PM3125: Lectures 6 to 9

1
PM3125 Lectures 6 to 9
Content of Lectures 6 to 12 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
What is Heat?
3
What is Heat?

• Heat is energy in transit.

4
Units of Heat

• The SI unit is the joule (J),
• which is equal to Newton-metre (Nm).
• Historically, heat was measured in terms of the
  ability to raise the temperature of water.
• The calorie (cal) amount of heat needed to raise
  the temperature of 1 gramme of water by 1 C0
  (from 14.50C to 15.50C)
• In industry, the British thermal unit (Btu) is
  still used amount of heat needed to raise the
  temperature of 1 lb of water by 1 F0 (from 630F
  to 640F)

5

• Conversion between different
• units of heat
• 1 J 0.2388 cal 0.239x10-3 kcal 60.189 Btu
• 1 cal 4.186 J 3.969 x 10-3 Btu

6
Sensible Heat

• What is 'sensible heat?

Sensible heat is associated with a temperature
change
7
Specific Heat Capacity

• To raise the temperature by 1 K, different
  substances need different amount of energy
  because substances have different molecular
  configurations and bonding (eg copper, water,
  wood)
• The amount of energy needed to raise the
  temperature of 1 kg of a substance by 1 K is
  known as the specific heat capacity
• Specific heat capacity is denoted by c

8
Calculation of Sensible Heat
Q is the heat lost or gained by a substance m is
the mass of substance c is the specific heat of
substance which changes with temperature T is the
temperature
When temperature changes causes negligible
changes in c,
m c ?T
where ?T is the temperature change in the
substance
9
Calculation of Sensible Heat
When temperature changes causes significant
changes in c,
Q m c ?T cannot be used.
Instead, we use the following equation
Q ?H m ?h
where ?H is the enthalpy change in the substance
and ?h is the specific enthalpy change in the
substance.
To apply the above equation, the system should
remain at constant pressure and the associated
volume change must be negligibly small.
10
Calculation of Sensible Heat
Calculate the amount of heat required to raise
the temperature of 300 g Al from 25oC to 70oC.
Data c 0.896 J/g oC for Al
Q m c ?T (since c is taken as a constant)
(300 g) (0.896 J/g oC)(70 - 25)oC 12,096
J 13.1 kJ
11
Exchange of Heat
Calculate the final temperature (tf), when 100 g
iron at 80oC is tossed into 53.5g of water at
25oC. Data c 0.452 J/g oC for iron and 4.186
J/g oC for water
Heat lost by iron Heat gained by water
(m c ?T)iron (m c ?T)water (100 g) (0.452
J/g oC)(80 - tf)oC
(53.5 g) (4.186 J/g oC)(tf - 25)oC
80 - tf 4.955 (tf -25)
tf 34.2oC
12
Latent Heat

• What is latent heat?

Latent heat is associated with phase change of
matter
13
Phases of Matter
14
Phase Change

• Heat required for phase changes
• Melting solid ? liquid
• Vaporization liquid ? vapour
• Sublimation solid ? vapour
• Heat released by phase changes
• Condensation vapour ? liquid
• Fusion liquid ? solid
• Deposition vapour ? solid

15
Phase Diagram Water
16
Phase Diagram Water
Compressed liquid
Saturated liquid
Superheated steam
Saturated steam
17
Phase Diagram Water
Explain why water is at liquid state at atm
pressure
18
Phase Diagram Carbon Dioxide
Explain why CO2 is at gas state at atm pressure
Explain why CO2 cannot be made a liquid at atm
pressure
19
Latent Heat
Latent heat is the amount of heat added per unit
mass of substance during a phase change Latent
heat of fusion is the amount of heat added to
melt a unit mass of ice OR it is the amount of
heat removed to freeze a unit mass of
water. Latent heat of vapourization is the
amount of heat added to vaporize a unit mass of
water OR it is the amount of heat removed to
condense a unit mass of steam.
20
Water Specific Heat Capacities and Latent Heats
Specific heat of ice 2.06 J/g K (assumed
constant) Heat of fusion for ice/water 334 J/g
(assumed constant) Specific heat of water 4.18
J/g K (assumed constant) Latent heat of
vaporization cannot be assumed a constant since
it changes significantly with the pressure, and
could be found from the Steam Table How to
evaluate the sensible heat gained (or lost) by
superheated steam?
21
Water Specific Heat Capacities and Latent Heats
How to evaluate the sensible heat gained (or
lost) by superheated steam?
Q m c ?T cannot be used since changes in c
with changing temperature is NOT negligible.
Instead, we use the following equation
Q ?H m ?h
provided the system is at constant pressure and
the associated volume change is negligible.
Enthalpies could be referred from the Steam Table
22
Properties of Steam
Learnt to refer to Steam Table to find properties
of steam such as saturated (or boiling point)
temperature and latent heat of vapourization at
give pressures, and enthalpies of superheated
steam at various pressures and temperatures.
Reference Chapter 6 of Thermodynamics for
Beginners with worked examples by R.
Shanthini (published by Science Education Unit,
Faculty of Science, University of
Peradeniya) (also uploaded at http//www.rshanthi
ni.com/PM3125.htm)
23
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
24
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
25
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
120.2oC
boiling point of water at 2 bar
Boiling point of water at 1 atm pressure is
100oC. Boiling point of water at 2 bar is
120.2oC. Refer the Steam Table.
0oC melting point of ice
-20oC ice
26
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
150oC superheated steam
Specific heat
120.2oC
boiling point of water at 2 bar
Latent heat
Specific heat
0oC melting point of ice
Latent heat
Specific heat
-20oC ice
27
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
Specific heat required to raise the temperature
of ice from -20oCto 0oC (2 kg) (2.06 kJ/kg oC)
0 - (-20)oC 82.4 kJ
Latent heat required to turn ice into water at
0oC (2 kg) (334 kJ/kg) 668 kJ
Specific heat required to raise the temperature
of water from 0oC to 120.2oC (2 kg) (4.18 kJ/kg
oC) 120.2 - 0)oC 1004.9 kJ
28
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
Latent heat required to turn water into steam at
120.2oC and at 2 bar (2 kg) (2202 kJ/kg)
4404 kJ Latent heat of vapourization at 2 bar
is 2202 kJ/kg as could be referred to from the
Steam Table
Specific heat required to raise the temperature
of steam from 120.2oC to 150oC (2 kg) (2770
2707) kJ/kg 126 kJ Enthalpy at 120.2oC and
2 bar is the saturated steam enthalpy of 2707
kJ/kg and the enthalpy at 150oC and 2 bar is 2770
kJ/kg as could be referred to from the Steam
Table
29
Warming curve for water
What is the amount of heat required to change 2
kg of ice at -20oC to steam at 150oC at 2 bar
pressure?
Total amount of heat required 82.4 kJ 668 kJ
1004.9 kJ 4404 kJ 126 kJ 6285.3 kJ
30
Application Heat Exchanger
It is an industrial equipment in which heat is
transferred from a hot fluid (a liquid or a gas)
to a cold fluid (another liquid or gas) without
the two fluids having to mix together or come
into direct contact.
Cold fluid at TC,in
Cold fluid at TC,out
Hot fluid at TH,in
Heat lost by the hot fluid Heat gained by the
cold fluid
Hot fluid at TH,out
31
Application Heat Exchanger
32
Heat Exchanger
Heat lost by the hot fluid Heat gained by the
cold fluid
mass flow rate of hot fluid
mass flow rate of cold fluid
Specific heat of hot fluid
Specific heat of cold fluid
Temperature increase in the cold fluid
Temperature decrease in the hot fluid
33
Heat Exchanger
Heat lost by the hot fluid Heat gained by the
cold fluid

• The above is true only under the following
  conditions
• Heat exchanger is well insulated so that no heat
  is lost to the environment
• There are no phase changes occurring within the
  heat exchanger.

34
Heat Exchanger
If the heat exchanger is NOT well insulated, then
Heat lost by the hot fluid Heat gained by the
cold fluid Heat lost to the environment
35
Worked Example 1 in Heat Exchanger
High pressure liquid water at 10 MPa (100
bar) and 30oC enters a series of heating tubes.
Superheated steam at 1.5 MPa (15 bar) and 200oC
is sprayed over the tubes and allowed to
condense. The condensed steam turns into
saturated water which leaves the heat exchanger.
The high pressure water is to be heated up to
170oC. What is the mass of steam required per
unit mass of incoming liquid water? The heat
exchanger is assumed to be well insulated
(adiabatic).
36
Solution to Worked Example 1 in Heat Exchanger
37
Solution to Worked Example 1 in Heat Exchanger
contd.
High pressure (100 bar) water enters at 30oC and
leaves at 198.3oC. Boiling point of water at 100
bar is 311.0oC. Therefore, no phase changes in
the high pressure water that is getting heated up
in the heater. Heat gained by high pressure
water ccold (TC,out TC,in) (4.18
kJ/kg oC) x (170-30)oC 585.2 kJ/kg You
could calculate the above by taking the
difference in enthalpies at the 2 given states
from tables available.
38
Solution to Worked Example 1 in Heat Exchanger
contd.
Superheated steam at 1.5 MPa (15 bar) and 200oC
is sprayed over the tubes and allowed to
condense. The condensed steam turns into
saturated water which leaves the heat
exchanger. Heat lost by steam heat lost by
superheated steam to become saturated steam
latent heat of steam lost for saturated steam
to turn into saturated water
Enthalpy of superheated steam at 15 bar and 200oC
Enthalpy of saturated steam at 15 bar
Latent heat of vapourization at 15 bar (2796
kJ/kg 2792 kJ/kg) 1947 kJ/kg 1951 kJ/kg
39
Solution to Worked Example 1 in Heat Exchanger
contd.
Since there is no heat loss from the
heater, Heat lost by steam Heat gained by high
pressure water Mass flow rate of steam x 1951
kJ/kg Mass flow rate of water x 585.2
kJ/kg Mass flow rate of steam / Mass flow rate
of water 585.2 / 1951 0.30 kg stream
/ kg of water
40
Assignment
Give the design of a heat exchanger which has the
most effective heat transfer properties.

• Learning objectives
• To be able to appreciate heat transfer
  applications in pharmaceutical industry
• To become familiar with the working principles of
  various heat exchangers
• To get a mental picture of different heat
  exchangers so that solving heat transfer problems
  in class becomes more interesting

41
Worked Example 2 in Heat Exchanger
Steam enters a heat exchanger at 10 bar and
200oC and leaves it as saturated water at the
same pressure. Feed-water enters the heat
exchanger at 25 bar and 80oC and leaves at the
same pressure and at a temperature 20oC less than
the exit temperature of the steam. Determine the
ratio of the mass flow rate of the steam to that
of the feed-water, neglecting heat losses from
the heat exchanger. If the feed-water
leaving the heat exchanger is fed directly to a
boiler to be converted to steam at 25 bar and
300oC, find the heat required by the boiler per
kg of feed-water.
42
Solution to Worked Example 2 in Heat Exchanger

• - Steam enters at 10 bar and 200oC and leaves it
  as saturated water at the same pressure.
• - Saturation temperature of water at 10 bar is
  179.9oC.
• - Feed-water enters the heat exchanger at 25 bar
  and 80oC and leaves at the same pressure and at a
  temperature 20oC less than the exit temperature
  of the steam, which is 179.9oC.
• Boiling point of water at 25 bar is
  (221.8226.0)/2 223.9oC.
• Therefore, no phase changes in the feed-water
  that is being heated.
• Heat lost by steam Heat gained by feed-water
  (with no heat losses)
• Mass flow rate of steam x 2829 2778 2015
  kJ/kg
• Mass flow rate of feed-water x 4.18
  x (179.9-20-80) kJ/kg

Mass flow of steam / Mass flow of feed-water
333.98 / 2066 0.1617 kg stream / kg of water
43
Solution to Worked Example 1 in Heat Exchanger
contd.

• If the feed-water leaving the heat exchanger is
  fed directly to a boiler to be converted to steam
  at 25 bar and 300oC, find the heat required by
  the boiler per kg of feed-water.
• Temperature of feed-water leaving the heat
  exchanger is 159.9oC
• Boiling point of water at 25 bar is
  (221.8226.0)/2 223.9oC
• The feed-water is converted to superheated steam
  at 300oC
• Heat required by the boiler per kg of feed-water
• 4.18 x (223.9-159.9) (18501831)/2
  
• (31383117)/2 (28022803)/2
  kJ/kg
• 267.52 1840.5 3127.5 2802.5 kJ/kg
• 2433 kJ/kg of feed-water

44
Heat Transfer

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

45
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)

46
Mechanisms of Heat Transfer
47
Conduction
HOT (lots of vibration)
COLD (not much vibration)
Heat travels along the rod
48
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.
49
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?
50
Thermal Conductivities
Substance Thermal Conductivity k W/m.K Substance Thermal Conductivity k W/m.K
Syrofoam 0.010 Glass 0.80
Air 0.026 Concrete 1.1
Wool 0.040 Iron 79
Wood 0.15 Aluminum 240
Body fat 0.20 Silver 420
Water 0.60 Diamond 2450
51
Conduction through Single Wall
Use Fouriers Law
T1
k A (T1 T2)
T2??? T1

x
?x
?x
52
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)
52
53
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
53
54
Conduction through Composite Wall
T1 T4

54
55
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
56
Example 1 continued
(1000 40) A

(0.03/0.07)
(0.21/1.04)
1522.6
W/m2
A
57
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
58
Conduction through hollow-cylinder
ro
Ti
ri
To
L
Ti To

ln(ro/ri) / 2pkL
59
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
60
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
61
Example 3 continued
2 p L ( 600 100)

ln(5/2) / 0.2
ln(2/1) / 19
680 W/m
L
62
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)

63
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.
64
Convection
It explains why breezes come from the ocean in
the day and from the land at night
65
Convection Newtons Law of Cooling
Flowing fluid at Tfluid
Heated surface at Tsurface
Area exposed
Heat transfer coefficient (in W/m2.K)
66
Convection Newtons Law of Cooling
Flowing fluid at Tfluid
Heated surface at Tsurface
Tsurface Tfluid

1/(hA)
Convective heat resistance (in K/W)
67
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
68
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.
69
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
70
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
71
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.
72
Overall Heat Transfer through a Plane Wall
Fluid A at TA gt T1
T1
T2
Fluid B at TB lt T2
x
?x
73
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
74
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
75
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?
76
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
77
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
78
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)

?
79
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.
80
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.
81
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.
82
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    
83
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
84
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
85
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
86
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
87
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.
88
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)