Submission details
This prac will run over 2 weeks. You will need to submit your answers to all three parts of the prac. Hand in Qn 1 and 2 on paper with your name and student ID (indiviudal report). Qn 3 will be submitted electronically – instructions are found with the question. For Qn3 you are encourage to work in pair and hand in one group report.

Some fundamentals
The Earth’s geotherm:  In the Earth, temperature increases with depth for three reasons:
1/ The radioactive decay of radiogenic elements (mainly K⁴⁰, U²³⁵, U²³⁸, Th U²³²) involves exothermic reactions that liberate thermal energy.
2/ During its formation, the Earth has trapped a finite amount of accretional energy (gravitational energy transformed into heat).
3/ Last but not least, the Earth is cooled at the surface since it is suspended into the chilling ~0 K Universe.

 Thermal expansion and gravitational instabilities:  Upon heating, rocks expand and consequently their density decreases.  Since temperature increases with depth one concludes that for a given mineralogical composition the density of rock decreases.  It can be shown that a system where density increases with depth has a lower gravitational potential energy compared to system where density decreases. As a system naturally evolves to minimize its internal energy, one can see the Earth's mantle is gravitationally unstable.

 Mantle convection: The way the mantle minimizes its energy is by flowing upward deep, hot and low-density material but to do so it must also flush down an equivalent volume of cooler and heavier rock.  The trouble is that as the low-density material moves upward its temperature decreases forcing its density to increase.  The opposite happens to the cold material flowing downward.  This results in a self-sustained convective motion.  The energy consumed by this process is thermal energy: mantle convection acts as a giant heat exchanger.

 Rayleigh number and the strength of convection:  The buoyancy force - that arises due to volumetric expansion (called thermal expansion) - drives mantle convection.  On the other hand, the viscous force (due to the viscosity of the mantle) and the thermal diffusivity (strong diffusivity will smooth out thermal gradient) oppose mantle convection.  The Rayleigh number is a dimensionless number that expresses the ratio of the driving forces to the opposing forces.  The Rayleigh Number takes slightly different forms depending on the mode of heating (internal heating, basal heating, or mixed heating mode), and velocity boundary conditions (free surface vs fixed surface, ie zero velocity at the surface).