Heat Transfer

1
Chapter 15

• Heat Transfer

2
Second Law of Thermodynamics

• Heat flows naturally from hot to cold objects.
  Heat will not flow spontaneously from cold object
  to hot object.

3
Methods of Heat Transfer

• Need to know the rate at which energy is
  transferred
• Need to know the mechanisms responsible for the
  transfer
• Methods include
• Conduction
• Convection
• Radiation

4
Conduction

• The transfer can be viewed on an atomic scale
• It is an exchange of energy between microscopic
  particles by collisions
• Less energetic particles gain energy during
  collisions with more energetic particles
• Rate of conduction depends upon the
  characteristics of the substance

5
Conduction example

• The molecules vibrate about their equilibrium
  positions
• Particles near the stove coil vibrate with larger
  amplitudes
• These collide with adjacent molecules and
  transfer some energy
• Eventually, the energy travels entirely through
  the pan and its handle

6
Conduction, cont.

• In general, metals are good conductors
• They contain large numbers of electrons that are
  relatively free to move through the metal
• They can transport energy from one region to
  another
• Conduction can occur only if there is a
  difference in temperature between two parts of
  the conducting medium

7
Conduction, equation

• The slab allows energy to transfer from the
  region of higher temperature to the region of
  lower temperature
• Rate of heat transfer (L?x)

8
Conduction, equation explanation

• A is the cross-sectional area
• L ?x is the thickness of the slab or the length
  of a rod
• ?Q is in Joules and ?t is in seconds
• k is the thermal conductivity of the material
• Good conductors have high k values and good
  insulators have low k values

Good copper k385 W/mC Intermediate concrete
k0.8 W/m C Insulator air k0.024 W/m C
9
Example

• 3mX15m concrete wall is 30 cm thick.
• Outside surface 10 C, inside 20 C. What rate
  does heat transfer through it? (k40x10-4
  cal/cmsC for concrete)

10
Example

• What is equivalent thickness of glass wool?
  (k9.3x10-5 cal/cmsC for glass wool)

Glass wool is a much better insulator than
concrete!!
11
Example

• 30 cm concrete house wall with 2.0 cm wood
  paneling. 10 C outside and 18C inside.What is
  temperature _at_ wood/concrete interface?
• (k2.4x10-4 cal/cmsC for wood)

12
Home Insulation

• Substances are rated by their R values
• R L / k L in inches,
• k in BTUin/ft2hourF
• For multiple layers, the total R value is the sum
  of the R values of each layer
• Wind increases the energy loss by conduction in a
  home

Glass wool k0.27 BTU in/(ft2 hour
F) R(1/k)thickness 3.7thickness
13
Conduction and Insulation with Multiple Materials

• Each portion will have a specific thickness and a
  specific thermal conductivity
• The rate of conduction through each portion is
  equal

14
Example

• 7 ft2 sheet of material allows 80 BTU to flow
  through it in 40 minutes when temperature
  difference across it is 35F. What is R-value for
  the sheet?

15
Convection

• Energy transferred by the movement of a substance
• When the movement results from differences in
  density, it is called natural convection
• When the movement is forced by a fan or a pump,
  it is called forced convection

16
Convection example

• Air directly above the flame is warmed and
  expands
• The density of the air decreases, and it rises
• The mass of air warms the hand as it moves by

17
Convection applications

• Boiling water
• Radiators
• Upwelling
• Cooling automobile engines
• Algal blooms in ponds and lakes

18
Convection Current Example

• The radiator warms the air in the lower region of
  the room
• The warm air is less dense, so it rises to the
  ceiling
• The denser, cooler air sinks
• A continuous air current pattern is set up as
  shown

19
Heat Transfer by Convection

• ?T temperature difference
• A area of contact
• h convection surface coefficient

20
Example

• Heat transfer from glass to outside through
  convection. Assume window area to be 1 m2, glass
  temperature 5 C and outside temperature 15C.
  For air in contact with solid surface h1.5-2.5
  W/m2C. Amount of heat
• lost in a day?

21
Radiation

• Radiation does not require physical contact
• All objects radiate energy continuously in the
  form of electromagnetic waves due to thermal
  vibrations of the molecules
• Rate of radiation is given by Stefans Boltzmann
  Law

22
Radiation example

• The electromagnetic waves carry the energy from
  the fire to the hands
• No physical contact is necessary
• Cannot be accounted for by conduction or
  convection

23
Radiation equation

• The power is the rate of energy transfer, in
  Watts
• s 5.6696 x 10-8 W/m2.K4
• A is the surface area of the object
• e is a constant called the emissivity
• e varies from 0 to 1
• T is the temperature in Kelvins

24
Example

• A square steel plate 10 cm on a side at
• 800 C. Find the rate of heat radiated.
• In one hour?

25
Example

• Temperature of a hot plate is doubled from 100 C
  to 200 C. How is the rate of heat radiated
  changed?