Convection in a planetary body
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Convection in a planetary body. Geosciences 519 Natalie D. Murray April 2, 2002. Convection. Process of heat transfer ( from hotter to colder regions) by the bulk motion of a fluid More efficient in heat transfer than conduction Needs: Temperature gradient Gravity .

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Convection in a planetary body

Convection in a planetary body

Geosciences 519

Natalie D. Murray

April 2, 2002


Convection

Convection

  • Process of heat transfer ( from hotter to colder regions) by the bulk motion of a fluid

  • More efficient in heat transfer than conduction

  • Needs:

    • Temperature gradient

    • Gravity


Convection in a planetary body

Temperature structure of the mantle– superadiabatic temperature gradient due to heating from beneath (from the core) and radiogenic heat production

http://www.ldeo.columbia.edu/users/jcm/Topics3/Topics3.html


Buoyancy

Buoyancy

  • Parcel – unit volume of a fluid

  • Adiabatic process – no exchange of heat with surroundings

  • Simple process :

  • Parcel is heated from below

  • Temperature increases causing density changes

  • Density of parcel is less than that of surrounding material

  • Parcel is more buoyant and will rise

  • Since the temperature gradient is superadiabatic and the parcel rises adiabatically, the parcel is warmer than the surroundings and will continue to rise.


Navier strokes equations

Navier-Strokes Equations

Momentum equation

Mass Conservation equation

Conservation of Energy

Hydrostatic Equation


Boussinesq approximation

Boussinesq Approximation

Density variations are ignored except when coupled with gravity and give rise to buoyancy (gravitational force)

Prandtl Number

  • Virtually infinite in the mantle

    • Inertial forces are insignificant

    • Convection depends on pressure, temperature and viscosity


Forces opposing convection

Forces opposing convection

Viscosity – opposes fluid flow (for the Mantle – about the same as for steel 1E20 Pa s)

Thermal diffusivity - suppress the temperature fluctuation by causing the rising plume of hot fluid to equilibriate with surrounding fluid (weakens the buoyancy force)


Rayleigh number

Rayleigh Number

Ratio of buoyancy force to the viscous – diffusive force

Convection due to superadiabatic temperature gradient

Critical Rayleigh Number – value that if exceeded convection is certain

Rayleigh Number for the mantle is super critical

Thermal expansion coeff – the more a fluid expands, the more it’s density is lowered

Typical values for coefficients can be found on Lowrie pg 328 Table 6.2

Convection due to radiogenic heat

Lowrie pg 328


Stability

Stability

http://www.seas.smu.edu/~arunn/html/convect/rbconvect/rbcon.html


Simple convective cell

Simple Convective Cell

http://ldeo.columbia.edu/users/jcm/Topics3/Topics3.html


Rayleigh benard convection

Rayleigh-Benard Convection

  • Simple model of convection

  • Thermal convection – transfer of heat through a fluid

  • Parcel will rise to the level of neutral buoyancy

  • The hot layer will try to rise while the cold layer will try to sink.

  • Breaks up into convective cells

  • In the form of rolls, hexagon cells, etc.


Rayleigh benard convection1

Rayleigh-Benard Convection

http://www.seas.smu.edu/~arunn/html/convect/rbconvect/rbcon.html


Rayleigh benard convection2

Rayleigh-Benard Convection

http://www.ldeo.columbia.edu/users/jcm/Topics3/Topics3.html


Convective cells in the mantle

Convective Cells in the Mantle

http://geollab.jmu.edu/Ficher/plateTect/heathistory.html


Helpful websites

Helpful Websites

http://scienceworld.wolfram.com

http://www.psigate.ac.uk/


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