Heat Transfer Module

1. HEAT TRANSFER

2. Content
• Modes of heat transfer?
• Fourier Law of heat conduction
• Convective heat coefficient
• Radiant heat coefficient
• Overall heat transfer coefficient
• Hands-on example

3. Temperature
• A measure of energy due to level of heat
– Freezing point of water is 0 ˚ C
– Boiling point of water is 100 ˚ C

4. Common Temperature Scales

5. 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

6. 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

7. 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

8. 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

9. Change Of State
• Heat that brings about a change in potential
energy of the molecules (temperature remains
constant). Also called the latent heat.

10. 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)

11. Sizing Heating Capacity
Quantity of heat required  mass x specific heat x T
Example:
What is the heat required to raise air
temperature from 15 ˚C to 25 ˚C at a
flow rate of 2000 l/s?

12. Heat Transfer
• If there is a temperature difference in a
system, heat will always move from higher to
lower temperatures
What is actually flowing?

13. Heat Transfer Modes
There are 3 modes
of heat transfer.
1. Conduction
2. Convection
3. Radiation

14. Conduction
• Heat transfer through a solid medium via
direct contact
• Expressed by Fourier’s Law

15. Fourier’s Law
T2 T1
dT
q"  k
Q
dx X
k = thermal conductivity (W/ m K)
T = temperature (K)
q” = heat flux (W/m2)
Heat flow rate = q” x area (W)

16. Fourier’s law at steady state
dT
q"   k (Fourier Law)
dx
Tout  Tin
q"   k (Steady State)
L
Tout  Tin
q"  
L/k
Heat transfer rate
q
Q  q" x Area of heat flow
T2
T T
  out in T1
L / kA
R=L/k
Unit thermal resistance

17. 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

18. Thermal Conductivity, k (W/m K)
Liquids Common Metals
Water: 0.556 Copper: 385
Ammonia: 0.54 Aluminum: 221
Gases Steel: 50
Air : 0.024 Non-metals
Water vapor: 0.021 Common brick: 0.6
Mineral wool: 0.04
Ceiling board: 0.06

19. 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?

20. Electrical- Thermal Analogy
q
T2
Electrical (Ohm' s Law) T1
Voltage Potential R=L/kA
Current, I 
Re sis tan ce
Thermal
Temperature difference
Heat flux, q 
Re sis tan ce

21. Composite Wall
Using the resistance concept,
T 2 T1
q" 
R1 R 2
x1
R1 
k1
x2
R1 R2 T2 R2 
T1 k2
Q

22. Example 2
A wall of a Switchgear room consists the
following:
6mm 100mm 25mm
TNF panel
k2 k = 0.02 W/m K
35 C q2 22 C
Q
Q
Q
Steel plate
Firebatt
k = 50 W/m K
k = 0.04 W/m K
Determine Q, if the wall is 3m x 4m ?

23. 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

24. Convective Heat Transfer
y Ta
Newton's Law of cooling q
q"  hc (Ts  Ta ) air flow
(Ts  Ta ) Ts
q" 
1
hC where:
h c is convection coefficient (W/m2C),
1 Ts is surface temperature (C),
Rc  T a is surrounding air temperature (C)
hc
Rc= unit convective resistance.

25. Magnitude of Convection Coefficients
Arrangement h, W/m2 K Btu/(h.ft2.F)
Air, free (indoor) 10-30 1-5
Air, forced 30-300 5-50
(outdoor)
Oil, forced 60-1800 10-300
Water, forced 300-6000 50-1000
Steam, condensing 6000-120000 1000-20000

26. Example 3
The same as Example 2. Consider convection of
the exposed surfaces, calculate Q.
6mm 100mm 25mm
TNF panel
k2 k = 0.02 W/m K
35 C q2 22 C
Q
Q
Q
Steel plate
Firebatt
k = 50 W/m K
k = 0.04 W/m K

27. 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
Example :
Hot Body Solar radiation
Radiator

28. 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

29. Solar Radiation
• 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

30. Solar Radiation Spectrum
99% of solar radiation is between 0.3 to 3 µm.

31. Wien’s Law
2900
m  m
T

32. Wien’s Law

33. The Black Body
4
E = AT
• 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)

34. The Grey Body
For an actual body,
E   Eb   A(T ) where
4
  emissitivity
 0.8 - 0.9 for common materials
 0.02 - 0.07 for polished metals

35. Net Radiant Heat
• If a hot object is radiating to a cold
surrounding, the radiation loss is
q   A(Th 4  Tc 4 )

36. Quiz
How much energy does human body radiate?
• Body temperature is 37 C
• Body area is 1.5 m2
• ε= 0.7

37. Radiant Heat Transfer
• Unit thermal resistance for radiation is written
as q"  hr ( T)
1
Rc 
hr
Radiation coefficient is a function of
temperature, radiation properties and
geometrical arrangement of the enclosure
and the body in question.

38. Combined convection and radiant
Coefficient
• The heat transfer is combination of convection
and radiation
q"  qc  qr
q"  ( hc  hr )(T )
Combined thermal resistance,
1
R
hc  hr

39. Combined Surface Coefficients
• Some practical values of surface coefficients:
(source: ASHRAE Fundamentals 1989)
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

40. Combined modes
Thot
Thot
Outside
R3=1/hhot
T3
T3
k2 T2
k1
R2=L1/k1 + L2/K2
T1
Inside T1
R1=1/hcold
Tcold
T
Tcold
Resistance in parallel, R= R1 + R2 +R3

41. Compute
Thot
R  R1  R 2  R 3
R3=1/hhot
1 L1 L 2 1
R  / 
hcold k 1 k 2 hhot
Thot  Tcold T2
q"  R2=L1/k1 + L2/k2
1 / hhot  1 / hcold  L1 / k 1  L 2 / k 2
T1  Tcold
q"  T1
1 / hcold
T2  Tcold R1=1/hcold
q" 
1 / hcold  L1 / k 1  L 2 / k 2
Tcold

42. 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  R1  R 2  R 3  .......
1
U 
R

43. Example
• Find the overall heat
transfer coefficient of
a flat roof having the
construction shown in
the figure.

44. Solution
T1
R1
R2
R3
R4
R5
R6
T2

45. 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

46. Solution
Overall heat transfer coefficien t
1 1
U   0.40 W/m K 2
R 2.48

47. Heat Transfer Loop
in a DX System

48. Heat Exchanger Coil
Heat is exchanged between
2 fluids.
Q= UA ∆T
For cross flow,
Q= UA (LMTD)

49. Heat Exchanger- Mean Temperature
Difference
Heat Transfer, Q  U x Area x LMTD
GTD - LTD
Q  U x Area x
GTD
Ln
LTD

50. 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.