Heat Transfer:
Conduction I
We will now enter a new area, heat conduction.
This is not really a move away from energy
conversion because most of our examples will be
based on our home and how to conserve heating and
cooling costs using better insulating materials.
Figure 1:
In the kitchen you use an aluminum pot for good Equipment for Heat Transfer: Conduction I
heat transfer from the stove to your food, but your
copper rod
refrigerator is insulated with Styrofoam® to reduce
glass rod
conduction of heat. How do we describe the
liquid nitrogen
difference between the two materials?
propane torch
thermometers (2)
If you hold one end of a copper rod and place the
other end in a flame, the end you are holding gets hotter and hotter, even though it is not in direct
contact with the flame. Heat reaches the cooler end by conduction through the material. On the
atomic level, the atoms in the hotter regions have more kinetic energy, on the average, than their
cooler neighbors, and so it goes through the material. The atoms themselves do not move from
one region to another but their energy does.
In metals, electron motion provides another mechanism for heat transfer. Most metals are
good conductors of electricity because some electrons can leave their parent atoms and wander
through the crystal lattice. These "free" electrons can carry energy from the hotter to the cooler
regions of the metal. Good thermal conductors such as silver, copper, gold, and aluminum are
also good electrical conductors.
Objectives [At the end of this lesson students will be able to...]


develop an equation governing heat conduction.
apply this equation to practical situations.
Start-up questions
1. How many different types of heat transfer can you think of?
2. Under what conditions does each apply?
3. What parameter(s) do they have in common?
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Heat Transfer: Conduction I -- Page 1 of 4
Thermal Energy Transfer: Heat Conduction, part 1
Net heat transfer occurs only between regions at different temperatures, and the direction of
heat flow is always from higher to lower temperature. We will develop the basic formula for heat
flow. Some thermal conductivities (k) are listed in the following charts.
Thermal Conductivities of Some Common Metals
Metal
Thermal Conductivity, k (in unit of W/m·K)
Aluminum
205.0
Brass
109.0
Copper
385.0
Lead
34.7
Mercury
8.3
Silver
406.0
Steel
50.2
Thermal Conductivities of Other Materials
Materials, k (in unit of W/m·K)
Materials, k (in unit of W/m·K)
Brick (insulating), 0.15
Nylon, 0.30
Brick (red), 0.60
Polystyrene, 0.033
Charcoal, 0.055
Rubber (92% dense), 0.16
Concrete, 0.80
Rubber (sponge), 0.05
Cork, 0.040
Styrofoam, 0.01
Felt, 0.050
Dry sand, 0.33
Fiberglass, 0.040
Oak wood, 0.16
Glass, 0.80
Pine wood, 0.26
Ice, 1.60
Air, 0.024
Sheet rock, 0.10
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Heat Transfer: Conduction I -- Page 2 of 4
Here we introduce the basic equation for thermal conductivity and emphasize the intrinsic
and extrinsic factors, heat flow, thermal conductivity and temperature gradient. (this is a good
time to review scientific units)
heat flow rate = thermal conductivity × temp difference × area / length
Q
=
k
×
× A / L
T
Note that the "Q" in this equation is in Watts; it is essentially power, or energy per unit time.
Because in some other cases "Q" is used to represent energy alone, this sometimes causes
confusion for students. The best advice here is to follow the units.
We will use fire (high temperature), liquid nitrogen (low temperature), copper and quartz to
illustrate the effect of conductivity. We will need a propane torch, liquid nitrogen, copper bar,
quartz or glass bar, and thermometers. We will NOT be able to measure thermal conductivity in
class (it is not easy to do quickly). WHY is it difficult?
Assessment questions
1. Which would make for better insulation for your home, glass or copper?
2. How is thermal conductivity related to heat flow (directly proportional, inversely
proportional, etc.)?
3. Why does fiberglass have a much lower thermal conductivity than glass?
Example problem
Example using conduction through a picnic cooler: A Styrofoam® box used to keep drinks cold at
a picnic has total wall area (including the lid) of 1.2 m² and a wall thickness of 1.6 cm. It is filled
with ice, water, and drinks at 0.0°C. What is the rate of heat flow into the cooler if the
temperature of the outside wall is 28.0°C?
Solution:
Use heat flow rate = thermal conductivity × temp difference × area / length
Q
=
k
×
× A / L
T
T = 28°C degree same as 28 K
k(thermal conductivity) = 0.01 W/m·K
A = 1.2 m²
L = 1.6 cm = 0.016 m
Q = 20 W (remember significant figures)
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Heat Transfer: Conduction I -- Page 3 of 4
Homework
Heat conduction through a wall with a window: During the winter, heat flows out of a house
through the walls. Assume that it is 0°C outside and 21°C inside and I have a wall with a total
area of 25 m² with a window of 1 m². The window is made of a single sheet of normal glass 0.2"
thick. The rest of the wall is made of insulating brick with a thickness of 4 inches.
a. What is the heat flow through the window? (your answer should have a unit of Watt)
b. What is the heat flow through the rest of the wall? (should also have the same unit of
Watt)
c. If the average difference in temperature between the inside and the outside of the wall is
21°C and the heating cost is 8 ¢/kW·h, how much does it cost for the heat lost through
this wall for 1 month?
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Heat Transfer: Conduction I -- Page 4 of 4