heat treats

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HEAT TRANSFER
Content
• Modes of heat transfer?
• Fourier Law of heat conduction
• Convective heat coefficient
• Radiant heat coefficient
• Overall heat transfer coefficient
• Hands-on example
Temperature
• A measure of energy due to level of heat
– Freezing point of water is 0 ˚ C
– Boiling point of water is 100 ˚ C
Common Temperature Scales
What is Heat?
Heat is the total internal kinetic energy due to
molecular motion in an object
Quantity of heat is BTU or Kilo Joule (kJ)
• One BTU is the amount of heat required to raise 1
lb of water by 1 ˚ F
• One calorie is required to raise 1 g of water by 1 ˚
C
1 cal = 4.187 J
• 1 BTU= 1.055 kJ= 1055 J
Heat Vs Temperature
• Heat energy depends on mass. Temperature is
independent of mass.
– 2 litres of boiling water has more heat energy than
1 litre of boiling water
• Temperature is not energy, but a measure of it
• Heat is energy
Heat is Energy
When heat (ie energy) goes into a substance,
one of two things can happen:
1. Temperature goes up
2. Change of state
Temperature Goes Up
• Heat that causes a rise in temperature e.g.
heating water before boiling
• The heat energy is used to increase the kinetic
energy of the molecules in the substance
• This is also known as the sensible heat
Change Of State
• Heat that brings about a change in potential
energy of the molecules (temperature remains
constant). Also called the latent heat.
Specific Heat
• It is the heat required to the temperature of 1
kg (lb) a substance by 1 ˚ K (F)
• Example:
water’s specific heat is 1 btu/ lb F (4.2 kJ/kg K)
air’s specific heat is 0.24 btu/ lb F (1.0 kJ/kg K)
Sizing Heating Capacity
T heat x specific x mass required heat of Quantity A =
Example:
What is the heat required to raise air
temperature from 15 ˚C to 25 ˚C at a
flow rate of 2000 l/s?
Heat Transfer
• If there is a temperature difference in a
system, heat will always move from higher to
lower temperatures
What is actually flowing?
Heat Transfer Modes
There are 3 modes
of heat transfer.
1. Conduction
2. Convection
3. Radiation
Conduction
• Heat transfer through a solid medium via
direct contact
• Expressed by Fourier’s Law
Fourier’s Law
Q
X
T2 T1
dx
dT
k q ÷ = "
k = thermal conductivity (W/ m K)
T = temperature (K)
q” = heat flux (W/m
2
)
Heat flow rate = q” x area (W)
Fourier’s law at steady state
kA L
T T
q
k L
T T
q
L
T T
k q
dx
dT
k q
in out
in out
in out
/
flow heat of Area x " Q
rate fer Heat trans

/
"
State) (Steady "
Law) (Fourier "
÷
÷ =
=
÷
÷ =
÷
÷ =
÷ =
T1
T2
q
R=L/k
Unit thermal resistance
Example 1
• Temperature of 35 C and 22 C are maintained
on opposite sides of a steel floor of 6mm
thick. Compute the heat flux through the
floor.
• Thermal conductivity for steel = 50 W/m K
Thermal Conductivity, k (W/m K)
Liquids
Water: 0.556
Ammonia: 0.54
Gases
Air : 0.024
Water vapor: 0.021
Common Metals
Copper: 385
Aluminum: 221
Steel: 50
Non-metals
Common brick: 0.6
Mineral wool: 0.04
Ceiling board: 0.06
Quiz
• Suppose a human could live for 2 h unclothed
in air at 45 ˚F. How long could she live in water
at 45 ˚F?
Electrical- Thermal Analogy
ce sis
ce sis
tan Re
difference e Temperatur
q flux, Heat
Thermal
tan Re
Potential Voltage
I Current,
Law) s (Ohm' Electrical
=
=
T1
T2
q
R=L/kA
Composite Wall
Using the resistance concept,
T1
T2
R1 R2
Q
2
2
2
1
1
1
2 1
1 2
"
k
x
R
k
x
R
R R
T T
q
=
=
+
÷
=
Example 2
A wall of a Switchgear room consists the
following:
Q
Q
q
2
k
2
35 C 22 C
6mm 25mm 100mm
TNF panel
k = 0.02 W/m K
Firebatt
k = 0.04 W/m K
Steel plate
k = 50 W/m K
Q
Determine Q, if the wall is 3m x 4m ?
Convection
• Energy transfer by fluid
motion
• Two kinds of convection
– Forced convection: Fluid is
forced
– Natural or free convection:
fluid is induced by
temperature difference
where:
h
c
is convection coefficient (W/m
2
C),
T
s
is surface temperature (°C),
T
a
is surrounding air temperature (°C)
Rc= unit convective resistance.
Convective Heat Transfer
air flow
T
a
T
s
y
q
c
c
C
a s
a s
c
h
R
h
T T
q
T T h q
1
1
(
"
) ( "
cooling of Law s Newton'
)
=
÷
=
÷ =
Magnitude of Convection Coefficients
Arrangement h, W/m2 K Btu/(h.ft2.F)
Air, free (indoor) 10-30 1-5
Air, forced
(outdoor)
30-300 5-50
Oil, forced 60-1800 10-300
Water, forced 300-6000 50-1000
Steam, condensing 6000-120000 1000-20000
Example 3
The same as Example 2. Consider convection of
the exposed surfaces, calculate Q.
Q
Q
q
2
k
2
35 C 22 C
6mm 25mm 100mm
TNF panel
k = 0.02 W/m K
Firebatt
k = 0.04 W/m K
Steel plate
k = 50 W/m K
Q
Radiation
• Energy emitted by object that is at any
temperature above absolute zero
• Energy is in the form electromagnetic waves
• No medium needed and travel at speed of
light
Hot Body
Radiator
radiation olar
: Example
S
Radiation
• Important mode of heat at high temperatures,
e.g. combustion furnace
• At room temperature it may just be
measurable.
• Intensity depends on body temperature and
surface characteristics
• Solar radiation is the radiation emitted by the
sun due to nuclear fusion reaction
• Solar Constant: The amount of solar energy
arriving at the top of the atmosphere
perpendicular to the sun’s rays.
• = 1375 W m
-2
Solar Radiation
Solar Radiation Spectrum
99% of solar radiation is between 0.3 to 3 µm.
Wien’s Law
m µ ì
T
2900
m=
Wien’s Law
The Black Body
E = AoT
4
• E =The amount of energy (W )
emitted by an object
• o = Stefan-Boltzmann constant =
5.67 x 10
-8
W m
-2
K
-4
• T = Temperature (K)
• A= area (m2)
The Grey Body
metals polished for 0.07 - 0.02
materials common for 0.9 - 0.8
ty emissitivi
where ) ( E E
body, actual an For
4
b
=
=
=
= =
c
co c T A
Net Radiant Heat
• If a hot object is radiating to a cold
surrounding, the radiation loss is
) ( q
4 4
c h T T A ÷ =co
Quiz
How much energy does human body radiate?
• Body temperature is 37 C
• Body area is 1.5 m2
• ε= 0.7
Radiant Heat Transfer
• Unit thermal resistance for radiation is written
as
r
c
r
h
1
R
T) ( h q"
=
A =
Radiation coefficient is a function of
temperature, radiation properties and
geometrical arrangement of the enclosure
and the body in question.
Combined convection and radiant
Coefficient
• The heat transfer is combination of convection
and radiation
r c h h
1
R
, resistance thermal Combined
) )( ( "
"
+
=
A + =
+ =
T h h q
q q q
r c
r c
Combined Surface Coefficients
Air velocity Emissivity, ε=0.9
3.5 m/s h = 22.7 W/m2 K
7 m/s h = 35 W/m2 K
Still air h = 8.5 W/ m2 K
• Some practical values of surface coefficients:
(source: ASHRAE Fundamentals 1989)
k2
Combined modes
T
k1
Outside
Inside
T
hot
T
cold
T
1
T
3
R2=L1/k1 + L2/K2
R3=1/h
hot
R1=1/h
cold
T
2
T
1
T
cold
T
hot
Resistance in parallel, R= R1 + R2 +R3
T
3
Compute
2 2 1 1
2
1
2 2 1 1
2
2
1
1
3 2 1
/ / / 1
"
/ 1
"
/ / / 1 / 1
"
1
/
1
k L k L h
T T
q
h
T T
q
k L k L h h
T T
q
h k
L
k
L
h
R
R R R R
cold
cold
cold
cold
cold hot
cold hot
hot cold
+ +
÷
=
÷
=
+ + +
÷
=
+ + + =
+ + =
T
hot
T
cold
T
1
T
2
R2=L1/k1 + L2/k2
R3=1/h
hot
R1=1/h
cold
Overall Heat Transfer Coefficient
• Heat transfer processes includes conduction,
convection and radiation simultaneously
• The total conduction heat transfer for a wall or
roof is expressed as
Q = A x U x ∆T where
U is the overall heat transfer coefficient (or U-
value)
R
U
R R R R
1
....... 3 2 1
=
+ + = +
Example
• Find the overall heat
transfer coefficient of
a flat roof having the
construction shown in
the figure.
Solution
T
2
T
1
R3
R1
R2
R4
R5
R6
Solution
Resistance Construction Unit resistance (m2 K/ W)
R1 Outside air
R2 steel
R3 Mineral wool
R4 Air space
R5 Ceiling board
R6 Inside air
Total R
Solution
K W/m 40 . 0
48 . 2
1
R
1
U
t coefficien fer heat trans Overall
2
= = =
Heat Transfer Loop
in a DX System
Heat Exchanger Coil
Heat is exchanged between
2 fluids.
Q= UA ∆T
For cross flow,
Q= UA (LMTD)
Heat Exchanger- Mean Temperature
Difference
LTD
GTD
Ln
LTD - GTD
x Area x U Q
LMTD x Area x U Q Transfer, Heat
=
=
Heat transfer optimization
• We have the following relations for heat transfer:
– Conduction: Q = k A ∆T /d
– Convection: Q = A h
c
∆T
– Radiation: Q = A h
r
∆T
• As a result, when equipment designers want to improve
heat transfer rates, they focus on:
– Increasing the area A, e.g. by using profiled tubes and ribbed
surfaces.
– Increasing AT (which is not always controllable).
– For conduction, increasing k /d.
– Increase h
c
by not relying on natural convection, but
introducing forced convection.
– Increase h
r
, by using “black” surfaces.

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