Thermal expansion is the change in dimensions of a material due to a change in temperature. Most materials expand when heated and contract when cooled. The factors that affect thermal expansion are the amount of temperature change, the type of material, and the original dimensions. Thermal expansion can be linear, affecting length, or volumetric, affecting the overall volume. Different materials have different coefficients of thermal expansion that quantify how much the material expands or contracts with temperature changes.

1. THERMAL EXPANSION
TEMPERATURE

2. • Change in the dimension(s) of a substance
due to change in temperature.
• Most materials expand when its
temperature increases and contract when
its temperature decreases.
THERMAL EXPANSION

3. 1. TEMPERATURE
• Higher change in temperature, the
higher the expansion
• ΔT for the symbol
FACTORS AFFECTING
THERMAL EXPANSION

4. 2. KIND OF MATERIAL (α)
• Quantified by a constant value for
coefficient of thermal expansion for
some materials
• The higher the coefficient, the higher
the expansion
FACTORS AFFECTING
THERMAL EXPANSION

5. 3. ORIGINAL DIMENSION
• Greater original dimension, greater the
expansion.
• L for linear
• A for area
• V for volume
FACTORS AFFECTING
THERMAL EXPANSION

6. KINDS OF THERMAL
EXPANSION

7. •The expansion in length of solid
bodies on heating
•The change in length is directly
proportional to the change in
temperature : ΔL ≈ ΔT
LINEAR EXPANSION

8. ΔL = α·L·ΔT 0
Change in
dimension
Coefficient of
expansion
Original
length
Change in
temperature

9. MATERIAL a per °C a per °F
1. Aluminum 23 x ퟏퟎ−ퟔ 13x ퟏퟎ−ퟔ
2. Brass 19x ퟏퟎ−ퟔ 11x ퟏퟎ−ퟔ
3. Copper 17x ퟏퟎ−ퟔ 9.3x ퟏퟎ−ퟔ
4. Germanium 6.0x ퟏퟎ−ퟔ 3.3x ퟏퟎ−ퟔ
5. Glass, ordinary 9x ퟏퟎ−ퟔ 5x ퟏퟎ−ퟔ
6. Glass, Pyrex 3.3x ퟏퟎ−ퟔ 1.8x ퟏퟎ−ퟔ
7. Invar (nickel-steel alloy) 0.9x ퟏퟎ−ퟔ 0.5x ퟏퟎ−ퟔ
8. Iron 12x ퟏퟎ−ퟔ 6.6x ퟏퟎ−ퟔ
9. Platinum 9.0x ퟏퟎ−ퟔ 5.0x ퟏퟎ−ퟔ
10. Fused quartz 0.5x ퟏퟎ−ퟔ 0.27x ퟏퟎ−ퟔ
11. Silicon 2.4x ퟏퟎ−ퟔ 1.3x ퟏퟎ−ퟔ
12. Steel 11x ퟏퟎ−ퟔ 6.1x ퟏퟎ−ퟔ
13. Tungsten 4.4x ퟏퟎ−ퟔ 2.5x ퟏퟎ−ퟔ
14. Uranium 15x ퟏퟎ−ퟔ 8.2x ퟏퟎ−ퟔ
15. Wood, along grain (3 to 6) x ퟏퟎ−ퟔ (2 to 4) x ퟏퟎ−ퟔ
16. Wood, across grain (35-60) x ퟏퟎ−ퟔ (20 to 35) x ퟏퟎ−ퟔ

10. •A copper bar is 8.0 ft long at
68°F and has an expansivity
of 9.3 x ퟏퟎ−ퟔ/°F. What is its
increase in length when
heated to 110°F?
Exercise #1

11. •A steel plug has a diameter
of 10 cm at 30.0°C. At what
temperature will the
diameter be 9.986 cm? What
is the required temperature?
Exercise #2

12. •A silicon gel with a length of
132 cm was heated at 20°C.
If heated to 100°C, what
would be the change in
dimension?
Exercise #3

13. • Sometimes called the “cubic
expansion”
• The volume of an object changes
when its temperature changes.
VOLUME EXPANSION

14. •ΔV = β·V0·ΔT
VOLUME EXPANSION

15. LIQUID β, per °C β, per °F
Alcohol,
ethyl
1.0xퟏퟎ−ퟑ 6.1xퟏퟎ−ퟒ
Mercury 1.8xퟏퟎ−ퟒ 1.0xퟏퟎ−ퟒ
Water (15-
3.7xퟏퟎ−ퟒ 2.0xퟏퟎ−ퟒ
100°)
VOLUME EXPANSIVITY OF
LIQUIDS

16. • A glass flask whose volume is 1000
cm3 at 0.0 °C is completely filled with
mercury at this temperature. When
flask and mercury are warmed to 80
°C, 12.5cm3 of mercury overflow.
Compute the change in volume.
Exercise #4

17. •A mug measuring 90cm3 at
45°C temperature, contains
ethyl alcohol. At what
temperature will the alcohol
flow 92cm3?
Exercise #5

18. HEAT TRANSFER

19. METHODS OF HEAT TRANSFER
• Conduction
- use of thermal conductor (ex.
Metals)
• Convection
- use of fluids (liquids or gas)
• Radiation
- no medium, uses EM wave to
transfer heat

20. • Heat has traveled through the metal rod
• Metals have many free electrons. They are
good heat conductors.
• Non-metals such as wood or cloth have
few free electrons. They are poor heat
conductors or thermal insulator
CONDUCTION

21. If Q represents the heat flow in J/s (watts), then
Q = k A (T1 – T2) / d
Where:
Q rate of heat flow (in J/s or W)
k thermal conductivity (in W/m K)
A area over which heat is passing (in m2)
T1 hot face temperature (in K)
T2 cold face temperature (in K)
d thickness or distance between
hot face and cold face (in m)

22. Substance Thermal Conductivity k (푾/풎 푲 )
Aluminum 205
Copper 385
Iron and Steel 50.2
Silver 406
Transformer Oil 0.18
Water 0.57
Air 0.024
Brick 0.71
Concrete 0.8
Styrofoam 0.01
Wood, oak 0.15
Vacuum 0

23. • Calculate the heat transfer through a
flat copper 200mm by 300mm wide
and 25mm thick when the surface
temperatures are 150°C and 55°C.
Example #1

24. • A Styrofoam box used to keep drinks
cold at a picnic has a total area of 0.80
m2 and wall thickness of 2.0 cm. it is
filled with ice, water, and cans of
Omni-Cola at 0°C. What is the rate of
heat flow into the box if the
temperature of the outside wall is
30°C?
Example #2

25. • A silver bar with length of 200 cm with
a cross sectional area of 4 cm2 is put in
contact with steam at 100°C at one end
and with water at 20°C on the other
end. Compute for the heat current if
the silver bar is perfectly insulated.
Example #3

26. • The outer surface of a boiler is covered with
insulating material of thermal conductivity 0.04
W/m K. It is 125 mm thick and has a surface
area of 50 m2. The inside edge of the insulating
material has an average temperature of 423 K
and the temperature of the outside surface is 303
K. Calculate the heat loss through the insulation
per hour.
Example #4

27. • Transfer of heat by mass motion of a
fluid from one region of space to
another.
Example
- house cooling and heating system
- cooling system of automobile
CONVECTION

28. • Forced convection – if the fluid moves by using a pump.
Example:
- blood circulation (heart-pump)
• Natural convection or free convection – if the flow is
caused by difference in density.
Example:
- daily weather
CONVECTION

30. • When the fluid outside the solid
surface is in forced or natural
convective motion, the expression of
the rate of heat transfer from the solid
to the fluid, or vice versa, is as follows:
Q = h A (Ts – Tf)
CONVECTION

31. Q = rate of heat transfer convection in J/s or W
A = Area of heat transfer, m2
Ts = The temperature of the solid surface, K
(hot)
Tf = The average temperature of the fluid, K
(cold)
h = The convection heat transfer coefficient,
W/m2/K
CONVECTION

32. ARRANGEMENT h, W/풎ퟐ.K Btu/(h.풇풕ퟐ.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
6,000-120,000 1,000-20,000

33. • A refrigerator stands in a room where
air temp. is 20°C. The surface
temperature on the outside of ref is
16°C. The sides are 10풎ퟐ thick. The
heat transfer coefficient is 10W/풎ퟐk.
What will be the heat transfer rate?
EXAMPLE #1

34. • Calculate the heat transfer per square
meter between a fluid with a bulk
temperature of 66°C with a wall, with a
surface temperature of 25°C given h = 5
W/풎ퟐK.
EXAMPLE #2

35. • Transfer of heat by electromagnetic waves
such as visible light, infrared and ultraviolet
radiation.
• Most heat are transferred through radiation
Example:
- heat from the sun
- heat from charcoal grill
RADIATION

36. Q = 흈 ε A (Tퟐퟒ – Tퟏퟒ)
Where:
Q – is the heat radiated from the hot surface (W)
ε – is the emissivity
A – is the surface area radiating heat (m2)
T2 – higher temp (K)
T1 – lower temp (K)
흈 – Stefan-Boltzmann constant= 56.7xퟏퟎퟗW/풎ퟐ푲ퟒ
RADIATION

37. Q =
흈푨 (푻ퟏퟒ−푻ퟐퟒ)
RADIATION
ퟏ
εퟏ
ퟏ
εퟐ
+
If two bodies have different
emissivities.

38. Surface Emissivity (ε)
Furnace interior 1.00
Iron oxide surface 0.82
Oxidized copper surface 0.79
Refractory bricks 0.78
Aluminum paints 0.50
Polished copper 0.04
Polished Aluminum 0.04
Oxidized Aluminum 0.15
RADIATION

39. •A body with 266 K temperature
was radiated by aluminum paints
having 399 K temperature. Per 2
square meter, compute the heat
radiated.
EXAMPLE #1

40. • An oxidized aluminum and
polished aluminum foils were
both radiated by each other. The
first body is 54°C and the other
one is 39°C. Calculate the heat
transfer in 23 square meter.
EXAMPLE #2