12
Geodynamics www.helsinki.fi/yliopisto Geodynamics Heat conduction and production Lecture 7.2 - Heat conduction Lecturer: David Whipp [email protected] 1
Geodynamics www.helsinki.fi/yliopisto
Geodynamics
Heat conduction and production Lecture 7.2 - Heat conduction
Lecturer: David Whipp [email protected]
1
Goals of this lecture
• Introduce heat conduction and how it is represented mathematically
2
Basic ideas of heat conduction
• The conduction of heat in solids is adiffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion
• Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient
• What would this relationship look as an equation?
3
Basic ideas of heat conduction
• The conduction of heat in solids is adiffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion
• Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient
• What would this relationship look as an equation?
3
Basic ideas of heat conduction
• The conduction of heat in solids is adiffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion
• Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient
• What would this relationship look as an equation?
4
Basic ideas of heat conduction
• The conduction of heat in solids is adiffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion
• Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient
• What would this relationship look as an equation?
4
Fourier’s first law
• In 1D, the mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is
• Here, 𝑇 represents temperature and 𝑦 represents spatial position, depth in the Earth for our example
• Thus, 𝑑𝑇/𝑑𝑦 is the change in temperature with distance, the thermal gradient
• The proportionality constant 𝑘 is known as the thermal conductivity
5
q = �kdT
dy
Fourier’s first law
• In 1D, the mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is
• Why is there a negative sign?
6
q = �kdT
dy
What is thermal conductivity?
• The mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is
• Thermal conductivity is a proportionality factor
• As you can easily see, rocks with a “high” thermal conductivity will produce a large heat flow, whereas rocks with a “low” thermal conductivity will have near zero heat flow
• Thermal conductivity of most crustal rocks is 2-3 W m-‐1 K-‐1
7Stüwe, 2007
Sandstone
Salt
q = �kdT
dy
Global heat flow map
9
http://www.cbe.cornell.edu
Here we can clearly see the connection between geodynamic setting and heat flow
Global average: 87 mW m-2
Continents: 65 ± 1.6 mW m-2
Oceans: 101 ± 2.2 mW m-2
Let’s see what you’ve learned…
• If you’re watching this lecture in Moodle, you will now be automatically directed to the quiz!
10
