Lecture 8:
Heat Flow and Thermal Structure
Lecture Outline:
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Three mechanisms of heat flow:
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Conduction
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Convection
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Radiation
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Conductive Heat Flow
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Heat flow is proportional to the temperature gradient.
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Different materials conduct heat at different rates
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Conduction is a slow process (diffusive) relative to advection
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Thermal diffusivity describes the relationship between length
and time scales of heat flow. In particular, the length that a thermal
perturbation travels is proportional to the square root of time.
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Some geologically interesting thermal profiles or "geotherms"
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Steady state heat flow is characterized by a linear temperature
gradient
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Time dependent heat flow is characterized by a non-linear
temperature gradient
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Convective Heat Flow
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A pot of water heated from below
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A pot of water heated internally (for example, in a microwave)
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A pot of wax heated internally
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Comparisons of above with convective motion in the Earth.
Earth's Source of Heat Production
Radioactivity
|
Rock
|
U (ppm)
|
Th (ppm)
|
K (ppm)
|
cal/gm/sec
|
ergs/gm/year
|
|
Granite
|
4
|
13
|
4
|
2.28x10^-13
|
300
|
|
Basalt
|
.5
|
2
|
1.5
|
3.81x10^-14
|
50
|
|
Peridotite
|
.02
|
.06
|
.02
|
7.59x10^-16
|
1
|
TOTAL HEAT PROCUDED
Crust:
3.99x10^12 cal/sec
Mantle:
3.03x10^12 cal/sec
Core:
Supposedly much less than above.
Total:
~7x10^12 cal/sec