jan 2010 past paper
Additional Data i) Heat transfer rate through
the pipe wall is given by,
where L is the length of pipe, T1 and T2 are the
respective temperatures at the inner and outer
surfaces of the insulated pipe, r1 and r2 are
the respective inner and outer radius of the
steel pipe, and r3 is the outer radius of the
insulated pipe. ii) Latent heat of
vapourization of steam could be taken as 2200
kJ/kg.
75
Group Assignment will be uploaded at
http//www.rshanthini.com/PM3125.htm (keep
track of the site)
76
End of slides for the heat transfer lecture
77
Additional material not used in the lectures.
78
Critical Radius of Insulation
To
r
Pipe
Insulation
ro
Ti
ri
Ti To

ln(ro/ri) /2pkPL
ln(r/ro) /2pkIL 1/hairA
Pipe resistance could be neglected
A 2 p r L
79
Critical Radius of Insulation
Ti To

ln(r/ro) /2pkIL 1/(hair 2prL)
2p L ( Ti To)

ln(r/ro) /kI 1/(hair r)
Convective resistance
Insulation resistance
Increasing r increases insulation resistance and
decreases heat transfer.
Increasing r decreases convective resistance and
increases heat transfer.
80
Critical Radius of Insulation
d
0 at the critical radius of insulation,
which leads to rcr kI / hair
/dr
If the outer radius of the pipe (ro) lt rcr and if
insulation is added to the pipe, heat losses will
first increase and go through a maximum at the
insulation radius of rcr and then decrease.
If the outer radius of the pipe (ro) gt rcr and if
insulation is added to the pipe, heat losses will
continue to decrease.