Thermal Expansion & Heat Transfer

THERMAL EXPANSIONTEMPERATURE

THERMAL EXPANSION

•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.

FACTORS AFFECTING

THERMAL EXPANSION

1. TEMPERATURE

•Higher change in temperature, the

higher the expansion

• ΔT for the symbol

FACTORS AFFECTING

THERMAL EXPANSION

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

3. ORIGINAL DIMENSION

•Greater original dimension, greater the

expansion.

•L for linear

•A for area

•V for volume

KINDS OF THERMAL

EXPANSION

LINEAR EXPANSION

•The expansion in length of solid

bodies on heating

•The change in length is directly

proportional to the change in

temperature : ΔL ≈ ΔT

ΔL ·ΔT= α·L0

Change in

dimensionCoefficient of

expansionOriginal

length

Change in

temperature

MATERIAL a per °C a per °F

1. Aluminum 23 x 𝟏𝟎−𝟔 13x 𝟏𝟎−𝟔

2. Brass 19x 𝟏𝟎−𝟔 11x 𝟏𝟎−𝟔

3. Copper 17x 𝟏𝟎−𝟔 9.3x 𝟏𝟎−𝟔

4. Germanium 6.0x 𝟏𝟎−𝟔 3.3x 𝟏𝟎−𝟔

5. Glass, ordinary 9x 𝟏𝟎−𝟔 5x 𝟏𝟎−𝟔

6. Glass, Pyrex 3.3x 𝟏𝟎−𝟔 1.8x 𝟏𝟎−𝟔

7. Invar (nickel-steel alloy) 0.9x 𝟏𝟎−𝟔 0.5x 𝟏𝟎−𝟔

8. Iron 12x 𝟏𝟎−𝟔 6.6x 𝟏𝟎−𝟔

9. Platinum 9.0x 𝟏𝟎−𝟔 5.0x 𝟏𝟎−𝟔

10. Fused quartz 0.5x 𝟏𝟎−𝟔 0.27x 𝟏𝟎−𝟔

11. Silicon 2.4x 𝟏𝟎−𝟔 1.3x 𝟏𝟎−𝟔

12. Steel 11x 𝟏𝟎−𝟔 6.1x 𝟏𝟎−𝟔

13. Tungsten 4.4x 𝟏𝟎−𝟔 2.5x 𝟏𝟎−𝟔

14. Uranium 15x 𝟏𝟎−𝟔 8.2x 𝟏𝟎−𝟔

15. Wood, along grain (3 to 6) x 𝟏𝟎−𝟔 (2 to 4) x 𝟏𝟎−𝟔

16. Wood, across grain (35-60) x 𝟏𝟎−𝟔 (20 to 35) x 𝟏𝟎−𝟔

Exercise #1

•A copper bar is 8.0 ft long at

68°F and has an expansivity

of 9.3 x 𝟏𝟎−𝟔/°F. What is its

increase in length when

heated to 110°F?

Exercise #2

•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 #3

•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?

VOLUME EXPANSION

•Sometimes called the “cubic

expansion”

•The volume of an object changes

when its temperature changes.

VOLUME EXPANSION

•ΔV = β·V0·ΔT

VOLUME EXPANSIVITY OF

LIQUIDS

LIQUID β, per °C β, per °F

Alcohol,

ethyl

1.0x𝟏𝟎−𝟑 6.1x𝟏𝟎−𝟒

Mercury 1.8x𝟏𝟎−𝟒 1.0x𝟏𝟎−𝟒

Water (15-

100°)

3.7x𝟏𝟎−𝟒 2.0x𝟏𝟎−𝟒

Exercise #4

•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 #5

•A mug measuring 90cm3 at

45°C temperature, contains

ethyl alcohol. At what

temperature will the alcohol

flow 92cm3?

HEAT TRANSFER

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

CONDUCTION

• 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

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)

Substance Thermal Conductivity k (𝑾/𝒎 𝑲 )

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

Example #1

•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 #2

•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 #3

•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 #4

• 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.

CONVECTION

•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

• 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

• 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

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

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,

condensing6,000-120,000 1,000-20,000

EXAMPLE #1

•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 10𝒎𝟐 thick. The

heat transfer coefficient is 10W/𝒎𝟐k.

What will be the heat transfer rate?

EXAMPLE #2

•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/𝒎𝟐K.

RADIATION

• 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

Q = 𝝈 ε A (T𝟐𝟒 – T𝟏𝟒)

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)

𝝈 – Stefan-Boltzmann constant= 56.7x𝟏𝟎𝟗W/𝒎𝟐𝑲𝟒

RADIATION

Q = 𝝈𝑨 (𝑻𝟏𝟒−𝑻𝟐𝟒)

𝟏

ε𝟏 +𝟏

ε𝟐If two bodies have different

emissivities.

RADIATION

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

EXAMPLE #1

•A body with 266 K temperature

was radiated by aluminum paints

having 399 K temperature. Per 2

square meter, compute the heat

radiated.

EXAMPLE #2

•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.