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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
Theat x specific x mass requiredheat ofQuantity
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
dTkq "
k = thermal conductivity (W/ m K)T = temperature (K)q” = heat flux (W/m2)
Heat flow rate = q” x area (W)
Fourier’s law at steady state
kAL
TT
q
kL
TTq
L
TTkq
dx
dTkq
inout
inout
inout
/
flowheat of Area x "Q
ratefer 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)
LiquidsWater: 0.556Ammonia: 0.54GasesAir : 0.024Water vapor: 0.021
Common Metals Copper: 385 Aluminum: 221Steel: 50 Non-metalsCommon brick: 0.6 Mineral wool: 0.04Ceiling 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
cesis
cesis
tanRe
difference eTemperaturq flux,Heat
Thermal
tanRe
Potential VoltageI Current,
Law) s(Ohm' Electrical
T1T2
q
R=L/kA
Composite Wall
Using the resistance concept,
T1
T2R1 R2
Q
2
22
1
11
21
12"
k
xR
k
xR
RR
TTq
Example 2A wall of a Switchgear room consists the
following:
q2
k2
35 C 22 C
6mm 25mm100mm
TNF panelk = 0.02 W/m K
Firebattk = 0.04 W/m K
Steel platek = 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/m2C),
Ts is surface temperature (C),
T a is surrounding air temperature (C)
Rc= unit convective resistance.
Convective Heat Transfer
air flow
Ta
Ts
y
q
c
c
C
as
asc
hR
h
TTq
TThq
1
1
("
)("
cooling of Law sNewton'
)
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.
q2
k2
35 C 22 C
6mm 25mm100mm
TNF panelk = 0.02 W/m K
Firebattk = 0.04 W/m K
Steel platek = 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
radiationolar
: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
mT
2900 m
Wien’s Law
The Black Body
E = AT4
• E =The amount of energy (W ) emitted by an object
• = Stefan-Boltzmann constant =5.67 x 10-8 W m-2 K-4
• T = Temperature (K)
• A= area (m2)
The Grey Body
metals polishedfor 0.07-0.02
materialscommon for 0.9-0.8
tyemissitivi
where)(E E
body, actualan For 4
b
TA
Net Radiant Heat
• If a hot object is radiating to a cold surrounding, the radiation loss is
)( q 44ch TTA
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"
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
rc hh
1R
,resistance thermalCombined
))(("
"
Thhq
qqq
rc
rc
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
Thot
Tcold
T1
T3
R2=L1/k1 + L2/K2
R3=1/hhot
R1=1/hcold
T2
T1
Tcold
Thot
Resistance in parallel, R= R1 + R2 +R3
T3
Compute
2211
2
1
2211
2
2
1
1
321
///1"
/1"
///1/1"
1/
1
kLkLh
TTq
h
TTq
kLkLhh
TTq
hk
L
k
L
hR
RRRR
cold
cold
cold
cold
coldhot
coldhot
hotcold
Thot
Tcold
T1
T2R2=L1/k1 + L2/k2
R3=1/hhot
R1=1/hcold
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 asQ = A x U x ∆T whereU is the overall heat transfer coefficient (or U-value)
RU
RRRR
1
.......321
Example
• Find the overall heat transfer coefficient of a flat roof having the construction shown in the figure.
Solution
T2
T1
R3
R1
R2
R4
R5
R6
SolutionResistance 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/m40.048.2
1
R
1U
tcoefficienfer heat trans Overall
2
Heat Transfer Loop in a DX System
Heat Exchanger Coil
Heat is exchanged between 2 fluids.Q= UA ∆TFor cross flow,Q= UA (LMTD)
Heat Exchanger- Mean Temperature Difference
LTD
GTDLn
LTD-GTD x Areax 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 T (which is not always controllable).– For conduction, increasing k /d.– Increase h c by not relying on natural convection, but
introducing forced convection.– Increase hr, by using “black” surfaces.