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| Temperature and Heat |
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| The rate at which heat is gained or lost is simply the sum of the rates of the mechanisms and processes producing, consuming, or transporting heat. For continental geotherms, the main mechanisms are: heat conduction, heat advection, and the heat produced by the decay of radiogenic isotopes. |
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Heat conduction
Conduction transports heat from hot to cold regions. The flow of heat (Q) is proportional to the temperature gradient (∂T/∂z) between the cold and the hot region, with the coefficient of proportionality being the conductivity (k). Mathematically this translates into: Q = -k. ∂T/∂z. Units: Q (W.m-2); k (W.m-1.K-1) |
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| If the incoming and outgoing heat flows are the same, there is no gain or loss in heat, the temperature remains constant. Temperature changes when the heat flow leaving the volume over a time interval is different to the heat flow entering it. |
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| Let’s assume that Q(z) is the heat flow coming out a small cylinder or rock of section a. The entering heat flow at the other end of the cylinder is Q(z+∂z) and can be approximated with a Taylor serie in which only the two first terms are of significance: |
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| The increment of heat (∂Ec) gained or lost in an increment of time ∂t is: |
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