There are three main mechanisms of heat transfer: conduction, convection, and radiation. Conduction involves the direct contact and transfer of kinetic energy between molecules. The rate of conductive heat transfer depends on the temperature gradient, surface area of contact, and the material's thermal conductivity. Materials with high thermal conductivity like metals are good conductors, while still air and materials that trap air are good insulators. Thermal resistance can be used to calculate the rate of heat transfer through multiple conducting layers.

1. Conduction

2. Transfer Mechanisms
 Heat can be transferred in three ways.
 Transfer can include more than one way.
 Conduction  Convection  Radiation
• Energy flow • Fluid flow • Energy radiating
from direct carrying energy from an object
thermal contact into
surroundings

3. Direct Contact
 Items in direct contact
transfer heat.
 Molecules in hot regions
have greater kinetic energy.
• Elastic collisions with cool
molecules
• Kinetic energy transfer at
boundary

4. Thermal Conductivity
 Heat flow within an object is Material Thermal Cond.
due to transfer by Air 0.026 W/m-K
conduction. Stryrofoam 0.029 W/m-K
Wood 0.11 W/m-K
 Thermal conductivity (κ) Water 0.61 W/m-K
measures the ability for heat
to move in a material. Glass 0.8 W/m-K
• Measured in W / m-K Concrete 1.0 W/m-K
• High number means high Steel 46 W/m-K
rate of transfer Aluminum 240 W/m-K
Copper 400 W/m-K

5. Heat Flow Rate
 The rate of heat flow
depends on the temperature
gradient.
A • Change in temperature with
H distance
T + ∆T T
 Depends on surface area A
for contact.
∆x
∆Q ∆T
H= = −κA
∆t ∆x

6. Conductors and Insulators
 Thermal conductors have
high values of k.
• Metals with conducting
electrons
• Greater than 10 W/m-K
 Still air is an excellent
thermal insulator.
• Materials that trap air are
good: wood, styrofoam
 Vacuum would be the best.

7. Swimming Hole
 A lake with a flat bottom and  Convert area to m2.
steep sides has a surface  1.5 km2 = 1.5 x 106 m2
area 1.5 km2 and is 8.0 m
deep. The surface is at 30  Use the equation for heat
°C and the bottom is at 4 °C.
flow.
 H = -kA(∆T/∆x)
 What is the rate of heat  -(0.61 W/m-K)(1.5 x 106 m2)
conduction through the lake? (26 K) / (8.0 m)
 H = -3.0 x 106 W.

8. Two Layers
 If there are two layers in
thermal contact, the rate of
T3 T2 T1
heat flow must be the same
H H for both.
• Energy doesn’t accumulate
in the layer.
∆x2 ∆x1
T3 − T2 T −T
H = −κ 2 A = −κ1 A 2 1
∆x 2 ∆x1

9. Thermal Resistance
 For an arbitrary set of layers
the intermediate temperature
T3 T2 T1
is unknown.
H H • Define thermal resistance
∆x
R=
R2 R1 κA
• For multiple layers R adds
∆T
H=
R R = R1 + R2

10. R-Factor
 In the US, thermal resistance Material R-factor
is measured per unit area. Glass (1/8”) 1
• R = ∆x / k
Brick (3½”) 0.6 – 1
• Units are ft2 °F hr / BTU
Plywood (1/2”) 0.6
• 1 BTU = 1055 J
Fiberglass
insulation (1”) 4
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